PLEASE HELP
What is the probability that
both events will occur?
Two dice are tossed.
Event A: The first die is a 1 or 2
Event B: The second die is 4 or less
P(A and B) = P(A) • P(B)
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answers
The probability of event A (the first die being a 1 or 2) is 2/6 or 1/3, since there are two out of six possible outcomes where the first die is a 1 or 2.
The probability of event B (the second die being 4 or less) is 4/6 or 2/3, since there are four out of six possible outcomes where the second die is 4 or less.
Therefore, the probability of both events A and B occurring is:
P(A and B) = P(A) * P(B)
P(A and B) = (1/3) * (2/3)
P(A and B) = 2/9
Rounded to the nearest hundredth, the probability is 0.22. So, the answer is 0.22.
The probability that both events will occur is 0.22.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The probability of Event A is 2/6 or 1/3
(since there are two ways to get a 1 or 2 on a six-sided die).
The probability of Event B is 4/6 or 2/3
(since there are four ways to get a number 4 or less on a six-sided die).
Using the formula for the probability of the intersection of two independent events.
P(A and B)
= P(A) x P(B)
= (1/3) x (2/3)
= 2/9
Rounded to the nearest hundredth,
The probability that both events will occur is 0.22.
Thus,
The probability that both events will occur is 0.22.
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Related Questions
Jacinta compares the volume of two boxes. Both boxes have a width of 2. 5 inches, and a height of 10 inches. The larger box has a length of 8 inches. The smaller box has a length that is 75 % of the length of the larger box.
Volume of large box =
Volume of small box =
What is the difference in the volumes of the two boxes?
Which units should be used for each of these answers?
Answers
The volume of the large box is 200 cubic inches. The volume of the small box is 150 cubic inches. The difference in the volumes of the two boxes is 50 cubic inches. The units that should be used for each of these answers is cubic inches.
To find the volume of each box, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.
For the larger box, the dimensions are:
Length = 8 inches
Width = 2.5 inches
Height = 10 inches
Volume of large box = 8 × 2.5 × 10 = 200 cubic inches
For the smaller box, its length is 75% of the larger box's length:
Length = 0.75 × 8 = 6 inches
The width and height remain the same, so the dimensions are:
Length = 6 inches
Width = 2.5 inches
Height = 10 inches
Volume of small box = 6 × 2.5 × 10 = 150 cubic inches
The difference in the volumes of the two boxes is:
200 cubic inches - 150 cubic inches = 50 cubic inches
So, the difference in the volumes of the two boxes is 50 cubic inches. The units used for these answers are cubic inches.
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On a certain map, 0.4" represents 2 miles. If the actual distance between point A and point B is 8
miles, what is the distance in inches between point A and B on the map?
(A) 0.8"
(B) 1.6"
(C) 2"
(D) 2.4"
(E) 3.6"
Answers
Answer:
B
Step-by-step explanation:
0.4 inches = 2 miles
x inches = 8 miles
Cross multiplication:
0.4 * 8 = 2 * x
3.2 = 2x
x = 1.6''
solve each system by substitution
y=-2x-7
2x-8y=-16
Answers
y = -2x - 7
We can then substitute this expression for y into the second equation:
2x - 8y = -16
2x - 8(-2x - 7) = -16
Simplifying the equation, we get:
2x + 16x + 56 = -16
18x = -72
x = -4
Now that we have found the value of x, we can substitute it back into either equation to find the value of y. Let's use the first equation:
y = -2x - 7
y = -2(-4) - 7
y = 1
Therefore, the solution to the system of equations is x = -4 and y = 1.
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Answers
Answer:
48
Step-by-step explanation:
can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48
A 2 column by 10 row table. column 1 is titled how energy is used with the following entries: computers, cooking, electronic, lighting, refrigeration, space cooling, space heating, water heating, wet cleaning, other. column 2 is titled energy used in percent with the following entries: 2, 4, 5, 6, 4, 9, 45, 18, 3, 7. a carbon footprint is a measure of the amount of carbon human activities, like using energy, release into the atmosphere. which activity would help decrease the greatest carbon-releasing activity in us homes? limiting time in hot showers wearing layers of clothing turning off lights when leaving a room unplugging electronics when not in use
Answers
Limiting space heating would help decrease the greatest carbon-releasing activity in US homes.
From the table, we can see that space heating accounts for the largest percentage of energy use in US homes at 45%. Therefore, by limiting space heating, we can significantly reduce the amount of carbon released into the atmosphere, thus decreasing our carbon footprint.
Other activities like limiting time in hot showers, wearing layers of clothing, and turning off lights and electronics when not in use can also help reduce our carbon footprint, but they are not as effective as limiting space heating.
Additionally, we can consider using energy-efficient heating systems, improving insulation, and reducing air leaks to further reduce our energy use and carbon footprint.
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A group of friends Anna (A), Bjorn (B), Candice (C), David (D) and Ellen (E) want to enter a basketball contest that caters for teams of different sizes. A team with n players is called an n-team. A player can be in several different teams, including teams of the same size. There is a restriction however: players in a 2-team cannot play together in any larger team. For example, if friends A,B,C,D form the teams AB, BCD, ACD, then they cannot also form the teams BD or ABC, among others.
a) List all different 3-teams that the friends could enter.
b) What is the maximum number of teams that the friends can enter if they want to include exactly two 3-teams and at least one 2-team, but no other size teams.
c) What is the maximum number of teams that the friends can enter if they want to include exactly three 3-teams and at least one 2-team, but not other size teams.
d) The five friends want to enter 8 teams including at least one 2-team and at least one 3-team and no team of any other size. Find three ways of doing this with a different number of 3-teams in each case
Answers
The number of 3-teams is different, and there is at least one 2-team and one 3-team, fulfilling the requirements.
a) To list all different 3-teams that the friends (A, B, C, D, E) could enter, we can find all the possible combinations of choosing 3 friends out of 5. These combinations are:
1. ABC
2. ABD
3. ABE
4. ACD
5. ACE
6. ADE
7. BCD
8. BCE
9. BDE
10. CDE
b) To maximize the number of teams with exactly two 3-teams and at least one 2-team, we can form the following teams:
1. ABC (3-team)
2. ADE (3-team)
3. BC (2-team)
Here, we have formed 1 two-team and 2 three-teams.
c) To maximize the number of teams with exactly three 3-teams and at least one 2-team, we can form the following teams:
1. ABC (3-team)
2. ADE (3-team)
3. BCE (3-team)
4. CD (2-team)
Here, we have formed 1 two-team and 3 three-teams.
d) The friends want to enter 8 teams, including at least one 2-team and at least one 3-team. We can find three ways of doing this with a different number of 3-teams in each case:
1. Two 3-teams: ABC, ADE (3-teams); BC, BD, BE, CD, CE, DE (2-teams)
2. Three 3-teams: ABC, ADE, BCE (3-teams); AC, AD, AE, BD, BE, CD (2-teams)
3. Four 3-teams: ABC, ADE, BCE, BCD (3-teams); AB, AC, AD, AE (2-teams)
In each case, the number of 3-teams is different, and there is at least one 2-team and one 3-team, fulfilling the requirements.
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A person stands on level ground 60 m from the nearest point of a cylindrical tank of radius length 20 m. Calculate:
a- the circumference of the tank
b the percentage of the circumference that is visible to the person
Answers
The circumference of the tank is is 125.66m and the percentage of the circumference that is visible to the person is 10.24%.
a) To calculate the circumference of the cylindrical tank, using the formula C = 2πr, where C is the circumference and r is the radius of the tank. In this case, r = 20 m, so:
C = 2π(20 m) ≈ 125.66 m
b) To determine the percentage of the circumference visible to the person, we first need to calculate the angle (in degrees) that subtends the visible arc. This can be done using the inverse tangent function:
angle = atan(opposite/adjacent) = atan(20 m/60 m)
angle ≈ 18.43°
Since the visible arc is symmetrical on both sides, the total angle of the visible arc is twice the calculated angle:
total angle ≈ 36.86°
Now, calculate the percentage of the circumference that is visible by dividing the total angle by 360° and multiplying by 100%:
percentage = (36.86°/360°) × 100% ≈ 10.24%
So, the visible percentage of the circumference to the person is approximately 10.24%.
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What is the answer to this
Answers
The temperature are the times indicated are:
T( 0) = 5.800°
T( 0.22) = -4.9094 °
T (0.44) = -2.6792 °
T(0.66) = 2.3244°
T(0.88) = 4.8184°
T(1.1) = -4.1686 °
How did we get the above ?To solve the above, we need to use the formuala that we given which is T(x) = 5.8cos(3.8πx)
Entering the various values of x, can can obtain
T(0) = 5.8 cos (3.8π (0) ) = 5.8cos(0) = 5.800
T(0.22) = 5.8 cos (3.8 π(0.22)) ≈ -4.9094
T(0.44) = 5.8cos (3.8π (0.44) ) ≈ - 2.6792
T(0.66) = 5.8cos(3.8π (0.66)) ≈ 2.3244
T(0.88) = 5.8cos(3.8π(0.88)) ≈ 4.8184
T(1.1) = 5.8 cos(3.8π(1.1 )) ≈ -4.1686
So the above answers are correct.
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Josh wants to simplify the expression (-8)(10+(-5)+(-8))
Answers
Therefore, the simplified expression is 24.
To simplify the expression (-8)(10+(-5)+(-8)), you first need to solve the parentheses, following the order of operations, which requires solving the addition and subtraction within the parentheses before multiplying.
So, you have (-8)(10-5-8), which becomes (-8)(-3) after solving the parentheses. Finally, you can solve the multiplication by multiplying -8 by -3, resulting in 24.
It's important to remember the order of operations when simplifying expressions, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
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A cook is adding soup to a 10-liter
capacity pot. The equation
y = 1.5x + 2.5 relates the liters
of soup y added to the pot in
x minutes.
Part A
How much soup was in the pot to
start with?
____liters
Part B
At what rate does the cook fill
the pot?
_______liters per minute
Answers
The required answers are 2.5 liters and 1.5 liters per minute.
How to deal with the equation of variable at different value?Part A:
If we know that the pot has a capacity of 10 liters, we can use the equation y = 1.5x + 2.5 to determine how much soup was in the pot to start with, since at x = 0 minutes, no soup has been added yet.
Substituting x = 0 in the equation, we get:
y = 1.5(0) + 2.5
y = 2.5
Therefore, the pot had 2.5 liters of soup to start with.
Part B:
The equation y = 1.5x + 2.5 tells us how much soup is added to the pot in x minutes, so the rate at which the cook fills the pot can be found by taking the derivative of y with respect to x:
dy/dx = 1.5
Therefore, the rate at which the cook fills the pot is 1.5 liters per minute.
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can someone help me please
Answers
The circumference of a circle is the distance around the edge or perimeter of the circle.
What is the circumference of a circle?1) Radius = 5cm/2 = 2.5 cm
2) Radius = 28 mm/2 = 14 mm
3) Radius = 3 1/2 m * 1/2 = 3/4 m
4) diameter = 2 * 6cm = 12 cm
5) diameter = 2 * 2m = 4 m
6) diameter = 2 * 0.8 ft = 1.6 ft
Circumference can be calculated using the formula:
C = 2πr
7) circumference = 2πr = 2 * 3.14 * 10/2 = 31.4 in
8) circumference = 2 * 7 * 3.14 = 43.96 in
9) Circumference = 2 * 3.14 * 18/2 = 56.52 in
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A company has 14 employees at the cental, 8 employees at the north and 6 employees at the south. They want to lay off 12 employees. In how many ways can this be done?
Answers
Here are 98,280 ways to lay off 12 employees from the company.
What is combination?
In mathematics, a combination is a way of selecting objects from a set, where the order in which the objects are selected does not matter. Combinations are used in various areas of mathematics and statistics, as well as in real-world applications such as probability theory, genetics, and computer science.
We can solve this problem using combinations. We need to choose 12 employees out of a total of 14+8+6=28 employees. The number of ways to do this is:
[tex]{28 \choose 12} \\= \frac{28!}{12!16!} = 98,!280[/tex]
Therefore, there are 98,280 ways to lay off 12 employees from the company.
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Billy has $80 to spend. He spent $54.50 on Bruno Mars Tickets. If Stickers cost $1.34 each, what is the maximum number of Stickers he can buy? Define a variable then write and solve an inequality. Write your answer using a complete sentence.
Answers
Answer:
Billy can buy 19 or less than 19 stickers.
Step-by-step explanation:
Solving inequality:Let the unknown variable - number of stickers be 'x'.
Cost of one sticker = $1.34
Cost of 'x' stickers = 1.34 * x = 1.34x
Maximum amount that can be spent for buying stickers = 80 - 54.50
= $25.50
Inequality:
1.34x ≤ 25.50
Solving:
Divide both sides by 1.34,
[tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]
x ≤ 19.03
x ≤ 19
Billy can buy 19 or less than 19 stickers.
If the peaches are placed on a scale that can mesure weight to the nearest thousandth of a pound wouls you expectt the scale to show the weight of 4. 168 pounds or 4. 158 pounds
Answers
The scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.
What is measurement?
Measurement is the process of assigning numerical values to physical quantities such as length, mass, time, temperature, and many others.
It depends on the actual weight of the peaches. If the weight of the peaches is closer to 4.158 pounds, then the scale would show 4.158 pounds. Similarly, if the weight of the peaches is closer to 4.168 pounds, then the scale would show 4.168 pounds.
Since the scale can measure weight to the nearest thousandth of a pound, it can differentiate between weights that differ by one-thousandth of a pound.
Therefore, the scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.
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Joshua is building a model airplane that measures 45 inches. The measurements of the model can vary by as much as 0. 5 inches.
PART 2: Solve the equation to find the minimum and maximum measurements. Round to the nearest tenth if necessary
Answers
The minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.
Joshua is building a model airplane. Solve the equation to find the minimum and maximum measurements of the airplane.To find the minimum and maximum measurements of Joshua's model airplane, we need to subtract and add 0.5 inches to the given length of 45 inches, respectively.
Minimum measurement:
45 - 0.5 = 44.5 inches
Maximum measurement:
45 + 0.5 = 45.5 inches
Therefore, the minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.
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100 more points Help asap!
Answers
The answers to the questions on linear combination have been solved below
How to solve the linear combination1. We can start by multiplying both sides by -2 to eliminate the x-term:
2x + 4y = 0
-2(2x + 4y) = -2(0)
-4x - 8y = 0
Now, we have:
-4x - 8y = 0
9x + 4y = 28
We can now use linear combination by adding these two equations to eliminate the y-term:
(-4x - 8y) + (9x + 4y) = 0 + 28
5x = 28
Dividing both sides by 5, we get:
x = 28/5
Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the second equation:
2x + 4y = 0
2(28/5) + 4y = 0
56/5 + 4y = 0
4y = -56/5
y = -14/5
Therefore, the solution to the system of equations is:
x = 28/5
y = -14/5
We can check that these values satisfy both equations:
9x4y = 28
9(28/5)(-14/5) = 28
-352/25 = 28/25 (true)
2x + 4y = 0
2(28/5) + 4(-14/5) = 0
56/5 - 56/5 = 0 (true)
Therefore, the solution is verified.
2. The system of equations is:
5x + 3y = 41
3x - 6y = 9
We can simplify the second equation by dividing both sides by 3:
3x - 6y = 9
x - 2y = 3
Now we can use linear combination by multiplying the first equation by 2 to eliminate the y-term:
2(5x + 3y) = 2(41)
10x + 6y = 82
(x - 2y) + (10x + 6y) = 3 + 82
11x = 85
Dividing both sides by 11, we get:
x = 85/11
Now we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:
5x + 3y = 41
5(85/11) + 3y = 41
425/11 + 3y = 41
3y = 41 - 425/11
3y = (451 - 425)/11
y = 26/33
Therefore, the solution to the system of equations is:
x = 85/11
y = 26/33
We can check that these values satisfy both equations:
5x + 3y = 41
5(85/11) + 3(26/33) = 41
425/11 + 26/11 = 41
451/11 = 41 (true)
3x - 6y = 9
3(85/11) - 6(26/33) = 9
255/11 - 52/11 = 9
203/11 = 9 (true)
Therefore, the solution is verified.
3.
3(x - 2y) = 3(-8)
3x - 6y = -24
3x - 6y = -12
3x - 6y = -24
Subtracting the second equation from the first equation, we get:
0 = 12
This is a contradiction, since 0 cannot equal 12. Therefore, there is no solution that satisfies both equations.
This means that the system is inconsistent, and there are no solutions.
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Lamarr has budgeted $35 from his summer job earnings to buy shorts and socks for
soccer. he needs 5 pairs of socks and a pair of shorts. the socks cost different
amounts in different stores. the shorts he wants cost $19.95.
a. let x represent the price of one pair of socks. write an expression for the total cost
of the socks and shorts.
b. write and solve an equation that says that lamarr spent exactly $35 on the socks
and shorts.
c. list some other possible prices for the socks that would still allow lamarr to stay
within his budget.
d. write an inequality to represent the amount lamarr can spend on a single pair of
socks.
Answers
Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.
a. The total cost of the socks and shorts can be represented by the expression:
Total cost = Cost of shorts + Cost of 5 pairs of socks
= $19.95 + 5x
where x is the price of one pair of socks.
b. To write an equation that says Lamar spent exactly $35 on the socks and shorts, we can equate the total cost expression to $35:
$19.95 + 5x = $35
To solve for x, we can first subtract $19.95 from both sides:
5x = $15.05
Then, divide both sides by 5:
x = $3.01
So, Lamar spent $19.95 + 5($3.01) = $35 on the socks and shorts.
c. Other possible prices for the socks that would still allow Lamar to stay within his budget of $35 can be found by plugging in values of x that satisfy the inequality:
Cost of 5 pairs of socks = 5x ≤ $15.05
For example, if the socks cost $2.99 per pair, then the total cost would be:
$19.95 + 5($2.99) = $34.90
which is within Lamar's budget.
d. We can write an inequality to represent the amount Lamar can spend on a single pair of socks as:
x ≤ (35 - 19.95)/5
This simplifies to:
x ≤ $3.01
So, Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.
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Help with this please
Answers
Answer:
sin(θ) = (2/9)√14; csc(θ) = (9√14)/28cos(θ) = 5/9; sec(θ) = 9/5tan(θ) = (2/5)√14; cot(θ) = (5√14)/28Step-by-step explanation:
Given cos(θ) = 5/9, you want the six trig functions of θ.
IdentitiesThe relevant identities are ...
sin(θ) = ±√(1 -cos(θ)²)tan(θ) = sin(θ)/cos(θ)csc(θ) = 1/sin(θ)sec(θ) = 1/cos(θ)cot(θ) = 1/tan(θ)SineThe sine of θ is ...
sin(θ) = √(1 -(5/9)²) = √(81 -25)/9 = (√56)/9
sin(θ) = (2/9)√14
Then the cosecant is ...
csc(θ) = 1/sin(θ) = (9/2)/√14
csc(θ) = (9√14)/28
TangentThe tangent of θ is ...
tan(θ) = sin(θ)/cos(θ) = ((2/9)√14)/(5/9)
tan(θ) = (2/5)√14
Then the cotangent is ...
cot(θ) = 1/tan(θ) = (5/2)/√14
cot(θ) = (5√14)/28
SecantThe secant of θ is ...
sec(θ) = 1/cos(θ) = 1/(5/9)
sec(θ) = 9/5
The cosine is given in the problem statement.
Draw a rectangle that is 4 squares long and
1/2 of a square wide.
then add up the partial squares to find the area.
multiply to check your answer
Answers
The exact area of our rectangle is 2 square units
The total area of the rectangle can be found by adding up the area of each square. We have four unit squares and one half-square, which can be represented as 4 + 1/2. To add these two values, we need to find a common denominator, which is 2.
Thus, we can represent the area of the rectangle as
=> 8/2 + 1/2 = 9/2 square units.
We know that the area of a rectangle is calculated by multiplying its length by its width. Thus, we can represent the area of our rectangle as follows:
A = lw
where A is the area, l is the length, and w is the width.
Now, we need to differentiate this equation with respect to the width w. This means we are finding the rate of change of the area with respect to the width. Using the product rule of differentiation, we get:
dA/dw = l * dw/dw + w * dl/dw
Since the width is constant (it does not change), the second term on the right-hand side of the equation is zero. Thus, we are left with:
dA/dw = l
To calculate the exact area of our rectangle, we can use the concept of limits. We can start by approximating the area of our rectangle with a width of 1 square unit. In this case, the area of the rectangle would be 4 square units.
We can then approach the width of 1/2 of a square unit by taking the limit as the width approaches 1/2. Using the derivative we calculated earlier, we can represent this limit as follows:
lim(w→1/2) A = lim(w→1/2) lw = l * lim(w→1/2) w = 4 * (1/2) = 2 square units
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1) harriett has a cylindrical pool with a diameter of 11 feet and a height of 2 feet.
the inside of the pool is lined with a plastic material. how many square feet of plastic material does the pool have? use 3.14 for pi. round your answer to the nearest tenth.
please help me because i really need with this question <3
Answers
The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.+
To calculate the surface area of the pool that is lined with plastic material, we need to find the area of the curved part and the area of the top and bottom circles.
First, let's find the radius of the pool, which is half of the diameter:
radius = 11 feet / 2 = 5.5 feet
The curved part of the pool is a cylinder with a height of 2 feet and a circumference of [tex]2 * π *radius:[/tex]
curved area = height * circumference
[tex]curved area = 2 feet * 2 * 3.14 * 5.5 feet[/tex]
[tex]curved area = 68.2 square feet[/tex]
The top and bottom of the pool are two circles with a radius of 5.5 feet:
circle area = π * radius²
[tex]circle area = 3.14 * 5.5 square feet[/tex]
[tex]circle area = 95.0 square feet[/tex]
To find the total surface area of the pool that is lined with plastic material, we add the area of the curved part and the area of the top and bottom circles:
Total area = curved area + 2 * circle area
Total area = 68.2 square feet + 2 * 95.0 square feet
Total area = 258.2 square feet
The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.
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Find the diameter of a circle with a circumference of 63 feet. Round your answer to the nearest thousandth.
Answers
Answer: 20.054
Step-by-step explanation:
D = 2R
R = (C/2π)
Find x.
Round to the nearest tenth:
12 cm
22 cm
42°
x = [? ]°
Law of Sines: sin A
sin B
sin C
а
vt6
b
Enter
Answers
The value of x is approximately 61.7 degrees using the Law of Sines.
To find the value of x, we can use the Law of
Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. Mathematically, we can write:
a/sin A = b/sin B = c/sin C
where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.
Using the given information, we can set up the
equation as follows:
12/sin 42° = 22/sin x
Multiplying both sides by sin x°, we get:
sin x = (22/12) x sin 42°
sin x = 1.6977
Taking the inverse sine of both sides, we get:
x* = sin" (1.6977)
x = 61.7°
Rounding to the nearest tenth, we get:
x = 61.7°
Therefore, the value of x is approximately 61.7
degrees.
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The complete question is:
In the given figure , find the X (round to the nearest tenth) , where the sides are marked as 12cm and 22 cm with the angle of 42°.
If theta is a first-quadrant angle in standard position with p(u, v) = (3, 4), evaluate tan1/2 theta
o 1/4
o 1/2
o 2/3
Answers
We can use the given point P(3, 4) to find the values of sin(theta) and cos(theta) as follows:
[tex]sin(theta) = opposite/hypotenuse = 4/5[/tex]
[tex]cos(theta) = adjacent/hypotenuse = 3/5[/tex]
Since theta is a first-quadrant angle, we know that tan(theta) = sin(theta)/cos(theta).
Using the half-angle formula for tangent, we have:
[tex]tan(1/2 * theta) = ±√((1 - cos(theta))/2) / (1 + √((1 - cos(theta))/2))[/tex]
We can substitute the values of sin(theta) and cos(theta) that we found earlier:
[tex]tan(1/2 * theta) = ±√((1 - 3/5)/2) / (1 + √((1 - 3/5)/2))[/tex]
[tex]tan(1/2 * theta) = ±√(1/5) / (1 + √(1/5))[/tex]
[tex]tan(1/2 * theta) = ±√5 - 1[/tex]
Since theta is in the first quadrant, tan(1/2 * theta) is positive. Therefore:
[tex]tan(1/2 * theta) = √5 - 1[/tex]
We can simplify this expression by rationalizing the denominator:
[tex]tan(1/2 * theta) = (√5 - 1) / (√5 + 1) * (√5 - 1) / (√5 - 1)[/tex]
[tex]tan(1/2 * theta) = (5 - 2√5)[/tex]
So the answer is (5 - 2√5), which is approximately 0.382. Therefore, the answer is not one of the choices given.
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down 9 units and left 2 units what coordinates would you end up at? What quadrant would you be in?
Answers
So, depending on the original coordinates, moving down 9 units and left 2 units will end up in either the third or fourth quadrant of the coordinate plane.
What is coordinate?A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In a two-dimensional space, such as the Cartesian plane, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal position (or abscissa) of the point and y represents the vertical position (or ordinate) of the point.
Here,
Starting from an arbitrary point (x, y), if we move down 9 units and left 2 units, we will end up at the point with coordinates (x - 2, y - 9). The new x-coordinate is obtained by subtracting 2 from the original x-coordinate, since we moved 2 units to the left. The new y-coordinate is obtained by subtracting 9 from the original y-coordinate, since we moved 9 units down.
The quadrant we end up in depends on the original coordinates (x, y) and the direction of the movement. If we start in the first quadrant (x > 0, y > 0) and move down and left, we will end up in the third quadrant (x < 0, y < 0).
If we start in the second quadrant (x < 0, y > 0) and move down and left, we will also end up in the third quadrant (x < 0, y < 0).
If we start in the third quadrant (x < 0, y < 0) and move down and left, we will end up in the fourth quadrant (x > 0, y < 0).
If we start in the fourth quadrant (x > 0, y < 0) and move down and left, we will still end up in the fourth quadrant (x > 0, y < 0).
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10-2 skills practice simplifying radical expressions square root of 5 over 3
Answers
Step-by-step explanation:
sqrt (5/3) = sqrt 5 / sqrt 3
multiply by ONE in the form sqrt (3) / sqrt 3
sqrt 5 / sqrt 3 * sqrt 3 / sqrt 3
= sqrt 15 / 3
Or maybe you meant
sqrt (5) / 3 = .745
From a distance of 300 m, Susan looks up at the top of a lighthouse. The angle of elevation is 5',
Determine the height of the lighthouse to the nearest meter,
Answers
If Susan stands 300 m away from the lighthouse and looks up at it with an angle of elevation of 5 degrees, the height of the lighthouse is approximately 26 meters. This calculation is important for navigation and other purposes.
To determine the height of the lighthouse, we can use trigonometry. We know that the angle of elevation, which is the angle between Susan's line of sight and the ground, is 5'. We also know the distance between Susan and the lighthouse, which is 300 m.
We can use the tangent function to find the height of the lighthouse:
tan(5') = height/300
To solve for height, we can cross-multiply and simplify:
height = 300 x tan(5')
Using a calculator, we get that the height of the lighthouse is approximately 26.2 m.
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Part of the shape is drawn.
The line of symmetry of the shape is the dotted line.
complete the drawing of the shape and then rotate it by 180° about the origin
Answers
The remaining part of the given shape was drawn about to its symmetry. The complete shape obtained is similar to the Hexagon shape.
Given half shape has the following points,
(-3,-1)(-4,-1)(-5,-3)(-4,-4)(-3,-4)The points which are missing to complete the other symmetry are:
(-3,-1)(-2,-1)(-1,-3)(-2,-4)(-3,-4)By joining the above missing points, we can obtain the full symmetry of the shape.
To rotate the obtained shape of the Hexagon to 180° about the origin, we have to inverse the above complete symmetry points. It simply means if the above points are having positive values, we can inverse it to negative and vice-versa.
By rotating the obtained shape to 180° about the origin, we can obtain the below following points,
(3,1)(4,1)(5,3)(4,4)(3,4)(2,1)(1,3)(2,4)The images are attached below for the complete symmetry shape.
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Given question is not having enough required information, so I am attaching the image of the shape which we have to work on,
not all summer blockbusters are cinematic breakthroughs. subject term: summer blockbusters predicate term: cinematic breakthroughs which of the following statements is true of this categorical proposition? it is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p. it is a standard-form categorical proposition because it is a substitution instance of this form: no s are p. it is a standard-form categorical proposition because it is a substitution instance of this form: some s are p. it is a standard-form categorical proposition because it is a substitution instance of this form: all s are p. it is not a standard-form categorical proposition.
Answers
The statements is true of this categorical proposition is: It is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p option A.
A proposition or statement that is categorically affirmed or denied of all or part of the topic is known as a categorical proposition in syllogistic or classical logic. Hence, there are four fundamental types of categorical propositions: "Every S is P," "No S is P," "Some S is P," and "Some S is not P."
Every man is mortal, for instance, is an A-proposition since these forms are denoted by the letters A, E, I, and O, respectively. In particular, being declarations of reality rather than logical connections, they contrast significantly with hypothetical propositions, such as "If every man is mortal, then Socrates is mortal," which categorical propositions are to be differentiated from and enter into as integral words.
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Alec bought a house. By the end of the first year, the value of Alec's house had increased by 1%. By the end of the second year, its value had decreased by 10% of its value at the end of the first year. Use multipliers to work out the overall percentage decrease in the value of Alec's house for this two-year period
Answers
The overall percentage decrease in the value of Alec's house for the two-year period is 9.9%.
Let's assume the original value of Alec's house as $100. After the first year, the value of the house increased by 1%, which means the new value of the house is $101.
Now, in the second year, the value of the house decreased by 10% of its value at the end of the first year. Therefore, the new value of the house at the end of the second year can be calculated as $101 - (10/100)*$101 = $90.90.
To find the overall percentage decrease in the value of Alec's house for the two-year period, we can use the formula:
Overall percentage decrease = [(Original value - Final value)/Original value] * 100%
Substituting the values, we get,
Overall percentage decrease = [($100 - $90.90)/$100] * 100% = 9.9%
Therefore, the overall percentage decrease in the value of Alec's house for the two-year period is 9.9%.
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Jamel is painting his room he determins that 1/2 gallons container of pain will cover 1/6 of a wall how many gallons of paint are needed for an entire wall (assuming there no doors or windows) the answer is not 120 gallons.
A pair of shoes originally cost $35 but they are on sale for 15% off what is the sale price of the shoes?
The answer is not 5.25
A community center is offspring a discount on swimming passes the regular cost for a swimming pass is 6:00 Jake, Lisa, and Manuel each buy a swimming pass at the community center after the discount the total cost for the 3 passes is $14.40 what is the discount the community center is offspring
A. 20%
B. 42%
C. 72%
D. 80%
D. Is not the answer!
Answers
Answer:
Step-by-step explanation:
(for the first question)
1/2 gallons cover 1/6th of the wall then
1-gallon covers 1/3rd of the wall
so 3 gallons cover one wall
(second question)
you have to calculate 85% of $35 because it is 15% percent off.
35*0.85=29.75
The sale price is $29.75.
(third question)
6*3=18
14.4*100/18
1440/18
80
100-80 = 20
The answer is A (20%)
Answer:
3 gallons of paint
$29.75
20%
Step-by-step explanation:
1. Let's break this down:
1/2 gallon of paint covers 1/6 of his wall.
This means that we have to multiply 1/2 by 6, as there would be 6 1/2 gallon sections of his wall.
1/2·6=3
So, Jamel needs 3 gallons of paint.
2. If a pair of shoes has an original price of $35 but it on sale for 15%, we have to first find how much it's now on sale for:
15/100·35
=0.15·35
=5.25
This is the how much it's off, so subtract 5.25 from 35
35-5.25=$29.75
The shoes have a sale price of $29.75
Even though you said this was wrong, you may have to put a dollar sign in front of it.
3. This is worded a little, but assuming:
1 swimming pass is $6, 3 people buy the swimming pass, and the total cost for the 3 passes in total is $14.40, we have to find out the discount.
So, originally, before the discount, the total amount for the 3 swimming passes would've been $18, but there's been a discount and now they only had to pay $14.40.
To solve, we do the following:
subtract the original price by the sale price
18-14.40=3.6
divide by the original price
3.6/18=0.2
multiply by 100 to get into percent
0.2x100=20%
This means that A is the correct choice.
Hope this helps! :)
