The probability that the three marbles selected are all different colors is 0.224 or 22.4%.
To find the probability that the three marbles selected are all different colors from a box that contains 4 green marbles, 9 blue marbles, and 6 red marbles, one at a time, without replacement. We can use the probability formula as follows:P(all different colors) = Number of ways to choose 3 marbles of different colors / Total number of ways to choose 3 marbles
The total number of ways to choose 3 marbles from a total of 19 marbles in the box is given by:19C3 = (19 × 18 × 17) / (3 × 2 × 1) = 969The number of ways to choose 3 marbles of different colors from a box containing 4 green marbles, 9 blue marbles, and 6 red marbles, one at a time, without replacement can be obtained as follows:4C1 × 9C1 × 6C1 = (4 × 9 × 6) = 216
Therefore, the probability of choosing 3 marbles of different colors from the box is:P(all different colors) = Number of ways to choose 3 marbles of different colors / Total number of ways to choose 3 marblesP(all different colors) = 216/969P(all different colors) = 24/107 or 0.224 or 22.4%
Therefore, the probability that the three marbles selected are all different colors is 0.224 or 22.4%.
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PLEASE SHOW WORK!!!!!
The correct answer is D. Only statements I and III are true for pi < theta < 3.
What are trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. They are commonly used in geometry, physics, and engineering to solve problems involving triangles and periodic phenomena. The six basic trigonometric functions are:
Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.
Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.
Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.
Cosecant (csc): the reciprocal of the sine function.
Secant (sec): the reciprocal of the cosine function.
Cotangent (cot): the reciprocal of the tangent function.
To answer this question, we need to analyze the given range of values for theta, and determine the signs of the trigonometric functions involved.
For pi < theta < 3, we know that theta is in the second quadrant, where sine is positive and cosine is negative.
Therefore, statement I is true, since sine is positive for values of theta in this range.
Statement II is false, since cosine is negative in the second quadrant, and 2 cos theta is also negative.
Statement III is true, since tangent is negative in the second quadrant, and (1/3) tan theta is also negative.
So, the correct answer is D. Only statements I and III are true for pi < theta < 3.
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(Worth 20 points, will give brainliest if right)
If (r, s) is the solution to the system of equations, what is the value of r?
−8r − 8s = 100
r − 2s = 10
The measurement of an angle is 3/4 the measurement of its complement. What is the measure of the angle?
Answer:
270
Step-by-step explanation:
360×3/4=270 as per given information in the qustion a complete circle is 360 so then 3/4 × 360
Which expression is NOT equivalent to the others?
The expression [tex](2+7)^2[/tex] is not equivalent to the others as it is an exponential expression, while the others are all linear expressions.
The expression [tex](2+7)^2[/tex] is not equivalent to the others as it is an exponential expression, while the others are all linear expressions. An exponential expression is a mathematical expression that contains a variable in an exponent, meaning it is raised to a certain power, while a linear expression is a mathematical expression that contains two or more variables, where each has an exponent of 1. For example,[tex](2+7)^2[/tex] can be written as[tex]9^2[/tex]which is equal to 81. In contrast, the other expressions can be written as 2x+7y+3z which is equal to 2x+7y+3z. This means that the two expressions are not equivalent. To illustrate further, we can use a simple example. Let's say x=2, y=3, and z=4. Then the linear expression 2x+7y+3z would be equal to 2(2)+7(3)+3(4) = 22. The exponential expression[tex](2+7)^2[/tex] would be equal to [tex](2+7)^2 = 9^2 = 81[/tex]. We can see here that the two expressions are not equivalent.
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Which expression is NOT equivalent to the others?
A) 2 + 4
B) 6 - 2
C) 8 ÷ 4
D) 3 x 2
Help I do not know how to do this and now I’m stuck
Answer:
okay the answer is b[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Tu is a Tangent to the circle at v. Find the value of x
Answer:2.333...
Step-by-step explanation:
A tangent meets a radius (also works with diameters) at 90°.
This means (98 - 3x) = 90
98 = 90 + 3x
8 = 3x
x = 8 / 3 = 2.3333333......
Step-by-step explanation:
Arc wxv is 360 - 176 = 184 degrees
this makes angle 98-3x = 1/2 (184) = 92°
( 98 -3x )°= 92°
- 3x = -6
x = 3
Use Conditional Probability Notation to Describe Events Question Let M be the event that a randomly chosen student passes a math test. Let S be the event that a randomly chosen student studies every day. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen student studies every day, given that the student passes a math test Select the correct answer below: O P(MS) OPM AND S) O P(S) AND P(M) O P(SM)
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
The conditional probability that a randomly chosen student studies every day, given that the student passes a math test is O P(M|S). The correct option is A.
P(M|S) is the probability that a randomly chosen student passes a math test given that the student studies every day. But, the question is asking for the probability that a student studies every day given that the student passes a math test.
Considering an P(M|S) situation,
Option D: P(SM) is incorrect because it means the probability that both events S and M occur simultaneously.
Option C: P(S) and P(M) is incorrect because it shows the probabilities of two individual events, not the probability of one event given that the other event has occurred.
Option B: P(M AND S) is incorrect because it means the probability that both events M and S occur simultaneously.
The given problem is based on Conditional Probability Notation to Describe Events. The notation used for conditional probability is P(A|B). Where A and B are two events, the notation represents the probability of event A occurring, given that event B has occurred. Conditional probability can be described as the probability of one event happening given that another event has already happened.
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Calculate the money you will have in the following accounts after 5 years assuming you earn simple interest,
51. you deposit $700 in an account with an annual interest rate of 4%
54. you deposit $1800 in an account with an annual interest rate of 3.8%
We will have $840 and $2142 respectively. The solution has been obtained by using simple interest.
What is simple interest?
Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest.
We know that amount after simple interest is given by
A = P (1 + rt)
We are given that $700 are deposited in an account with an annual interest rate of 4%.
Here,
P = $700
r = 4%
t = 5 years
On substitution, we get
⇒A = 700 (1 + (0.04 * 5))
⇒A = 700 (1 + 0.2)
⇒A = 700 (1.2)
⇒A = $840
Similarly, in the second case,
P = $1800
r = 3.8%
t = 5 years
On substitution, we get
⇒A = 1800 (1 + (0.038 * 5))
⇒A = 1800 (1 + 0.19)
⇒A = 1800 (1.19)
⇒A = $2142
Hence, we will have $840 and $2142 respectively.
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Alicia spun a spinner 100 times, and the results are shown in the following table. What is the relative frequency for the spinner to land on number 1?
Responses
Answer:
3/25
Step-by-step explanation:
14. Find the measures of all the angles in the rectangle. 1 2 3 5 32 4
[tex]90^{0} - 32^{0} = 58^{0}[/tex]
1 = 4 = 90°
2 = 32°
3 = 5 = 58°
Answer:
∠1 = ∠4 = 90°∠2 = 32°∠3 = ∠5 = 58°Step-by-step explanation:
You want the measures of the marked angles in the rectangle, given one of the acute angles is 32°.
Complementary anglesThe corner angles of a rectangle are all 90°. That's part of the definition of a rectangle:
∠1 = ∠4 = 90°
That make angles 5 and 32° be complementary angles:
∠5 = 90° -32° = 58°
The angles at the opposite end of the diagonal are complementary to these, as the sum of angles in a triangle is 180°.
∠2 = 90° -58° = 32°
∠3 = 90° -32° = 58°
__
Additional comment
You may have noticed that angles on opposite sides and opposite ends of the diagonal have the same measure. This is no coincidence. These are called "alternate interior angles". As such, they are always congruent where a diagonal meets parallel lines. (The sides of a rectangle are parallel.)
If you have the right answer I will give you brainilest!!!
Please help me with this question. Thanks :)
Answer:
26
Step-by-step explanation:
Total pupils 60
32 boys and girls will be 28 (60-32)
Cola 12 boys
Water 4 boys 9 girls
Milk 21 pupils
Total results 12 + 4 +9+ 21 = 46
Outstanding girls will be 60 - 46
Girls who like coke 14
If 14 girls liked cola and 12 boys liked cola, total will be 14 + 12
I NEED THIS FAST PLEASEEE!!
The population of Cirque City was 43,129 in 1999 and was 56,780 in 2010. If the population was growing exponentially, what was the growth rate?
Answer:
Step-by-step explanation:
If we call 1999 year 0, then 2010 would be year 11. This makes the coordinates for our problem (0, 43129) and (11, 56780). That means that the initial value, a, is 43129 and we can use that to solve for b.
[tex]56780=43129(b)^{11[/tex]
Divide both sides by 43129 to get
[tex]1.31651557=b^{11[/tex] and take the 11th root on your calculator to get that
b = 1.025314051
Not sure how you need to round that.
Find the area of the parallelogram below:
What is the area?
Answer:
The area of the parallelogram is 630.4 square units, to the nearest tenth.
Step-by-step explanation:
The formula to find the area of a parallelogram is:
[tex]A=bh[/tex]
where b is the base and h is the height.
For the given parallelogram ABCD, BC and AD are the bases and h is the height. Therefore, we need to calculate the height, h, before we can calculate the area of the parallelogram.
The height of the parallelogram is also the side opposite angle 62° in the right triangle of the given diagram. As we also know the hypotenuse of this triangle, we can use the sine trigonometric ratio to find "h".
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given:
θ = 62°O = hH = 21Therefore, the expression for h is:
[tex]\implies \sin 62^{\circ}=\dfrac{h}{21}[/tex]
[tex]\implies h=21\sin 62^{\circ}[/tex]
Given the base of the parallelogram is 34 units, substitute b = 34 and the expression for h into the formula for the area:
[tex]\begin{aligned}\implies \textsf{Area}&=34 \cdot 21\sin 62^{\circ}\\&=630.424581...\\&=630.4\; \sf square\;units\;(nearest\;tenth) \end{aligned}[/tex]
Therefore, the area of the parallelogram is 630.4 square units, to the nearest tenth.
Please Help!
Drag each label to the correct location on the equation. Not all labels will be used.
Picture is linked below.
After answering the given query, we can state that Expression: A group variable of words, divided by signs for addition or subtraction.
What is a Variable?In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols. A wide variety of values can be assigned to characteristics known as variables. These factors include, among others, your size, age, wealth, place of birth, scholastic standing, and type of residence. Both numerical and categorical methods can be used to divide variables into two primary groups.
Here are where the labels should be placed based on the illustration:
Coefficient, label one
2nd label: variable
Label 4: the equals symbol Label 3: constant
5th label: term
Expression 6th label
The definition of each term is broken down as follows:
A integer multiplied by a variable in a term of an algebraic expression is referred to as a coefficient.
Variable: A symbol for a quantity that is subject to shift or variation.
A fixed, unchanging number is referred to as a constant.
The equals sign: Shows that the expressions on the left and right are equivalent.
Term: A grouping of variables multiplied by a coefficient and denoted by addition or subtraction marks.
Expression: A group of words, divided by signs for addition or subtraction.
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The pharaoh's outfitters, 'Cloaks and
Crowns', sell cloaks and crowns in 3
sizes - prince, king and emperor (in
increasing size order).
He wants to kit out his three sons for the
forthcoming festival of Ra. Ahmose
chooses a bigger cloak than Kamose,
but a smaller crown than Thutmose.
Both Thutmose's cloak and crown are
larger than Kamose's, but the size of
Thutmose's crown matches the size of
Kamose's cloak.
Which sizes did the
pharaoh's sons each get?
The largest marine animal is the blue whale, with an average mass of about 1.7×105 1.7 × 10 5 kg. The largest land animal ever is thought to be a dinosaur that had a mass of about 8×104 8 × 10 4 kg. What is the approximate difference in mass between these two animals
The approximate difference in mass between these two animals is 154,000 kg.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.
Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".
Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.
The difference in mass between these two animals is:
1.7 x 10⁵ kg - 8 x 10⁴ kg = 1.54 x 10⁵ kg
Therefore, the approximate difference in mass between these two animals is 154,000 kg.
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Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8. 11 and a standard deviation of 1. 46. Using the empirical rule, what percentage of American women have shoe sizes that are at least 11. 3
About 1.5% of American women have shoe sizes that are at least 11.3, using the empirical rule and a standard normal distribution table.
To use the empirical rule, we assume that the shoe sizes follow a normal distribution. We can then convert the shoe size 11.3 to a z-score using the formula:
z = (x - μ) / σ
where x is the shoe size, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
[tex]z = (11.3 - 8.11) / 1.46 = 2.17[/tex]
This tells us that a shoe size of 11.3 is 2.17 standard deviations above the mean.
The empirical rule enables us to determine that, with a normal distribution:
About 68% of the data falls within one standard deviation of the mean
The data is within two standard deviations of the mean for about 95% of the time
About 99.7% of the data falls within three standard deviations of the mean
Since 11.3 is more than two standard deviations above the mean, we know that fewer than 5% of women will have a shoe size this large. To find the exact percentage, we can use a standard normal distribution table (also known as a z-table) or a calculator to find the area under the curve to the right of z = 2.17.
Using a calculator or a table, we find that the area to the right of z = 2.17 is approximately 0.015, or 1.5%. Therefore, we can say that about 1.5% of American women have shoe sizes that are at least 11.3.
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Solve by Elimination:
5x+2y=−3
2x+3y=−10
Answer:
Multiplying the second equation by 2, we get:
4x + 6y = -20
Now we can subtract the first equation from this to eliminate x:
4x + 6y = -20
-(5x + 2y = -3)
-x + 4y = -17
Now we have one equation with only y. Solving for y:
-x + 4y = -17
4y = x - 17
y = (1/4)x - 17/4
Now we can substitute this expression for y into either equation to solve for x. Let's use the first equation:
5x + 2y = -3
5x + 2((1/4)x - 17/4) = -3
5x + (1/2)x - 17 = -3
(11/2)x = 14
x = 28/11
So the solution is (x,y) = (28/11, -17/11).
Step-by-step explanation:
Algebraic proofs geometry
The method used to prove the values of the variables consists of solving the equations as presented in the following section.
What is an equation?An equation is a statement of equivalence between two expressions which is indicated by joining them with an '=' sign.
8. Statement [tex]{}[/tex] Reasons
(5·y - 1)/2 = 7 [tex]{}[/tex] Given
5·y - 1 = 2 × 7 [tex]{}[/tex] Multiplicative property of equality
5·y = 2 × 7 + 1 = 10 [tex]{}[/tex] Additive property of equality
5 = 10/5 = 2 [tex]{}[/tex] Division property of equality
9. Statement [tex]{}[/tex] Reasons
10·k - 4 = 2·k - 20 [tex]{}[/tex] Given
10·k = 2·k - 20 + 4 = 2·k - 16 [tex]{}[/tex] Additive property of equality
10·k - 2·k = 8·k = -16 [tex]{}[/tex] Subtraction property of equality
k = -16/2 = -8 [tex]{}[/tex] Division property of equality
10. Statement [tex]{}[/tex] Reasons
-8·(w + 1) = -5·(w + 10) [tex]{}[/tex] Given
-8·w - 8 = -5·w - 50 [tex]{}[/tex] Distributive property of equality
-5·w + 8·w = 3·w = 50 - 8 = 42 [tex]{}[/tex] Subtraction property of equality
4 = 42/3 = 14 [tex]{}[/tex] Division property of equality
11. Statement [tex]{}[/tex] Reasons
14 - 2·(x + 8) = 5·x - (3·x - 34) [tex]{}[/tex] Given
14 - 2·x - 16 = 5·x - 3·x + 34 [tex]{}[/tex] Distributive property of equality
2·x + 2·x = 4·x = -2 - 34 = -36 [tex]{}[/tex] Subtraction property of equality
x = -36/4 = -9 [tex]{}[/tex] Division property of equality
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What is the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week
Answer:
Without more information about the specific survey and population being surveyed, it is difficult to provide a precise answer to this question. However, I can provide some general information on how probabilities can be calculated in surveys.
Assuming that the survey is a representative sample of college students and that the question about difficulty falling asleep is a binary (yes/no) question, we can calculate the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week as follows:
1. Determine the total number of surveyed college students who answered the question about difficulty falling asleep.
2. Determine the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week.
3. Divide the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week by the total number of surveyed college students who answered the question about difficulty falling asleep.
For example, if 1,000 college students were surveyed and 800 of them answered the question about difficulty falling asleep, and 200 of those 800 reported having a hard time falling asleep on 3 or more days in the last week, then the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week would be 200/800, or 0.25, or 25%.
At westville highschool there are 315 seniors and 389 juniors 65% of the seniors have parking passes and 42% of the juniors have parking passes the statistics teacher selects an SRS of 30 seniors and a seperate SRS of 30 juniors
The probability of selecting a senior who has a parking pass and a junior who has a parking pass is 0.2730.
At Westville Highschool, there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS (Simple Random Sample) of 30 seniors and a separate SRS of 30 juniors.
To determine the probability of selecting a senior who has a parking pass and a junior who has a parking pass, first the probability of selecting a senior who has a parking pass must be calculated. Since 65% of the seniors have parking passes, the probability of selecting a senior with a parking pass is 0.65. Secondly, the probability of selecting a junior with a parking pass must be calculated. Since 42% of the juniors have parking passes, the probability of selecting a junior with a parking pass is 0.42.The probability of selecting a senior who has a parking pass and a junior who has a parking pass can be found by multiplying the two probabilities. 0.65 x 0.42 = 0.2730.
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Gretchen is refinishing her gazebo that is in the shape of a regular octagon. The length of one side is 3 feet and the apothem is 3. 5 feet. What
is the area that Gretchen will be refinishing?
Answer:
10.5
Step-by-step explanation:
you just have to multiply 3 feet by 3.5 feet.
List three sides to a right triangle. Explain how you can use the Pythagorean theorem to know that your three sides will create a right triangle.
Answer: Three sides of a right triangle are the lengths of its legs and the length of its hypotenuse.
To know that three given sides will create a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Symbolically, if a, b, and c are the lengths of the sides of a right triangle, with c being the hypotenuse, then:
c^2 = a^2 + b^2
Therefore, if we are given the lengths of three sides, we can square the lengths of the legs, add them together, and then take the square root to find the length of the hypotenuse. We can then compare the squared length of the hypotenuse to the sum of the squares of the legs. If they are equal, the three sides form a right triangle. If the squared length of the hypotenuse is greater than the sum of the squares of the legs, the three sides form an obtuse triangle. If the squared length of the hypotenuse is less than the sum of the squares of the legs, the three sides form an acute triangle.
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answer: -5
Step-by-step explanation:
Handy Automobiles produces two scooters: Basic and Discord. These scooters are produced by assembling multiple units of two key components C1 and C2. The component usage for the two scooters is given below:
Basic Discord
C1 6 10
C2 10 4
These components are produced within the plant. Marginal production costs for C1 and C2 are $8 and $12 respectively. The selling price of Discord is $500 and that of Basic is $400. The demand for these products are uncertain. Handy has to plan for the following 3 demand scenarios:
Basic Discord Prob
Scenario 1 600 200 30%
Scenario 2 400 400 40%
Scenario 3 300 500 30%
Due to the long lead times associated with production, Handy has to produce the components before they know which of the demand scenarios they need to plan for. However the components can be assembled to produce the two products after demand information is available. Unused components have no value and are discarded.
1. Develop a production plan for Handy
2. Suppose Handy can retool its production system and develop an additional component C3 which can serve as a substitute for both C1 and C2. However, the marginal cost of production of this component is $14. Should they go ahead with the retooling? If so, what is their new production plan?
Handy should produce 5400 units of C1 and 5600 units of C2 and the production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.
1. To develop a production plan for Handy, we need to calculate the expected demand for each component under each scenario. This is done by multiplying the demand for each scooter by the number of components used in its production, and then multiplying by the probability of each scenario occurring.
Expected demand for C1 = (600 x 6 x 0.3) + (400 x 6 x 0.4) + (300 x 6 x 0.3) + (200 x 10 x 0.3) + (400 x 10 x 0.4) + (500 x 10 x 0.3) = 5400
Expected demand for C2 = (600 x 10 x 0.3) + (400 x 10 x 0.4) + (300 x 10 x 0.3) + (200 x 4 x 0.3) + (400 x 4 x 0.4) + (500 x 4 x 0.3) = 5600
Therefore, Handy should produce 5400 units of C1 and 5600 units of C2.
2. To determine whether Handy should retool its production system to develop C3, we need to compare the expected cost of production with and without the new component.
Without C3:
Expected cost = (5400 x $8) + (5600 x $12) = $43,200 + $67,200 = $110,400
With C3:
Expected cost = (5400 x $14) + (5600 x $14) = $75,600 + $78,400 = $154,000
Since the expected cost of production with C3 is higher than without C3, Handy should not retool its production system to develop the new component. The production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.
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please help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
3/8
Step-by-step explanation:
The graphic shows 2 lines and 2 rays that intersect at a point 0 to create 6 angles. What are TWO equations that can be used to find m∠3 if the measures of the other angles are known? Responses m∠1 + m∠2 + m∠3 = 180° m∠1 + m∠2 + m∠3 = 180° m∠2 + m∠3 + m∠4 = 180° m∠2 + m∠3 + m∠4 = 180° m∠3 + m∠4 + m∠5 = 180° m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 + m∠3 + m∠4 = 180° m∠1 + m∠2 + m∠3 + m∠4 = 180° m∠3 + m∠4 + m∠5 + m∠6 = 180°
Accοrding tο the angle sum prοperty οf a triangle, m∠1 + m∠2 + m∠3 = 180° and m∠3 + m∠4 + m∠5 = 180° these twο equatiοns can be used tο find m∠3.
What is the angle sum prοperty οf a triangle?The angle sum prοperty οf a triangle is a fundamental geοmetric prοperty that states that the sum οf the interiοr angles οf a triangle is always equal tο 180°. In οther wοrds, fοr any triangle, the sum οf the measures οf its three interiοr angles is always 180°.
This prοperty hοlds true fοr all triangles, regardless οf their size οr shape. It is an impοrtant cοncept in geοmetry and is used in variοus prοοfs and calculatiοns invοlving triangles.
One cοmmοn applicatiοn οf the angle sum prοperty οf a triangle is tο find the measure οf an unknοwn angle in a triangle if the measures οf the οther twο angles are knοwn. This can be dοne by subtracting the sum οf the knοwn angles frοm 180°.
The twο equatiοns that can be used tο find the measure οf angle 3 (m∠3) if the measures οf the οther angles are knοwn are:
m∠1 + m∠2 + m∠3 = 180°
This equatiοn can be used if the measures οf angles 1 and 2 are knοwn. We can find the measure οf angle 3 by subtracting the sum οf angles 1 and 2 frοm 180°.
m∠3 + m∠4 + m∠5 = 180°
This equatiοn can be used if the measures οf angles 4 and 5 are knοwn. We can find the measure οf angle 3 by subtracting the sum οf angles 4 and 5 frοm 180°.
Thus, m∠1 + m∠2 + m∠3 = 180° and m∠3 + m∠4 + m∠5 = 180° these twο equatiοns can be used tο find m∠3.
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6 A farmer has 2 400 sheep. He loses 32 and a half % due to the drought. After that he loses 15% due to sickness. How many sheep does he have now?
Answer: The farmer has 1377 sheeps.
Step-by-step explanation:
Farmer loses sheeps due to drought = 32½% of 2400
32½% of 2400
= 65 × 2400 × 1
2100
After cutting it will be,
65×12
=780
Number of sheeps that are left with him = 2400 - 780
=1620
After that,
The farmer loses due to sickness = 15% of 1620
15% of 1620
= 15 × 1620
100
After cutting it will be,
3 × 81
= 243
Total amount of sheeps that the farmer loses = 780 + 243
= 1023
Now the number of sheeps he has is 2400-1023
= 1377
The price of a jumper is reduced by 17% in a
sale. The sale price is £62.25.
What was the original price of the jumper?
Give your answer in pounds (£).
SALE
17% off!
Original price = £
Sale price = £62.25
Answer: it is $51.67 in dollars
Step-by-step explanation:
Answer:
£75
Step-by-step explanation:
To find the original price of the jumper using a formula, we can use the following formula:
Sale Price = Original Price - (Discount Rate x Original Price)
Where Sale Price is the price of the jumper after the 17% discount, Discount Rate is the percentage discount applied, and Original Price is the price of the jumper before the discount.
We know that the Sale Price is £62.25, and the Discount Rate is 17%, so we can substitute these values into the formula:
£62.25 = Original Price - (0.17 x Original Price)
Simplifying this equation, we get:
£62.25 = Original Price - 0.17Original Price
£62.25 = 0.83Original Price
Dividing both sides by 0.83, we get:
Original Price = £75
Therefore, the original price of the jumper was £75