The probability of selecting at random, without replacement, two blue marbles is 5/12.
What is Probability ?
Probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty and provide a basis for making informed decisions in various fields such as science, engineering, economics, and finance.
To solve the problem, we first need to find the total number of marbles in the urn. Since there are 3 red marbles and 6 blue marbles, there are a total of 9 marbles.
The probability of selecting a blue marble on the first draw is 6/9, since there are 6 blue marbles out of 9 total marbles.
Since we are selecting without replacement, the number of marbles left in the urn changes after each draw. After the first blue marble is selected, there are only 5 blue marbles left out of a total of 8 marbles. Therefore, the probability of selecting a second blue marble is 5/8.
To find the probability of selecting two blue marbles, we multiply the probability of the first draw (6/9) by the probability of the second draw (5/8):
(6/9) x (5/8) = 30/72 = 5/12
Therefore, the probability of selecting at random, without replacement, two blue marbles is 5/12.
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In a large population, 91% of the households have cable tv. A simple random sample of 196 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 87%?
a) 0.2786
b) 0.7214
c) 0.0126
d) 0.0252
e) 0.9748
Answer:
Step-by-step explanation:
B. Now, look at the list of verbs in part A. Select the correct subject pronoun for each verb.
11) ___ escribimos
A. ustedes
B. nosotros
in triangle ABC AC =10 in. ,BC =2.5 in., and m angle C =63°. what is the area of triangle ABC?
The area of triangle ABC is approximately 11.14 square inches.
What is the area of triangle ABC?To find the area of triangle ABC, we can use the formula:
Area = 1/2 * AC * BC * sin(C)
where the base is BC and the height is the perpendicular distance from A to BC.
To find the sine 63, we can use the sine of angle C:
sin C = sin(63)
Therefore, the area of triangle ABC is:
Area = 1/2 * 10 * 2.5 * sin(63)
When evaluated, we have
Area ≈ 11.14 square inches
So, the area of triangle ABC is approximately 11.14 square inches.
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Use the spinner below.
P(>7) =
The probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.
What is Probability ?
Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
If the spinner has 12 sections labeled with the numbers 1 through 12, then the probability of landing on a number greater than 7 would be:
There are 12 equally likely outcomes when the spinner is spun.
Out of these 12 outcomes, 4 are greater than 7: 8, 9, 10, and 11.
Therefore, the probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.
So P(>7) = 1÷3 or 0.333 or 33.3%.
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QUESTIONS
WHALE CAN FLY FASTER THAN A
CROW?
TRUE
FALSE
Answer: False
Step-by-step explanation: A whale can't fly
Answer:
False
Step-by-step explanation:
Because a whale cannot fly
Please help me solve A B and C
The shape of the cross - section can be described as being a rectangle.
The perimeter of the cross section can be found to be 28.98 inches.
The area of the cross - section is therefore 50.94 square inches.
How to find the area and perimeter of the cross - section ?Since the plane intersects the cube through four of its vertices and opposite edges, the shape of the cross-section is a rectangle.
To find the length of the diagonal of the cube's face, we can use the Pythagorean theorem for a right triangle with sides of 6 inches:
d^2 = 6^2 + 6^2
d^2 = 36 + 36
d^2 = 72
d = √72 = 8.49 inches
To find the perimeter of the cross-section, we use the formula for the perimeter of a rectangle:
P = 2(length + width) = 2(6 + 8.49) = 2(14.49) = 28.98 inches
To find the area of the cross-section, we use the formula for the area of a rectangle:
A = length × width = 6 × 8.49 = 50.94 square inches
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If you bet $5 in a Pick 4 lottery game, you either lose $5 or gain $9,995. (The winning prize is $10,000, but your $5 bet is not returned, so the net gain is $9,995.) The game is played by selecting
a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $5 on 1234, what is the expected value of your gain or loss? What is the probability of winning?
Answer:
the expected value of your gain or loss is a net loss of $0.5006.
The probability of winning is 1/10,000 = 0.0001.
Step-by-step explanation:
There are 10,000 possible four-digit numbers between 0000 and 9999. Only one of those numbers is the winning number. Therefore, the probability of winning the Pick 4 game is:
Probability of winning = 1/10,000 = 0.0001
If you bet $5 on 1234, there are two possible outcomes:
-You lose $5 with probability 0.9999
-You gain $9,995 with probability 0.0001
The expected value of your gain or loss is the sum of the products of each outcome and its probability:
Expected value = (-$5 x 0.9999) + ($9,995 x 0.0001)
Expected value = -$0.5006
Answer:
Step-by-step explanation:
A boat is heading towards a lighthouse, whose beacon-light is 136 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
6°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 19°. Find the distance from point A to point B.
Round vour answer to the nearest foot if necessary.
Answer:
Rounding to the nearest foot, the distance from point A to point B is 719 feet.
Given that sin(x)
A. 4
B.
11
NEF=
7
11
C. 11
7
D. 11
4
=
7
11'
find cos (90-x).
The value of cos (90 - x ) = sin (x) = 7/11.
option B.
What is the value of cos (90 - x)?In trigonometry identity, we know that sin(x) = opposite / hypotenuse. Therefore, we can draw a right triangle with an angle x and opposite side 7 and hypotenuse 11.
Using the Pythagorean theorem, we can find the adjacent side of the triangle:
adjacent² = hypotenuse² - opposite²
adjacent² = 11² - 7²
adjacent² = 120
adjacent = √(120)
adjacent = 2 √(30)
Now, we can use the definition of cosine to find cos(90 - x):
cos(90 - x) = sin(x)
Therefore, cos(90 - x) = 7/11.
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Find the area of this shape pls help
Answer:
Area = 63.2 cm²
Step-by-step explanation:
To find the area of the given shape, we can split it into two shapes: a trapezium and a rectangle (as shown in the attached diagram).
Doing so gives us a rectangle with a length of 10 cm and a breadth of 2.8 cm at the bottom of the shape. Therefore its area:
Area = length × breadth
= 10 cm × 2.8 cm
= 28 cm²
We also get a trapezium, whose area can be found using the following formula:
[tex]\boxed{\mathrm{Area = \frac{1}{2} \times (a + b) \times h}}[/tex]
where:
• a, b ⇒ length of the parallel sides of trapezium
• h ⇒ distance between the parallel sides a and b
From the diagram attached below, we can see that the two parallel sides have lengths of 10 cm and 6 cm. Moreover, the distance between the parallel sides is 7.2 - 2.8 = 4.4 cm.
Therefore, using the above formula and information, we can calculate the area of the trapezium:
Area = [tex]\frac{1}{2}[/tex] × (6 + 10) cm × 4.4 cm
= [tex]\frac{1}{2}[/tex] × 16 cm × 4.4 cm
= 35.2 cm²
Now that we have the areas of the rectangle and trapezium, we can find the area of the whole shape simply by adding those two areas:
Area of shape = 28 cm² + 35.2 cm²
= 63.2 cm²
Therefore, the area of the given shape is 63.2 cm².
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
Step-by-step explanation:
A circle with a diameter of 12 units and a center that lies on the y-axis would have an equation of the form:
(x - h)^2 + y^2 = r^2
where (h, 0) is the center of the circle, and r is the radius. We know that the diameter is 12 units, so the radius is half of that, which is 6 units.
Now we can check which of the given equations match this form:
x^2 + (y – 3)^2 = 36 : This is not in the required form, since the center is at (0, 3) and not on the y-axis.
x^2 + (y – 5)^2 = 6 : This is not in the required form, and also has a very small radius of sqrt(6), so it cannot have a diameter of 12 units.
(x – 4)² + y² = 36 : This is in the required form, with center at (4, 0), so it is a possible solution.
(x + 6)² + y² = 144 : This is in the required form, with center at (-6, 0), so it is also a possible solution.
x^2 + (y + 8)^2 = 36 : This is not in the required form, since the center is at (0, -8) and not on the y-axis.
Therefore, the two equations that represent circles with a diameter of 12 units and a center on the y-axis are:
(x – 4)² + y² = 36
(x + 6)² + y² = 144
an angle measure 14.6 degrees more than the measure of its supplementary angle. what is the measure of each angle?
The measure of the angles are 82. 7 degrees and 97. 3 degrees
What are supplementary angles?Supplementary angles are simply described as those angles whose sum is equal or equivalent to 180 degrees.
Note that pair of angles on a straight line are supplementary to each other.
From the information given, we have that;
Let the angle of one be x
Then,
Angle 1 = x
Angle 2 = 14. 6 + x
Equate the angles
x + 14. 6 + x = 180
collect the like terms, we get;
2x = 180 - 14. 6
subtract the values
2x = 165. 4
x = 82. 7 degrees
Then, the second angle = 82. 7 + 14. 6 = 97. 3 degrees
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How do you solve this?
Option B : The volume of the sphere with a diameter of 10 inches is approximately 523.6 cubic inches, and the closest answer choice is (B) 1150 cubic inches.
In the given diagram, we can see that the diameter of the sphere is 10 inches.
The volume of a sphere is given by the formula:
V = (4/3) * π * [tex]r^3[/tex]
where r is the radius of the sphere.
We know that the diameter of the sphere is 10 inches, so the radius is half of that, which is 5 inches.
Substituting the given values, we get:
V = (4/3) * π * [tex]5^3[/tex]
V = (4/3) * π * 125
V = 523.6 [tex]in^3[/tex] (rounded to one decimal place)
So, the closest answer choice to the volume of the sphere is (B) 1150 [tex]in^3[/tex].
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The perimeter of a rectangular garden is 372 m
If the width of the garden is 88 m, what is its length?
Answer:
Let L be the length of the rectangular garden. We know that the perimeter of a rectangle is given by: P = 2L + 2W where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter is 372 m and the width is 88 m. Substituting these values into the equation, we get: 372 = 2L + 2(88) Simplifying and solving for L, we get: 372 = 2L + 176 2L = 196 L = 98 Therefore, the length of the rectangular garden is 98 m.
Answer: L = 98 m
Step-by-step explanation:
The perimeter of a rectangle can be found with this formula:
P = 2W + 2L
➜ P is Perimeter
➜ W is Width
➜ L is Length
We will input known values and solve for the length. To solve, we will use multiplication and inverse operations.
372 m = 2(88 m) + 2L
372 m = 176 m + 2L
196 m = 2L
L = 98 m
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The length of a radius of a circle, measured in centimeters, is represented by the expression x + 1.5. The diameter of the circle is 9 2/5
cm.
What is the value of x?
Enter your answer as a decimal or mixed number in simplest form in the box.
X =
Answer:
The value of x of a circle with radius x + 1.5 and diameter of 9 2 / 5 cm is 7.9 cm
Radius of a circle
Radius of a circle is half of the diameter of a circle. The radius extend from the centre of the circle to the circumference.
Mathematically,
radius = 1 / 2 (diameter)
Therefore,
radius = (x + 1.5) cm
diameter = 9 2 / 5 cm = 47 / 5 cm
let's find x with the relationship above.
Therefore,
x + 1.5 = 47 / 5
subtract 1.5 from both sides
x + 1.5 - 1.5 = 9.4 - 1.5
x = 7.9 cm
Step-by-step explanation:
Which of the following equations are true for the number 9? Select all that apply. A. 4÷□=94 B. 19=□÷9 C. 7÷□=79 D. □÷19=81
In summary, equations A, C, and D are true for the number 9, while equation B is not.
How do we determine if a value satisfies an equation?In order to resolve this issue, we must substitute a number or expression that makes the equation true for the value 9 in the area denoted by the symbol "." Let's look at each equation individually:
A. 4 ÷ □ = 9/4
We can cross-multiply and simplify to find the answer to :
4(9/4) = □\s9 = □
Hence, for = 9, this equation is accurate.
B. 1/9 = □ ÷ 9
We may multiply both sides by 9 to find the answer to:
1 = □
This equation is valid for = 1, thus.
C. 7 ÷ □ = 7/9
We can cross-multiply and simplify to find the answer to :
7(9) = □\s63 = □
Hence, this equation is true for the value of = 63/7, which reduces to 9.
D. □ ÷ 1/9 = 81
We can multiply both sides by 1/9 to find the answer to:
□ = 81(1/9)\s□ = 9
So, this equation is true for □ = 9.
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a customer opens a checking account and a savings account at a bank. They will deposit a maximum of $600, some in the checking account and some in the savings account (They might not deposit all of it and instead keep some of it as cash.) If the costumer deposits $200 in their checking account what can you say about the amount they deposit in their savings account?
The customer can deposit up to $400 in their savings account as long as the total amount deposited between the two accounts does not exceed $600, since they deposited $200 in their checking account.
The problem tells us that the customer will deposit a maximum of $600 between their checking and savings accounts. This means that the total amount deposited in both accounts cannot be more than $600.
We also know that the customer deposited $200 in their checking account. Since they can deposit at most $600 in total, this means that they can deposit up to an additional $400 in their savings account. This is because $600 (maximum total deposit) - $200 (amount deposited in checking account) = $400 (maximum amount that can be deposited in savings account).
So, we can say that the amount the customer can deposit in their savings account is less than or equal to $400. In other words, they can deposit any amount from $0 to $400 in their savings account, as long as the total amount deposited between the two accounts does not exceed $600.
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Find the sample variance and standard deviation.
21, 12, 6, 9, 11
Choose the correct answer below. Fill in the answer box to complete your choice.
(Type an integer or a decimal. Round to one decimal place as needed.)
OA. 02:
=
O B.
11
Choose the correct answer below. Fill in the answer box to complete your choice.
(Round to one decimal place as needed.)
O A. S=
OB. o=
The sample variance and standard deviation of the data set {21, 12, 6, 9, 11} are approximately 31.2 and 5.6, respectively, rounded to one decimal place.
Standard deviation is another measure of how spread out the data points are from the sample mean. It is simply the square root of the variance. In other words, it measures the average amount of deviation of the data points from the sample mean.
To find the sample variance and standard deviation, we can use the following formulas:
The sample variance is 30.3 and the standard deviation is approximately 5.5.
To find the sample variance, we first find the sample mean:
(21 + 12 + 6 + 9 + 11) / 5 = 11.8
Then we use the formula for the sample variance:
where n is the sample size, x is the sample mean, xi is each data point, and is the total. When we enter the values, we obtain:
[tex]s^2[/tex] = [tex]((21 - 11.8)^2 + (12 - 11.8)^2 + (6 - 11.8)^2 + (9 - 11.8)^2 + (11 - 11.8)^2) / (5 - 1)[/tex]
[tex]s^2[/tex] ≈ 30.3
To find the standard deviation, we take the square root of the variance:
s ≈ √30.3 ≈ 5.5
Therefore, the answer is:
OA. 02:
OB. 11
OA. S = 5.5
OB. σ = 5.5
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Write the equation of the line in slope-intercept form.
Answer:
y = (- 3/4)x + 8---------------------
Slope-intercept form is:
y = mx + b, where, m - is the slope, b - is the y-interceptUse two points on the line:
(0, 8) and (4, 5)The first point represents the y-intercept, b = 8.
Find the slope, using the slope equation:
m = (y₂ - y₁)/(x₂ - x₁)m = (5 - 8)/(4 - 0) = -3/4Substitute the found values to get the equation of the line:
y = (- 3/4)x + 8A student is solving the equation 3(x−12)=9x . Which describes a first step the student could use to solve the equation correctly? Responses The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 36 = 9 x . The student can distribute 3 on the left side of the equation, resulting in 3x−12=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 12 = 9 x . The student can divide both sides of the equation by 3 , resulting in x−12=6x . The student can divide both sides of the equation by 3 , resulting in x − − 12 = 6 x . The student can divide both sides of the equation by 3 , resulting in x−4=3x .
Step-by-step explanation:
The correct first step the student could use to solve the equation 3(x-12)=9x is to distribute 3 on the left side of the equation, resulting in 3x - 36 = 9x.
This is because the distributive property states that a(b + c) = ab + ac. In this case, we have 3(x - 12), so we can distribute the 3 by multiplying it by both terms inside the parentheses: 3(x - 12) = 3x - 36.
Then, we can simplify the equation by subtracting 3x from both sides: -36 = 6x. Finally, we can solve for x by dividing both sides by 6: x = -6.
Therefore, the correct option is: "The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x."
The first step in solving the equation 3(x−12)=9x is to distribute the 3 on the left-hand side of the equation. You multiply each term inside the parentheses by 3, resulting in a simplified equation: 3x - 36 = 9x.
Explanation:If you're aiming to solve the equation 3(x−12)=9x, the initial step would be to distribute the 3 into the parentheses on the left side of the equation. This is achieved by multiplying each term inside the parenthesis by 3. Here's the process in detail:
Step 1: Start with the initial equation, which is 3(x−12)=9x.
Step 2: Remove the parentheses by distributing 3, resulting in 3x - 36 = 9x.
This is a viable initial step because now you have simplified equations on both sides, which helps you to get closer towards isolating the variable x.
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(Need help please and thank you!)
Answer:
Step-by-step explanation:
F
x=weeks
5=inital
y=total money saved
Your job is as an administrative assistant for factory operations for a company producing Whatchamacallits. Your boss hands you the information that the factory produces 4 Whatchas in the first hour, 8 total after hour 2, 12 total after 3 hours and 16 after 4 hours. You are tasked to produce an equation that models the number of Whatchas produced given the hours worked, and to find the predicted number of Whatchas produced if the factory can run for 50 hours uninterrupted.
Find an explicit formula for the nth term of the sequence 4,8,12,16... and use the equation to find the 50th term in the sequence. Show your reasoning for the equation.
Answer:
200
Step-by-step explanation:
[tex]a_n}[/tex] = a + (n-1)d
[tex]a_{50}[/tex] = 4 + (50 -1)4
[tex]a_{50}[/tex] = 4 + 49(4)
[tex]a_{50}[/tex] = 4 + 196
[tex]a_{50}[/tex] = 200
a = the initial value.
n = the term
d = the common difference
Helping in the name of Jesus.
One child can complete her homework twice as fast as her partner. When working together, both children can complete the homework in 45 minutes. If they work by themselves, how long will it take each child to complete the homework?
HINTS: 1) Let t = the time needed for the faster child to complete the homework.
2) Portion of the homework completed=rate ×time (P=rt)
3) When a child works alone the portion of the work completed is all the homework. That is (P=1)
1) The rate at which the faster child is working is ___________ Write an algebraic expression.
2) The rate at which the slower child is working is ___________Write an algebraic expression.
3) The part of the homework was done by the faster child in 45 minutes is ___________Write an algebraic expression.
4) The part of the homework was done by the slower child in 45 minutes is ___________ Write an algebraic expression.
5) The time taken by the faster child to do the homework by herself is _______________Give your answer in minutes.
6) The time taken by the slower child to do the homework by their self is _______________Give your answer in minutes.
1. The rate at which the faster child is working is 1/t.
2.The rate at which the slower child is working is 1/(2t)
3.The homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes.
4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4),
5.Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.
6. Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.
What is time?Time is a concept used to describe the progression of events from the past, through the present, and into the future. It is a measure of duration or an interval between two events, and it is often represented in units such as seconds, minutes, hours, days, weeks, months, and years.
1. Let t = the time needed for the faster child to complete the homework.
The faster child completes the homework twice as fast as the partner. Therefore, the rate at which the faster child is working is 1/t.
2.The rate at which the slower child is working is 1/(2t) since the slower child takes twice as long as the faster child to complete the homework.
3.The part of the homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the faster child completes 3/4 of the homework because she is working at a rate of 1/t, while the slower child is working at a rate of 1/(2t).
4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the slower child completes 3/4 of the homework because she is working at a rate of 1/(2t), while the faster child is working at a rate of 1/t.
5.Let's use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/t (since the faster child completes the homework in t time). Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.
6.Similarly, we can use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/(2t) (since the slower child takes twice as long as the faster child to complete the homework). Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.
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I really need help please help
Answer:
Question 7 is correct.
205,000 (For Question 8)
Step-by-step explanation:
First, we need to find the value of x.
We need to subtract 1995 from 2010 to find out how many years would have passed.
This gives us 15, which is our x value.
Next, we need to solve for y.
We multiply 2000 by 15 to get 30,000.
Then, add 175,000 to 30,000 to get 205,000. That leaves us with the equation y = 205,000.
The Y value is equivalent to the population in 2010.
In a circle, an angle measuring
radians intercepts an arc of length
. Find the radius of the circle in simplest form.
The formula to find the length of an arc of a circle is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle measured in radians and the radius of the circle is 2.
To find the length of the arc, we use the formula L = rθ. Substituting the given values, we get:
L = rθ
L = r( [tex]\frac{\pi}{2}[/tex]) or ( [tex]\frac{\pi}{2}[/tex])r
We are also given that the length of the arc is 1π, so we can write:
( [tex]\frac{\pi}{2}[/tex])r = 1π
Simplifying this equation, we get:
r = (1π) ÷ ( [tex]\frac{\pi}{2}[/tex])
r = 2
We can say that the length of an arc that is intercepted by an angle of [tex]\frac{\pi}{2}[/tex] radians is equal to half the circumference of the circle. Since the length of the arc is given as 1π, we can find the radius of the circle by dividing 1π by [tex]\frac{\pi}{2}[/tex], which gives us 2.
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The complete question is:
In a circle, an angle measuring [tex]\frac{\pi}{2}[/tex] radians intercepts an arc of length 1π. Find the radius of the circle in simplest form.
5. A map is drawn to a scale of 1: 20 000. (a) The perimeter of a lake is 2.5 km. Find, in cm, the perimeter of the lake on the map. (b) The area of the lake on the map is 12.5 cm². Find, in km², the actual area of the lake.
Step-by-step explanation:
2.5 km = 250000 cm
250000 cm /20000 = 12.5 cm on the map
12.5 cm ^2 x 20 0000 x 20 000 = 5 000 000 000 cm^2 = 500 000 m^2
15) Find mMP
12x + 3
P
M
45°
S
R
3x + 12
Answer:
Determine the lengths of sides and measures of angles in a right triangle by ... 9 = 12x. Cross Products Property. 9 = 3x. Subtract 9x from each side. 3 = x.
Accidents can happen to anyone at any
time, and individuals must make
financial choices to help protect then in
case of unforeseen events. What
elements were in the Perez family's
financial plan before the accident that
helped them prepare for their
unexpected event (Camila's accident)?
What could the family have done to
better prepare financially for an
unexpected event?
Answer:
Step-by-step explanation:
there is no passage
Complete this proof using SSS.
Given: ∆ABD and ∆DCB; AB ≅ DC and AD ≅ BC Prove: ∆ABD ≅ ∆DCB
STATEMENTS
1. ∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
2. BD ≅ BD
3. ___
REASONS
1. ___
2. ___ Prop. of ≅
3. SSS
Answer (Please mark as brainliest):
STATEMENTS
∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
BD ≅ BD
∆ABD ≅ ∆DCB
REASONS
Given
Reflexive Property of Congruence
By SSS, since AB ≅ DC, AD ≅ BC, and BD ≅ BD.
Therefore, ∆ABD ≅ ∆DCB by SSS.
$1000 is deposited in an account with a 8.5% interest rate, compounded continuously. What is the balance after 5 years?
By answering the presented question, we may conclude that the balance interest after 5 years is approximately $1,484.71.
what is interest ?In mathematics, interest is the amount of money gained or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest per year for three years, for a total of $15.
for calculating the balance
[tex]A = Pe^(rt)\\[/tex]
this formula,
[tex]A = 1000e^(0.085*5)\\A = 1000e^(0.425)\\[/tex]
A ≈ $1,484.71
the balance after 5 years is approximately $1,484.71.
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Answer:1529.59
Step-by-step explanation:
1000e^(.085)5
What are the ordered pair solutions
for this system of equations?
y = -x² + 2
y = x
First, set the equations equal to each other and
move everything to one side.
A:-x²+x+2=0
C:-x² + 2 = x
B:x²+x-2 = 0
D:x²+x+2=0
To find the ordered pair solutions, we need to solve the system of equations by setting them equal to each other:
-x² + x + 2 = x
Simplifying:
-x² + 2x + 2 = 0
We can solve for x using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(-1)(2))) / (2(-1))
x = (-2 ± sqrt(12)) / (-2)
x = 1 ± sqrt(3)
So the x-values of the ordered pair solutions are:
x = 1 + sqrt(3)
x = 1 - sqrt(3)
To find the corresponding y-values, we can substitute these x-values into either equation. Let's use y = x:
When x = 1 + sqrt(3):
y = 1 + sqrt(3)
When x = 1 - sqrt(3):
y = 1 - sqrt(3)