The total number of probability options will be 8 options.
1. Red plain and Red striped.
2. Blue plain and Blue striped.
3. Yellow plain and Yellow striped.
4. Green plain and Green striped.
5. Red plain and Blue striped.
6. Blue plain and Yellow striped.
7. Yellow plain and Green striped.
8. Green plain and Red striped.
There are 8 socks in the basket, and you can choose 1 plain sock and 1 striped sock.
This means that there are 8 possible combinations of socks you could choose.
Count the number of socks in the basket. There are 8 total socks (4 plain and 4 striped).
The number of options: There are 8 possible combinations of socks you could choose, so you have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.
Therefore,
You have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.
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cars arrive randomly at a tollbooth at a rate of 25 cars per 11 minutes during rush hour. what is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
Therefore, the probability of exactly 5 cars arriving over a 5-minute interval during rush hour is approximately 0.017 or 1.7%.
To solve this problem, we first need to determine the rate of cars arriving per minute. We can do this by dividing 25 cars by 11 minutes, which gives us a rate of approximately 2.27 cars per minute.
Next, we need to use the Poisson distribution formula to calculate the probability of exactly 5 cars arriving over a 5-minute interval. The Poisson distribution is used to model the probability of a certain number of events occurring within a given time frame when those events occur randomly and independently of each other.
The formula for the Poisson distribution is:
[tex]P(X = k) = (e^-lambda * lambda^k) / k![/tex]
Where:
- P(X = k) is the probability of k events occurring within the specified time frame
- e is Euler's number (approximately equal to 2.718)
- λ is the average rate of events occurring per unit of time (in our case, 2.27 cars per minute)
- k is the number of events we want to calculate the probability for
- k! is the factorial of k (i.e., k! = k * (k-1) * (k-2) * ... * 2 * 1)
Plugging in the values we have, we get:
[tex]P(X = 5) = (e^-2.27 * 2.27^5) / 5![/tex]
P(X = 5) = (0.040 * 51.84) / 120
P(X = 5) = 0.017
Therefore, the probability of exactly 5 cars arriving over a 5-minute interval during rush hour is approximately 0.017 or 1.7%.
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The probability that exactly five cars will arrive over a 5-minute interval during rush hour is approximately 0.0126 or 1.26%.
To solve this problem, we will use the Poisson distribution formula.
Calculate the average arrival rate (λ) for a 5-minute interval.
Since 25 cars arrive in 11 minutes, we can find the rate per minute as follows:
(25 cars) / (11 minutes) ≈ 2.27 cars per minute
For a 5-minute interval, multiply the rate per minute by 5:
(2.27 cars per minute) × (5 minutes) ≈ 11.36 cars.
Use the Poisson distribution formula to find the probability.
The Poisson distribution formula is:
[tex]P(x) = (e^{-\lambda} * (\lambda^x)) / x![/tex]
In this problem, x = 5 (exactly five cars) and λ ≈ 11.36.
Calculate the probability.
P(5) = (e^(-11.36) × (11.36^5)) / 5!
P(5) ≈ 0.0126.
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# 15) A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of
113 feet above the water. Jeriel measures an angle of depression to the boat at point A to be
8°. At some later time, Jeriel takes another measurement and finds the angle of depression to
the boat (now at point B) to be 52°. Find the distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.
the distance between point A and point B is approximately 777.9 feet.
what is distance ?
Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.
In the given question,
Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.
From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:
tan(8) = 113/x
x = 113/tan(8)
x =802.5
From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:
tan(52) = 113/y
y = 113/tan(52)
y =72.4
Now we can use the Law of Cosines to find d:
d² = x² + y² - 2xy cos(130)
where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:
d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)
d =777.9
Therefore, the distance between point A and point B is approximately 777.9 feet.
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Does the image below prove ABC = DEF? Explain your answer.
Step-by-step explanation:
yes,because of SAS side angle side are equal.
A ball is dropped from a height of 32 m.
With each bounce, the ball reaches a
height that is half the height of
the previous bounce. After
which bounce will the ball
rebound to a maximum
height of 25 cm?
Calculate the lengths of the 2 unlabeled sides.
Leave your answer in exact form.
Answer:
BC=4
AC=[tex]4\sqrt{2}[/tex]
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.17. The probability that it will rain and the flight will be delayed is 0.02. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
The probability that the flight will leave on time when it is not raining is approximately 0.83.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).
According to the given information:
To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).
Let:
P(rain) = 0.07 (probability of rain)
P(delayed) = 0.17 (probability of delay)
P(rain and delayed) = 0.02 (probability of rain and delay)
We can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, we want to find P(on time | not raining), which can be expressed as:
P(on time | not raining) = P(on time and not raining) / P(not raining)
Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:
P(on time | not raining) = P(on time) / (1 - P(rain))
We can now substitute the given probabilities to calculate the required probability:
P(on time | not raining) = P(on time) / (1 - P(rain))
P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))
P(on time | not raining) = (1 - 0.17) / (1 - 0.07)
P(on time | not raining) = 0.83
So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).
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marvin company sells pens ($6) and flashlights ($10). if total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?
If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.
Let's start by assigning variables to represent the unknown quantities.
Let x be the number of flashlights sold.
Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.
The total sales can be expressed as the sum of the sales of each item:
10x (sales from flashlights) + 6(7x) (sales from pens) = 624
Simplifying this equation
10x + 42x = 624
52x = 624
x = 12
So, the number of flashlights sold is 12.
And the number of pens sold would be 7x = 7(12) = 84.
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x^2+3x=0 what is the gcf
Answer:
gcf is 'x'
Step-by-step explanation:
the common factor to the terms 'x²' and '3x' is 'x'
I need questions 26-31 for 5 STARS
Answer:
26) 1.32
27) 90
28) 0.00845
29) 2.56x10^-1
30) 9.5x10^-3
31) 7.8x10
the town mouse and the country mouse
1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.
2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.
What is The Town Mouse and The Country Mouse?"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.
3. The sequence of events in the story is as follows:
The country mouse invites the town mouse to visit him in the countryside.The town mouse accepts the invitation and visits the country mouse.The country mouse serves the town mouse simple food, which the town mouse finds unappetizing.The town mouse invites the country mouse to visit him in the town.The country mouse accepts the invitation and visits the town.The town mouse serves the country mouse luxurious food, but they both get scared and run away when the cat appears.The country mouse returns to his simple life, realizing that it's better to be safe and content than to live in luxury but in constant danger.4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.
5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.
6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.
7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.
8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.
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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.
can yall help me with this question this would rlly help me out!
Answer:
59.5[tex]cm^{2}[/tex]
Step-by-step explanation:
You have two shape: a square and a triangle
Square:
The area of a square is the sides squared
a = [tex]s^{2}[/tex] The side length is 7 (7 x 7 = 49)
a = [tex]7^{2}[/tex]
a = 49
Triangle:
a [tex]\frac{bh}{2}[/tex] The base times the height divided by 2
The base is 7 and the height is 3.
a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5
Add the two areas together: 49 + 10.5 = 59.5
Helping in the name of Jesus.
Kayla has three different sizes of plates. 7.G.4
Part A: The table shows the circumferences of the plates. Find the radius
and diameter for each plate. Use 3.14 for T.
43.96
28.26
Circumference (in.)
Radius (in.)
Diameter (in.)
21.98
Part B: How did you find the radius and the diameter of each plate?
So the radius and diameter for each plate are:
Plate 1: radius ≈ 7 in., diameter ≈ 14 in.
Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.
Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.
What is circumference?Circumference is the distance around the edge of a circle. It is the total length of the boundary of a circle. It is also referred to as the perimeter of a circle. The circumference of a circle can be calculated using the formula: C = 2πr where C is the circumference, r is the radius of the circle, and π is a mathematical constant with an approximate value of 3.14. The circumference of a circle is directly proportional to its radius; that is, as the radius of a circle increases, the circumference also increases.
Here,
Part A:
To find the radius and diameter of each plate, we can use the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:
r = C / 2π
Using the given circumferences and the value of π as 3.14, we can find the radius for each plate:
Plate 1:
C = 43.96 in.
r = 43.96 / (2 x 3.14) ≈ 7 in.
d = 2r ≈ 14 in.
Plate 2:
C = 28.26 in.
r = 28.26 / (2 x 3.14) ≈ 4.5 in.
d = 2r ≈ 9 in.
Plate 3:
C = 21.98 in.
r = 21.98 / (2 x 3.14) ≈ 3.5 in.
d = 2r ≈ 7 in.
So the radius and diameter for each plate are:
Plate 1: radius ≈ 7 in., diameter ≈ 14 in.
Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.
Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.
Part B:
To find the radius and diameter of each plate, we used the formula for the circumference of a circle and rearranged it to solve for the radius. We then used the formula for the diameter of a circle, which is simply twice the radius, to find the diameter. We also used the value of π as 3.14 in our calculations.
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Which table represents a function?
Answer:
Table 4 represents a function because each x-value corresponds to exactly one y-value.
Please help me with this homework
Answer:
14
Step-by-step explanation:
c = 2[tex]\pi r[/tex]
c = 2[tex]\pi[/tex]7
x = 14[tex]\pi[/tex]
Helping in the name of Jesus.
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
The correct answer is option b. Burger Quick, because it has a larger mean.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.
Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.
Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.
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If you have a 19 out of 30 what would be the percentage?
Answer:
63.3%
Step-by-step explanation:
30 divided by 100 and then multiplied by 19 gives u the answer
Suppose money grows according to the simple interest accumulation function a(t) = 1. 05t. How much money would you need to invest at time 3 in order to have $3,200 at time 8?
$2,560 needs to be invested at time 3 in order to have $3,200 at time 8.
Since the money grows according to the simple interest accumulation function a(t) = 1.05t, the amount of money A at time t, given an initial amount P, can be calculated using the formula:
A = P + Pr(t)
where r is the interest rate (in this case, 5% or 0.05) and t is the time period (measured in years).
To determine how much money needs to be invested at time 3 to have $3,200 at time 8, we can use the above formula and solve for P:
3200 = P + Pr(8-3)
3200 = P + 5P(0.05)
3200 = P + 0.25P
3200 = 1.25P
P = 3200 / 1.25
P = 2560
Therefore, an initial investment of $2,560 at time 3 would be needed to have $3,200 at time 8, assuming a simple interest accumulation function with an interest rate of 5%.
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The Gabrielsons ran a family relay race. The distance run by each family member (in kilometers) is listed below.
11
,
4
,
8
,
2
,
5
11,4,8,2,5
The Gabrielsons ran a total of 30 kilometers in the family relay race.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
It seems that there are five family members who participated in the relay race, and the distance run by each of them in kilometers is listed as follows:
11, 4, 8, 2, 5
To find the total distance run by the family, we simply add up the distances:
11 + 4 + 8 + 2 + 5 = 30
Therefore, the Gabrielsons ran a total of 30 kilometers in the family relay race.
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Type the correct answer in each box. Use numerals instead of words for numbers.
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is |
| =
.
The minimum possible diameter of a soccer ball is
, and the maximum possible diameter is
.
Reset
The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.
What is equations?
Equivalent equations are algebraic equations that are having identical roots or solutions.
The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.
This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.
It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.
Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.
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Happy birthday Rainbowww :)
Question: What is the pathagorean therom?
Answer: c=a2+b2
Step-by-step explanation:
Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4
We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,
To determine between which two integers 7/3 lies, we can use division and rounding.
Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:
7/3 = 2 + 1/3
Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.
This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.
Answer C, 2 and 3, is the correct answer.
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5 out of 7 questions. PLEASE help me.
Answer:
5 units is the distance
Step-by-step explanation:
7,2 is point c
7,7 is point d
7 - 7 = 0
7 - 2 = 5
5 is the answer
The area of LMN is 18 ft2, and the area of FGH is 32 ft². If LMN -FGH, what is the ratio of LM to FG?
A. 3:4
B. 3√2:4
C. √3:2
D. 4:3
Please select the best answer from the choices provided
The ratio of LM to FG is 3:4, so correct option is A.
Describe Triangles?A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.
The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.
Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.
Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.
If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.
Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).
So we have:
LMN / FGH = 18 / 32
(x²) = 18 / 32
x² = 9 / 16
x = (3 / 4)
Therefore, the ratio of LM to FG is 3:4, which is option A.
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What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?
The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.
The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.
First, we substitute w = 0.25 and j = 0.5 in the expression:
8(0.25) - 4(0.5)²
Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:
= 2 - 1
= 1
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The given question is incomplete, the complete question is:
What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number
The value of the expression as a single rational number is -8.
Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:
= -9.5 - (-8) - 6.5
= -9.5 + 8 - 6.5 (replacing -(-8) with its positive equivalent 8)
= (-9.5 - 6.5) + 8 (grouping like terms)
= -16 + 8 (simplifying)
= -8
Therefore, the value of the expression is -8, which is a single rational number.
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In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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Enrique has 1 gallon of milk and 1 pint of orange juice in his refrigerator how many cups of milk and orange juice does Enrique have in all
The total cups of milk orange juice Enrique has in refrigerator is equal to 18 cups.
Gallons of milk Enrique has in his refrigerator = 1 gallon
Pint of orange juice Enrique has in his refrigerator = 1 pint
Convert gallons to cups and pint to cups .
There are ,
16 cups = 1 gallon of milk
And 2 cups = 1 pint of orange juice
Enrique has 16 cups of milk
and 2 cups of orange juice.
Total cups of milk and orange juice in refrigerator
=16 cups of milk + 2 cups of orange juice
= 18 cups of milk and orange juice
Therefore, in total Enrique has 18 cups of liquid in his refrigerator.
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21. You are placing a circular drawing on a square piece of poster board. The poster board is 15 in wide. The part of the poster board not covered by the the function drawing will be painted blue. If the radius of the drawing is r, A = 225 - 3.14r^2 gives the area to be painted blue.
a. Graph the function.
b. What x-values make sense for the domain? Explain why.
c. What y-values make sense for the range? Explain why
(i need help)
a) The graph for the function [tex]A = 225 - 3.14r^2[/tex] is a downward sloping parabola.
b) The x-values make sense for the domain is a non-negative number.
c) The y-values make sense for the range is 0≤ A≤ 25.
What is graph?In mathematics, a graph is a collection of points, called vertices or nodes, and edges that connect pairs of vertices.
According to the given information:a. To graph the function [tex]A = 225 - 3.14r^2[/tex]. The graph should be a downward-sloping parabola, opening downwards.
b. The domain of the function represents the possible values of r. Since the radius of a circle cannot be negative, the x-values (or the values of r) that make sense for the domain are non-negative numbers, i.e., r >= 0.
c. The range of the function represents the possible values of A, the area to be painted blue. Since the poster board is 15 in wide, the maximum area that can be painted blue is 225 sq in (15 in x 15 in). Since the area of the circular drawing is given by [tex]3.14r^2[/tex], the area to be painted blue can be no greater than 225 sq in, which occurs when the circular drawing has a radius of 0. Therefore, the y-values (or the values of A) that make sense for the range are 0 <= A <= 225.
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Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:
Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out an orange tile? (5 points)
a
fraction 18 over 26
b
fraction 24 over 26
c
fraction 24 over 50
d
fraction 26 over 50
The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].
What is an Experimental Probability?Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).
Given:
[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]
Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.
We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:
The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50
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To the nearest tenth, the solution to the equation
4,300e^0.07x-123=5,000 is
The solution to the equation 4,300e^(0.07x) - 123 = 5,000 for x is 2.5.
Evaluating the equation for xWe can solve the equation 4,300e^(0.07x) - 123 = 5,000 for x by first adding 123 to both sides and then dividing both sides by 4,300 and taking the natural logarithm of both sides:
Using the above as a guide, we have the following:
4,300e^(0.07x) - 123 = 5,000
4,300e^(0.07x) = 5,123
e^(0.07x) = 5,123/4,300
e^(0.07x) = 1.1914
0.07x = ln(1.1914)
x = ln(1.1914)/0.07
Using a calculator, we get:
x ≈ 2.50
Rounding to the nearest tenth, the solution to the equation is approximately 2.5.
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