To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So 3/10 divided by 5/8 is equal to (3/10) * (8/5) which simplifies to 24/50 or 12/25 in its simplest form12. Therefore, 3/10 divided by 5/8 is equal to 0.48 when rounded to four decimal points
Hope this helps fellow friend!
The required answer is (3/10) ÷ (5/8) equals 12/25. in other words, the quotient fraction obtained is 12/25
To divide fractions, we can use the reciprocal (or multiplicative inverse) of the second fraction and then multiply the two fractions together. Let's solve the division problem (3/10) ÷ (5/8) step by step:
Step 1: Take the reciprocal of the second fraction. The reciprocal of 5/8 is 8/5.
Step 2: Multiply the first fraction by the reciprocal of the second fraction:
(3/10) * (8/5)
Step 3: Multiply the numerators together:
3 x 8 = 24
Step 4: Multiply the denominators together:
10 x 5 = 50
Step 5: Write the result as a fraction:
24/50
Step 6: Simplify the fraction, if possible:
Both the numerator and the denominator have a common factor of 2:
24 ÷ 2 = 12
50 ÷ 2 = 25
The simplified fraction is 12/25.
Therefore, (3/10) ÷ (5/8) equals 12/25.
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A theater has 31 rows of seats. The first row has 24 seats, the second row has 27 seats, the third row has 30 seats, and so on. How many seats are in the theater?
I neeeed help
Answer:
2,139 seats
Step-by-step explanation:
the seats increase by 3 every row so I'm going to make a chart to show you how much the seats increase to 31 rows then add all off them to find total.
1 : 24
2: 27
3 : 30
4 : 33
5 : 36
6 : 39
7 : 42
8 : 45
9 : 48
10 : 51
11 : 54
12 : 57
13 : 60
14 : 63
15 : 66
16 : 69
17 : 72
18 : 75
19 : 78
20 : 81
21 : 84
22 : 87
23 : 90
24 : 93
25 : 96
26 : 99
27 : 102
28 : 105
29 : 108
30 : 111
31: 114
You can see from the chart that the number of seats increases by 3 for each row, starting from 24 seats in the first row and ending with 114 seats in the 31st row. To find the total number of seats, you can add up all the numbers in the chart:
24 + 27 + 30 + 33 + ... + 111 + 114
This is an arithmetic series with a first term of 24, a common difference of 3, and 31 terms. You can use the formula for the sum of an arithmetic series to find the total:
Sum = n/2 * (a + l)
where n is the number of terms, a is the first term, and l is the last term.
n = 31, a = 24, and l = 114, so you can substitute these values into the formula and simplify:
Sum = 31/2 * (24 + 114)
Sum = 15.5 * 138
Sum = 2139
Therefore, the theater has a total of 2,139 seats, which agrees with the result obtained earlier.
Answer:
2139 seats
Step-by-step explanation:
24,27,30,.......
n = 31
This forms an arithmetic series. Sum of arithmetic series will give the number of seats in the theater.
a = first term = 24
d = difference = second term - first term
= 27 - 24
= 3
[tex]\sf \boxed{S_n=\dfrac{n}{2}[2a+(n-1)*d]}[/tex]
[tex]=\dfrac{31}{2}[2*24+30*3]\\\\=\dfrac{31}{2}[48+90]\\\\=\dfrac{31}{2}*138\\\\=31*69\\\\=2139[/tex]
Need help will give brainliest and 5 stars! (Check Picture)
Give the equation of a rational function which has all of the properties above.
Answer:
One possible rational function that satisfies the given properties is:
r(x) = (x-2)(x-6) / [(x-3)(x-5)]
Step-by-step explanation:
x-intercepts at (2,0) and (6,0)
The x-intercepts are the points where the function crosses the x-axis, i.e., where the function value is zero. Since we are given that the function has x-intercepts at (2,0) and (6,0), we know that the function can be factored as:
r(x) = A(x-2)(x-6)
where A is a constant that we need to determine.
A hole at x=1 and vertical asymptotes at x=5 and x=3
A hole in a rational function occurs when there are factors in the numerator and denominator that cancel out, leaving a "hole" in the graph. In this case, we are given that there is a hole at x=1, which means that there must be a common factor of (x-1) in both the numerator and denominator. So, we can write:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))
where B is another constant that we need to determine.
We are also given that there are vertical asymptotes at x=5 and x=3, which means that the denominator must have factors of (x-5) and (x-3) that do not cancel out with any factors in the numerator. So, we can write:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5)) = [A(x-2)(x-6)] / [(B(x-1))(x-3)(x-5)]
End behavior given by x → ∞ ,f(x) → 1 and x → -∞ ,f(x) → 1
The end behavior of a rational function is determined by the degree of the numerator and denominator. Since the numerator and denominator in this case have the same degree (3), we know that the end behavior is given by the ratio of the leading coefficients, which is A/B. We are told that the end behavior approaches 1 as x approaches infinity or negative infinity, so we can set A/B = 1 and solve for A in terms of B:
A/B = 1, so A = B
Putting it all together
We now have enough information to write the equation for the rational function with the given properties:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))
Using A = B, we get:
r(x) = A(x-2)(x-6) / [A(x-1)(x-3)(x-5)]
Canceling out the common factor of (x-1) in the numerator and denominator, we get:
r(x) = (x-2)(x-6) / [(x-3)(x-5)]
which is the equation for the desired rational function.
in a science experiment the intial temperature was 55 degrees faherheit
Answer:
Answer to your question ; f(t) = 55 = 4t
Use square roots to solve the equation x^2=-64
Answer:
x equals 8 due to 8^2 being 8x8=64
Step-by-step explanation:
A right rectangular prism has a base with an area of 25 1/2 square feet and a volume of 153 cubic feet. What is the height, in feet, of the right rectangular prism? Please help!!
Answer:
[tex]25.5h = 153[/tex]
[tex]h = 6[/tex]
The height is 6 feet, so A is correct.
Find the value of k.
k
H
140°
Not drawn accurately
40°
==============
Given a quadrilateral with four angles of:
k, two right angles, and 140°We know the sum of interior angles for quadrilateral, it is 360°. Let us set up an equation as follows:
k + 2*90° + 140° = 360°Solve it for k:
k + 180° + 140° = 360°k + 320° = 360°k = 360° - 320°k = 40°So the missing angle is 40°.
A walk alongside a railway track is represented on a map by an 86 mm straight line.
The walk is 17.2 km.
What is the scale of the map?
First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.
Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
What is the volume of a box that is 3 feet tall, 5 feet wide, and 6 feet long
Answer:
90 cubic feet
Step-by-step explanation:
3 feet × 5 feet × 6 feet = 90 cubic feet
Express answers in terms of pi.
1. The radius of a cylinder is 10; the height is 2. Find:
a. circumference of the base
b. area of the base
c. L.A.
d. T.A,
e. V
2. Repeat Excercise 1, using a cylinder in which r = 2 and h = 10.
a. b. c. d. e.
Answer:
1 b
2.c
ythis the best choice
The circumference and the areas and the volumes are calculated below
Calculating the circumference and the areasFor a cylinder with a radius of 10 and a height of 2:
a. The circumference of the base is 2πr = 2π(10) = 20π.b. The area of the base is πr² = π(10)² = 100π.c. The lateral area is 20π(2) = 40π.d. The total surface area is the sum of the lateral area and the areas of the two bases. 2πr² + 2πrh = 2π(10)² + 2π(10)(2) = 400π + 40π = 440π.The volume of the cylinder is given by the formula V = πr²h = π(10)²(2) = 200π.For a cylinder with a radius of 2 and a height of 10:
a. The circumference of the base is 2πr = 2π(2) = 4π.b. The area of the base is πr² = π(2)² = 4π.c. The lateral area is 4π(10) = 40π.d. The total surface area is 2πr² + 2πrh = 2π(2)² + 2π(2)(10) = 8π + 40π = 48π.e. The volume of the cylinder is given by the formula V = πr²h = π(2)²(10) = 40π.Read more about circumference at
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7. Fill in the bubbles to indicate whether
each expression is linear or not linear.
5x Linear or Nonlinear
6x+1 Linear or Nonlinear
10xy Linear or Nonlinear
17 Linear or Nonlinear
4x^2 Linear or Nonlinear
The type of the relation are
Linear: 5x, 6x + 1 and 16Nonlinear: 10xy and 4x^2Indicating whether each expression is linear or not linearA linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.
In the given expressions:
"5x" and "6x + 1" have only the variable "x" raised to the power of 1, making them linear."10xy" has the variables "x" and "y" both raised to the power of 1, making it nonlinear."17" is a constant term and has a degree of 0, making it linear."4x^2" has the variable "x" raised to the power of 2, making it nonlinear.Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".
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Construct the confidence interval for the population mean
A 90% confidence interval for µ is (8.92, 9.28).
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
The formula for a confidence interval for the population mean is:
CI = x ± z * (σ / sqrt(n))
where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the z-score associated with the desired confidence level, and CI is the confidence interval.
Given the values provided:
c = 0.90
x = 9.1
σ = 0.6
n = 45
First, we need to find the z-score associated with a 90% confidence level. We can use a standard normal distribution table or a calculator to find that z = 1.645.
Then, we can plug in the values and calculate the confidence interval:
CI = 9.1 ± 1.645 * (0.6 / sqrt(45))
= 9.1 ± 0.176
= (8.92, 9.28)
Therefore, a 90% confidence interval for µ is (8.92, 9.28).
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Work out sheet below please
Using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.
What is division?The division is one of the four basic arithmetic operations or the process by which two numbers are added together to produce a new number.
Multiplication, addition, and subtraction make up the remaining operations.
We may examine the quotient and the division's remainder using the division formula Dividend = (Divisor Quotient) + Remainder.
We can multiply our quotient by the divisor to check its accuracy if the remainder is 0.
If the product and dividend are equal, the quotient is correct.
So, the price per gram when pre-packed:
1.49/120 = £0.012
Now, the price per gram when the product is loose:
0.89/100 = £0.0089
Now, we know that per pound the loose sweets are better.
Therefore, using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.
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Please help me. Giving brainliest to whoever gets it right!!
The equation of the line is: y = 0.5x + 4 and the inequality is H > 74.25
The equation of the graphTo find the equation of a line that passes through two points, we need to use the slope-intercept form of a linear equation:
y = mx + b
The slope is calculated as
m = (y2 - y1) / (x2 - x1)
m = (11 - 4) / (14 - 0)
m = 7/14
m = 1/2
m = 0.5
Next, we have
y = mx + b
4 = 0.5(0) + b
b = 4
So the equation of the line is: y = 0.5x + 4
Jacy's music downloadPart A: The equation that could be used to find the value of s is:
12s + 5.04 = 15.48
To find the value of s, we need to isolate the variable on one side of the equation.
We can do this by subtracting 5.04 from both sides and then dividing both sides by 12:
12s + 5.04 - 5.04 = 15.48 - 5.04
12s = 10.44
s = 10.44/12
s = 0.87
Therefore, Jacy paid $0.87 to download each song.
Tara's inequalityTo represent the number of hours, h, that Tara plans to work this month as an inequality, we can use the fact that she plans to work more hours than last month.
Let H be the total number of hours that Tara works this month.
Then we can write:
H > 16.5 + 19 + 23 + 15.75
Simplifying the right-hand side, we get:
H > 74.25
Therefore, the inequality that represents the number of hours, h, Tara plans to work this month is: H > 74.25
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Your first job is to figure out the price of your candy selection. You have a goal to sell $250 per week of candy. You can buy a case of assorted candy snacks for $15.50 a case. Write an equation to show how many cases c you can buy.
The equation which shows how many cases c you can buy is $250 = $15.50 * c.
What is an equation?An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation represents a relationship between quantities, and it is often used to describe or model real-world situations or problems.
According to the given information:
Let's denote the number of cases of assorted candy snacks as "c". The price of one case of assorted candy snacks is $15.50. The goal is to sell $250 worth of candy per week.
The total cost of buying "c" cases of assorted candy snacks can be calculated by multiplying the price per case ($15.50) by the number of cases (c):
Total Cost = Price per case * Number of cases = $15.50 * c
The goal is to sell $250 worth of candy per week. So, we can set up an equation to represent this goal:
$250 = $15.50 * c
This equation shows the relationship between the number of cases of candy snacks (c) that you can buy and the total cost of buying those cases, which is equal to $250, your goal for weekly candy sales.
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In a certain trail mix, 65% of the total weight is made up of nuts. Of that 65%, 3/5 of the nuts are cashews. If the total weight of the trail mix is 200 grams, how many grams are cashews?
There are 78 grams of cashews in the trail mix.
What is weight?
Weight is the measure of the gravitational force exerted on an object due to its mass. It is commonly measured in units of mass, such as kilograms or pounds. Weight can vary depending on the gravitational pull of the planet or other celestial body on which the object is located. For example, an object that weighs 100 kilograms on Earth would weigh less on the Moon due to the Moon's lower gravitational force. It is important to distinguish between weight and mass, as they are not the same thing. Mass is a measure of the amount of matter in an object, whereas weight is a measure of the force exerted on an object by gravity.
If 65% of the total weight is made up of nuts, then the weight of nuts in the trail mix is 0.65 × 200g = 130g
Out of the 130g of nuts, 3/5 are cashews. So the weight of cashews in the trail mix is (3/5) × 130g = 78g
Therefore, there are 78 grams of cashews in the trail mix.
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Alex scored 7/20 of the points in a basketball game. How many of the team's 120 points did Alex score?
Answer:
Step-by-step explanation:
I think its 42 because 7/20ths of 120 is 42
7/20 x 120 =42
The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.8 years and a standard deviation of 15.1months. Complete parts (a) through (d).
The answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?
To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,
Z = (X - mean) / standard deviation
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.
(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?
We need to standardize the values of 16 and 18 using the mean and standard deviation provided.
Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.
(c) What is the age at which growth plates fuse for the top 5% of males?
We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).
Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.
Then, we can solve for X using the formula:
Z = (X - mean) / standard deviation
1.645 = (X - 18.8) / (15.1/12)
Simplifying the equation, we get:
X = 18.8 + (1.645)(15.1/12) = 20.24
Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.
(d) What percentage of males have growth plates that fuse before the age of 16?
We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).
Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.
Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.
hence, the answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
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Don has an album that holds 700 photos. Each page of the album holds 7 photos. If 24% of the album is empty, how many pages are filled with photos?
Answer: 76 pages
Step-by-step explanation:
700 photo spaces = 100%
-The total
168 photo spaces = 24%
-The number of empty spaces in the album.
- Find 24% of 700:
70(10%) x 2 = 140
7(1%) x 4 = 28
140 + 28 = 168
532 photo spaces = 76%
- The number of photos in the album
700 - 168 = 532
Finding the number of pages.
-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.
532 ÷ 7 = 76.
Michelle did an anyonymous survey and collected her friends' credit scores. The scores she found are listed in the table below. What is the
mean credit score in this group? (Round to the nearest whole point, if applicable.)
a. 698
b. 695
c. 676
d. 703
to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer
4.4.3 Quiz: Stretching and Compressing Functions
f(x) = x². What is g(x)?
10
g(x)
Y
5- f(x)
O B. g(x) =
(2,2)
Click here for long description
2
O A. g(x) = (x)²
O c. g(x) =
OD. g(x) = 2x²
2
5
x²
x²
X
The equation of the function g(x) is g(x) = 1/2x²
Calculating the function g(x)If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.
Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).
To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):
[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]
So, we have
a = 1/2
Recall that
g(x) = f(ax)
So, we have
g(x) = f(1/2x)
This means that
g(x) = 1/2x²
Hence. the function is g(x) = 1/2x²
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PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
$14,000 was invested at 5% and $49,500 was invested at 9%.
what is system of equations?
A system of equations is a collection of two or more equations that are to be solved simultaneously. In other words, it is a set of equations that must be satisfied by a common set of variables. These equations can be linear or nonlinear, and they can have one or more variables.
The goal of solving a system of equations is to find the values of the variables that satisfy all the equations in the system. This can be done by using various methods, such as substitution, elimination, or matrix methods. The number of equations in a system can be greater than or equal to the number of variables in the system.
Systems of equations are used in various fields such as engineering, physics, economics, and many more. They are also an essential part of algebra and mathematics education, as they provide a powerful tool for solving real-world problems that involve multiple variables and relationships.
Let's assume that x is the amount invested at 5% and y is the amount invested at 9%. We can write two equations based on the given information:
x + y = 63,500 (the total amount invested)
0.05x + 0.09y = 5155 (the total annual income)
We can use these equations to solve for x and y.
First, we can rearrange equation 1 to solve for one of the variables in terms of the other:
x = 63,500 - y
Then, we can substitute this expression for x into equation 2:
0.05(63,500 - y) + 0.09y = 5155
Simplifying this equation:
3175 - 0.05y + 0.09y = 5155
0.04y = 1980
y = 49,500
So we now know that $49,500 was invested at 9%. We can substitute this value into equation 1 to solve for x:
x + 49,500 = 63,500
x = 14,000
Therefore, $14,000 was invested at 5% and $49,500 was invested at 9%.
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You have a jar of marbles, each marble is numbered 1-35. 10 Marbles are Blue, 12 Marbles are Green, and 13 Marbles are Red. You draw a random marble.What is the probability that you pull out a marble that is Green or an even number.
The probability of drawing a marble that is green or even-numbered is 28/35
Calculating the probabilityThe total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.
We need to find the probability of drawing a marble that is green or an even number.
First, let's find the number of even-numbered marbles.
Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).
There are 12 green marbles, and 17 even-numbered marbles,
Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.
The probability of drawing a marble that is green or even-numbered is
28/35
So the probability of drawing a marble that is green or even-numbered is 28/35
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5. Apply Math Models A science teacher uses a fair spinner
simulate choosing 1 of 5 different field trips for her classes.
spinner has 5 equal sections, each representing a different
trip. The teacher spins the spinner 50 times and records the
results in the table below.
Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.
What is frequency?
Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).
The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.
The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.
The experimental and theoretical probabilities do not match exactly. For example, the experimental of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.
The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.
Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).
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Commplete Question:
A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:
Field Trip Number of times selected
A 8
B 16
C 9
D 12
E 5
Apply math models to analyze the data and answer the following questions:
What is the experimental probability of selecting each field trip?
What is the theoretical probability of selecting each field trip?
Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?
What is the relative frequency of selecting each field trip?
Based on the data, which field trip appears to be the most popular?
Find each value or measure.
x = _____
mJK=_____ degrees
mMJ=_____ degrees
mLMK=______ degrees
(30 points) will give brainiest for effort
The value or measure of following are :-
x = 17.18°
∠JK = 143.78°
∠MJ = 116.48°
∠LMK = 47.17°
What is an arc?A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.
Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:
∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°
∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°
We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:
∠MNJ = ∠LNK
The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:
½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK
2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ
11x - 9° = 2∠MNJ
∠MNL = ∠JNK
The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:
½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK
2.75x + 1.5° = 2∠JNK
1.375x + 0.75° = ∠JNK
Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:
2∠MNJ + 2∠JNK = 360°
Substituting the expressions we found for ∠MNJ and ∠JNK, we get:
22x - 18° = 360°
22x = 378°
x = 17.18° (rounded to two decimal places)
Now that we know x, we can find the values of the other angles of arc-
∠JNK = 1.375x + 0.75° = 24.43°
∠KNL = 8.5x - 20.5° = 119.35°
∠MNJ = (11x - 9°)/2 = 92.05°
∠LNK = ∠MNJ = 92.05°
∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°
∠JK = ∠JNK + ∠KNL = 143.78°
∠MJ = ∠MNJ + ∠JNK = 116.48°
∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°
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You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each
month to save or pay down your debts.
a. How many months will it take to pay off the credit card if you only put half of the available money
toward the credit card each month and make the payments at the beginning of the month?
b. How many months will it take to pay off the credit card if you put all of the available money toward the
credit card each month and make the payments at the beginning of the month?
Be sure to include in your response:
the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.
Define APR?APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.
a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:
PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)
where:
PV is the present value of the debt
PMT is the payment amount per period
r is the monthly interest rate
n is the number of periods
Substituting the values, we get:
754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV ×r / PMT)) / log(1 + r)
= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)
= 6.18
Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.
b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.
754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV × r / PMT)) / log(1 + r)
= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)
= 3.43
Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.
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A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
Rewrite 5x²+35x using distributive property
Answer:
5x (x + 7)
Step-by-step explanation:
5x² + 35x
First, we find the GCF! In this case, the GCF is 5x
Factor out 5x
5x (x + 7)
So, the answer is 5x (x + 7)
Suppose you want to make your own model of the geologic time scale. You decide to make a timeline with a scale of 1 centimeter equals 1 million years. Remember that 100 cm is equal to 1 meter, which is a little longer than 3 feet.
A timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.
What is the unit conversion?
Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement that is equivalent in value. The need for unit conversion arises because different units are used to measure the same physical quantity in different countries or regions, or in different fields of study.
Making a model of the geologic time scale with a scale of 1 centimeter equals 1 million years means that each centimeter on the timeline represents 1 million years of geologic time.
To create the model, we can start by determining the total length of the timeline we want to create.
Let's say we want to include the entire Phanerozoic Eon, which spans approximately 541 million years.
To represent this on our timeline, we would need a total length of 541 centimeters.
However, we need to keep in mind that 100 cm is equal to 1 meter, which is a little longer than 3 feet.
Therefore, a timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.
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Answer: The actual difference between the numbers is:
87.71 - 5.8 = 81.91
Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?
Step-by-step explanation:
To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.
Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.
The actual difference between the numbers is:
87.71 - 5.8 = 81.91
Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.
Answer:
Yasmine estimated the difference to be 82. The actual difference is 81.91.
Step-by-step explanation:
The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.
So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be
(88 - 6) = 82.
The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.
Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.