The value of the angle x using trigonometric ratio is: x = 53.13°
How to Solve Trigonometric ratios?Some of the trigonometric ratios in mathematics based on a right angle triangle are:
Sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Similarly:
cot x = 1/tan x
sec x = 1/cos x
cosec x = 1/sin x
We are given that:
sin x = 12/15
Thus:
x = sin⁻¹(12/15)
x = 53.13°
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1 point
Find the value of x:
10
15
Type your answer...
13
The value of x, considering the similar triangles, is given as follows:
x = 26.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The two triangles in this problem are similar, due to the bisection, hence the equivalent side lengths are given as follows:
10 and 15 - 10 = 5.x and 13.Then the proportional relationship is given as follows:
x/13 = 10/5.
Meaning that the value of x is given as follows:
x/13 = 2
x = 26.
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find the answer (please i need help asap)
Answer:
[tex]\frac{2xx^{\frac{1}{4} } }{y^{\frac{11}{3} } }[/tex]
Step-by-step explanation:
paint samples are often sold by the pint; a pint of paint will cover 50 square feet. if the dimensions of a room are 138 inches by 117 inches, how many pints of paint would you need to purchase to paint the ceiling of this room?
To paint the ceiling of a room that is 138 inches by 117 inches, you would need to purchase 3 pints of paint.
To find out how many pints of paint are needed to paint the room's ceiling, we must first convert its dimensions from inches to feet:138 inches is equivalent to 11.5 feet (138 ÷ 12 = 11.5)117 inches is equivalent to 9.75 feet (117 ÷ 12 = 9.75)To determine the total square footage of the room, multiply the room's length and width:11.5 feet × 9.75 feet = 112.125 square feet
To calculate the amount of paint needed, divide the total square footage by the number of square feet that one pint of paint will cover:112.125 square feet ÷ 50 square feet per pint = 2.24 pints
Therefore, you would need to purchase approximately 2.24 pints of paint to paint the ceiling of a room that is 138 inches by 117 inches. However, since paint is often sold in whole pints, you would need to purchase 3 pints of paint.
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please answer this questain with explanation
Answer:
It cannot be in the sequence because counting back in 0.4 will give you even numbers and not odd hence 1.5 cannnot be in the sequence.
PLEASE MARK IT THE BRAINLIEST!!!
On a farm in iowa lived grandpa bill in a big yellow house on the top of the hill. His 70th birthday was this very day. All of his family were on their way. His wife sue had baked a cake. They'd all eat it by the lake. After the party the grandkids would play with all of the dogs then roll in the hay. He'd look out the window and what would he see? EIGHTY-FOUR legs and heads THIRTY-THREE!! grandpa Bill's question for you is not very hard. How many dogs and grandchildren will be in the yard?
Answer:
187
Step-by-step explanation:
If 70th after he see 84 and legs 33 so the answer is 70+84+33=187
Complete the statements. Keith's strategy for finding the product is select and the product of 21. 5 and 5. 3 is select
When multiplying 31. 5 by 5. 3, Keith found the product using the following steps. (31 + 6. 5)(5 + 6. 3) = (35 * 5) + (5. 5 * 5. 3) = 155 + 5. 15
Keith found that the product of 31.5 and 5.3 is 160.15
Keith's strategy for finding the product is breaking the numbers into parts and then adding the results.
The product of 21.5 and 5.3 is
(20 + 1 + 0.5) × (5 + 0.3) = (20 × 5) + (20 × 0.3) + (1 × 5) + (1 × 0.3) + (0.5 × 5) + (0.5 × 0.3) = 100 + 6 + 5 + 0.3 + 2.5 + 0.15 = 114.95
When multiplying 31.5 by 5.3, Keith used a similar approach, breaking the numbers into parts and then adding the results. Specifically, he expanded the terms as (31 + 0.5)(5 + 0.3), added the partial products, and then rounded the result to two decimal places.
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Three numbers of the repeating decimal produced by the fraction 3/9
The repeating decimal produced by the fraction 3/9 is 0.33333..., with the digit 3 repeating infinitely.
What is fraction?A fraction is a way of expressing a part of a whole or a ratio between two quantities. It is represented as one quantity divided by another quantity, with a horizontal line called a fraction bar between them.
According to question:The fraction 3/9 can be simplified to 1/3 by dividing both the numerator and denominator by their greatest common factor, which is 3.
When we divide 1 by 3, we get a quotient of 0.3, and a remainder of 1. To continue the long division, we add a decimal point and a zero, and bring down the next digit, which is also a zero. We then divide 10 by 3, which gives us a quotient of 3, and a remainder of 1. We repeat the process, adding a decimal point and another zero, and bringing down another zero. We continue this process infinitely, getting a sequence of 3s that repeat without end.
Therefore, the repeating decimal produced by the fraction 3/9 is 0.33333..., with the digit 3 repeating infinitely.
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If ASTU-AXYZ,
UA is an
altitude of ASTU, ZB is an altitude
of AXYZ, UT = 8.5, UA = 6, and
ZB = 11.4, find ZY.
ASA
Type your answer....
16.15 is the value of ZY in triangle .
What is known as a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
The triangle's three angles add up to 180 degrees. There are three straight sides to this two-dimensional shape. An example of a 3-sided polygon is a triangle. Three triangle angles added together equal 180 degrees.
In ΔUST and ΔZXY
UT/ZY = UA/ZB
8.5/ZY = 6/11.4
6 * ZY = 11.4 * 8.5
ZY = 96.9/6
= 16.15
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What is the greatest common factor of −15x2y − 10xy3 5xy4? 5xy 5x2y4 5xy2 xy
the greatest common factor of the given expressions is -5xy.
To find the greatest common factor of the given expressions, we need to factor them first.
[tex]-15x^2y - 10xy^3 + 5xy^4 = -5xy(3x^2 + 2y^2 - y^3)\\5xy = 5xy(1)\\5x^2y^4 = 5xy^4(x^2)\\5xy^2 = 5xy^2(1)[/tex]
xy = xy(1)
Now, we can find the common factors by taking the minimum exponent of each variable in the factors:
The common factors are:5xy
Therefore, the greatest common factor of the given expressions is -5xy.
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Find the distance between 9.4− 6.2
Answer: 3.2
Step-by-step explanation: put the 9.4 over the 6.2 (not as a fraction) subtract and then you get 0.2 when you take the .4 - .2 and 9 - 6 is 3 then you would put the 0.2 with the 3 to get 3.2
a sample of 179 students using method 1 produces a testing average of 55.9 . a sample of 176 students using method 2 produces a testing average of 89.8 . assume the standard deviation is known to be 8.92 for method 1 and 16 for method 2. determine the 95% confidence
The 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is -36.54 to -31.26.
To calculate the 95% confidence interval for the true difference between the testing averages of the two instructional methods, we can use the following formula
Confidence interval = (X1 - X2) ± Z*(σ1^2/n1 + σ2^2/n2)^0.5
Where
X1 is the testing average for Method 1
X2 is the testing average for Method 2
Z is the critical value for a 95% confidence interval, which is 1.96
σ1 is the known standard deviation for Method 1
σ2 is the known standard deviation for Method 2
n1 is the sample size for Method 1
n2 is the sample size for Method 2
Substituting the values given in the problem, we get
Confidence interval = (55.9 - 89.8) ± 1.96*(8.92^2/179 + 16^2/176)^0.5
= -33.9 ± 2.64
Therefore, the 95% confidence interval using Method 1 and students using Method 2 is -36.54 to -31.26.
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The given question is incomplete, the complete question is:
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 179 students using Method 1 produces a testing average of 55.9. A sample of 176 students using Method 2 produces a testing average of 89.8. Assume the standard deviation is known to be 8.92 for Method 1 and 16 for Method 2. Determine the 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2
help!!
On a map, the distance between two cities is 5.6 inches. If the map uses a scale of 2 inches represents 20 miles, what is the actual distance between the two cities in miles?
56 miles
112 miles
50 miles
10.12 miles
Answer:
If 2inches= 20 miles then 1inches =10miles
5.6 inches=5.6*10
=56miles
Pls ad me brainliest.
Answer:
56 miles
Step-by-step explanation:
Use a proportion.
2 inches is to 20 miles as 5.6 inches is to x miles.
2:20 = 5.6:x
2/20 = 5.6/x
1/10 = 5.6/x
1 × x = 10 × 5.6
Cross multiply.
x = 56
Answer: 56 miles
1. Find the first term of the geometric progression:
b₁, b₂, 4, -8, ... .
a) 1; b) -1; c) 28; d) [tex]\frac{1}{2}[/tex]
2. A geometric progression is given: 1, [tex]\frac{3}{2}[/tex], ... .
Find the number of the member of this progression equal to [tex]\frac{729}{64}[/tex]
a) 5; b) 6; c) 7; d) there is no such number.
3. Find the sum of the first six terms of the geometric progression given by the formula bₙ=3ⁿ⁻²
a) [tex]\frac{728}{3}[/tex]; b) [tex]\frac{727}{6}[/tex]; c) [tex]\frac{727}{2}[/tex]; d) [tex]\frac{364}{3}[/tex]
4. The third term of the geometric progression is 2, and the sixth is 54.
Find the first term of the progression.
a) 1; b) 6; c) [tex]\frac{2}{3}[/tex]; d) [tex]\frac{2}{9}[/tex]
5. The sum of the first and third terms of the geometric progression is 10, and the sum of its second and fourth terms is -20.
What is the sum of the first six terms of the progression?
a) 126; b) -42; c) -44; d) -48
The first term of the geometric progression is 1.
What is geometric progression?
Each term in the sequence preceding it is multiplied by a fixed number called a common ratio to produce the next phrase in a series known as a geometric progression (GP). A geometric number sequence that follows a pattern is another name for this progression.
We are given a geometric progression as b₁, b₂, 4, -8, ....
From this, we get the common ratio as [tex]\frac{-8}{4}[/tex], which is -2.
Now, we know that
a₃ = 4 and r = -2
So,
⇒a₃ = a₁ [tex]r^{n-1}[/tex]
⇒4 = a₁ * [tex]-2^ {3-1}[/tex]
⇒4 = 4a₁
⇒a₁ = 1
Hence, the first term of the geometric progression is 1.
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Since, there are multiple questions, so the question answered above is:
Question: Find the first term of the geometric progression:
b₁, b₂, 4, -8, ...
a) 1; b) -1; c) 28; d) [tex]\frac{1}{2}[/tex]
A student is selected at random to work a problem on the
board.
What is the probability that the student selected is a female
junior?
0.15
0.25
0.20
0.50
The probability that the student selected to work on a problem on the board is C. 0. 20.
How to find the probability ?The total number of students in Junior grade can be found to be 11 by the graph. Out of this 11, the number of female students is:
= 11 - 6
= 5 students
The total number of students in the survey is:
= 7 sophomore + 11 junior + 7 senior
= 25 students
The probability that a female junior student is chosen is:
= 5 / 25 x 100 %
= 1 / 5 x 100 %
= 0. 20
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find the median of 14,19,16,13,16,14
Answer:
15
Step-by-step explanation:
Place the number in order from least to greatest. 13,14,14,16,16,19
then take one away from each side till there is one left. 14,14,16,16 14,16.
in this case there is two from this point on you find the average of the two number you have left so in this case, 14+16=30 30/2=15 The median is 15
Find the nth term of 23,17,11,5
Answer:
Find the nth term of 23,17,11,5:
23,17,11,5,-1,-7,-13...
Draw a number line, and create a scale for the number line. In order to plot the points
1) The line number and the plot of the numbers are shown in the graph that is attached.
2) The opposite of an integer is offset by the same amount from zero.
Explain how you found the opposite of each point.The three numerals on the number line and their corresponding opposites are shown in the pictures that are attached.
We must determine the number of places on the scale starting at zero to determine a number's opposite. The same amount of places is then counted starting from zero in the opposite direction.
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Complete question:
Draw a number line, and create a scale for the number line to plot the points −2, 4, and 6.
a. Graph each point and its opposite on the number line.
b. Explain how you found the opposite of each point.
An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 4 IQ points of the true mean. Assume that sigmaequals14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
81 must be the bare minimum acceptable sample size for a real-world computation.
Define Mean?The mean of a group of two or more integers is the straightforward mathematical average. The geometric mean approach, which uses the average of a set of products, and the arithmetic mean technique, which uses the sum of the series' values, are only two of the techniques available to calculate the mean for a given set of data.
Given: For the population of healthy people, the mean IQ score is μ =100 and the standard deviation is б =14.
Significance level : 1-0.99=.01
Critical value : zₐ/2=2.576
Margin of error : E=4
Standard deviation : б =14
The following equation determines the sample size:
n=( zₐ/2×б /E)²
n=(2.576×14/4)²
n=81.288≈81
Hence, the minimum reasonable sample size for a real world calculation must be 81.
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if f(x)=1-2x then what is 2f(x)
functions
The given function is f(x) = 1 - 2x.
To find 2f(x), we simply multiply the function f(x) by 2:
2f(x) = 2(1 - 2x)
Distributing the 2 across the expression, we get:
2f(x) = 2 - 4x
Therefore, 2f(x) = 2 - 4x.
What is one barrier that can affect the assessment phase of financial planning?
Clients may project their anxiety onto the financial counselor, causing them to make accusations and instigate conflicts
O Clients may have too much to assess at one given time, which can make developing a financial plan difficult and tedious.
O Clients may be anxious or embarrassed which can make them reluctant to share complete and accurate information
Clients may ask if the financial counselor could help another family member or friend free of charge while they are in the process of helping
the initial client
This can be done by actively listening to clients' concerns, being non-judgmental, and explaining the importance of accurate information in developing a comprehensive financial plan.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves methods for summarizing and describing data, making inferences and predictions about a population based on a sample, testing hypotheses, and identifying patterns and relationships within data. Statistics can be applied in a wide range of fields, including business, finance, social sciences, engineering, medicine, and more. It provides a framework for making informed decisions based on empirical evidence, and plays a crucial role in scientific research and data-driven decision making.
The barrier that can affect the assessment phase of financial planning is when clients may be anxious or embarrassed which can make them reluctant to share complete and accurate information. This can lead to incomplete or inaccurate financial plans, which can ultimately harm the client's financial well-being. It is important for financial counselors to establish trust and create a comfortable environment for clients to feel safe sharing their financial information. This can be done by actively listening to clients' concerns, being non-judgmental, and explaining the importance of accurate information in developing a comprehensive financial plan.
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The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α
= 0.01 is:
A) 2.33
B) 2.96
C) 2.05
D) 2.575
The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α = 0.01 is 2.575. The right option is (D).
What is a hypothesis test?In statistics, a hypothesis test is an examination of a particular hypothesis regarding a population parameter with the help of data from a sample. Hypothesis testing is a statistical method used to make decisions about a population based on a sample's data.
The following are the four stages of hypothesis testing:
1. Formulation of Hypothesis
2. Selection of a Significance Level
3. Calculation of Test Statistics
4. Acceptance or Rejection of the Null Hypothesis
The critical value for a two-tail hypothesis test is 2.575 when the sample size is greater than or equal to 30, the population standard deviation is known, and the significance level is α=0.01.
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you are a researcher studying the lifespan of a certain species of bacteria. a preliminary sample of 35 bacteria reveals a sample mean of hours with a standard deviation of hours. you would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.75 hours at a 95% level of confidence.what sample size should you gather to achieve a 0.75 hour margin of error? round your answer up to the nearest whole number.
A sample of 312 bacteria would be needed to estimate the mean lifespan of the species of bacteria within a margin of error of 0.75 hours with 95% confidence.
To determine the sample size required to estimate the mean lifespan of a certain species of bacteria within a margin of error of 0.75 hours with a 95% level of confidence, we can use the following formula:
n = [Z*(σ/ME)]^2
where:
n = sample size
Z = the z-score corresponding to the desired level of confidence, which is 1.96 for a 95% level of confidence
σ = the population standard deviation
ME = the desired margin of error
From the given information, we have:
sample mean = Xbar = hours
sample size = n = 35
sample standard deviation = s = hours
desired margin of error = ME = 0.75 hours
level of confidence = 95%, which corresponds to a z-score of 1.96
We do not know the population standard deviation, but we can use the sample standard deviation as an estimate since the sample size is greater than 30. Thus, we have:
σ ≈ s = hours
Substituting the values into the formula, we get:
n = [1.96*(6.81/0.75)]^2 ≈ 311.84
Rounding up to the nearest whole number, we get a sample size of 312 bacteria.
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Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion. HELP ASAP PLS (55 points)
Two quadratic equations can share a solution if one quadratic equation has a positive discriminant and another quadratic equation has a discriminant equal to 0
What is meant by quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means it involves an unknown variable (usually denoted as x) that is raised to the power of 2.
If one quadratic equation has a positive discriminant, it means that the quadratic equation has two distinct real roots. On the other hand, if another quadratic equation has a discriminant equal to 0, it means that the quadratic equation has only one real root that is repeated.
Therefore, it is possible for two quadratic equations to share a solution if one quadratic equation has a positive discriminant and another quadratic equation has a discriminant equal to 0, but only if the repeated root of the second quadratic equation is one of the two roots of the first quadratic equation.
To illustrate this, let's consider the following two quadratic equations:
Quadratic equation 1: [tex]$x^2 - 4x + 3 = 0$[/tex]
Quadratic equation 2: [tex]$x^2 - 2x + 1 = 0$[/tex]
The discriminant of quadratic equation 1 is [tex]$b^2-4ac = 4 - 4(1)(3) = -8$[/tex], which is negative. Therefore, quadratic equation 1 has two distinct real roots, which can be found using the quadratic formula:
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Substituting the values of a, b, and c from quadratic equation 1, we get:
[tex]$x=\frac{4\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex]
[tex]$x=2\pm\sqrt{1}$[/tex]
[tex]x=3$ or $x=1$[/tex]
Therefore, the roots of quadratic equation 1 are [tex]x=3$ and $x=1$[/tex].
The discriminant of quadratic equation 2 is [tex]$b^2-4ac = 2^2 - 4(1)(1) = 0$[/tex]. Therefore, quadratic equation 2 has one repeated real root, which is:
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Substituting the values of a, b, and c from quadratic equation 2, we get:
[tex]$x=\frac{2\pm\sqrt{2^2-4(1)(1)}}{2(1)}$[/tex]
[tex]$x=1$[/tex] (repeated root)
As we can see, the repeated root of quadratic equation 2 is equal to one of the roots of quadratic equation 1, which is [tex]$x=1$[/tex]. Therefore, these two quadratic equations share a solution.
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determine two functions, defined on the interval , whose wronskian is given by . are the functions that you found linearly independent on ? how do you know?
Two functions that satisfy the given condition and are linearly independent on (-∞,∞) are f1(x) = e^(x) and f2(x) = e^(x)
Let's start by recalling the definition of the Wronskian for two functions f1(x) and f2(x):
W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)
Given the Wronskian W(f1,f2)(x) = e^(2x), we can try to find functions f1(x) and f2(x) that satisfy this condition. One possible solution is:
f1(x) = e^(x)
f2(x) = e^(x + C)
where C is a constant. We can now calculate the Wronskian of f1(x) and f2(x):
W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)
= e^(x) [e^(x + C)]' - [e^(x)]' e^(x + C)
= e^(x) e^(x + C) - e^(x) e^(x + C)
= 0
This means that f1(x) and f2(x) are linearly dependent. However, we can modify our choice of f2(x) by setting C= -x, which gives:
f2(x) = e^(2x - x) = e^(x)
Now we can calculate the Wronskian again:
W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)
= e^(x) [e^(x)]' - [e^(x)]' e^(x)
= e^(2x)
Since the Wronskian is non-zero, this means that f1(x) and f2(x) are linearly independent on (-∞,∞).
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The given question is incomplete, the complete question is:
Determine two functions, defined on the interval (−∞,∞), whose Wronskian is given by W(f 1 ,f 2)=e ^2x. Are the functions that you found linearly independent on (−∞,∞)
James took a trip of 2400km ,travelling part by bus and part by plane. The average speed of the bus was 60km/h and the speed of the plane was 700km/h. If the total journey took 8hrs , how many kilometres did he travel by plane ?
Answer:
2100 km
Step-by-step explanation:
If the entire trip was 2400 km, then we can note that x km was flown by plane, and 2400 - x km by bus
The whole trip took 8 hours and we know that t = s/v:
[tex]t(by \: plane) = \frac{x}{700} [/tex]
[tex]t(by \: bus) = \frac{2400 - x}{60} [/tex]
Now we can form an equation:
[tex] \frac{x}{700} + \frac{2400 - x}{60} = 8 [/tex]
[tex] \frac{60x + 1680000 - 700x}{42000} = 8[/tex]
[tex] \frac{ - 640x + 1680000}{42000} = 8 [/tex]
Use the property of the proportion:
-640x + 1680000 = 336000
-640x = 336000 - 1680000
-640 x = -1344000 / : (-640)
x = 2100
Since we've noted that x is a path flew by the plane, we have the answer already
Please someone answer this for me 30 points
Answer:
Step-by-step explanation:
Use the model below to find 3/5 divided by 2/3
3/5 divided by 2/3 is equal to 9/10. We can also simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 1 in this case.
To divide fractions, we need to invert the second fraction and then multiply the two fractions together. This can be written as:
(a/b) ÷ (c/d) = (a/b) × (d/c)
In this case, a = 3, b = 5, c = 2, and d = 3. Substituting these values into the above equation, we get:
(3/5) ÷ (2/3) = (3/5) × (3/2)
To multiply fractions, we simply multiply their numerators together and their denominators together. So, we can rewrite the above equation as:
(3/5) × (3/2) = (3 × 3) / (5 × 2) = 9/10
Therefore, 3/5 divided by 2/3 is equal to 9/10. We can also simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 1 in this case. Therefore, the final answer is 9/10.
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The volume of a right cone is 33\piπ units^3
3
. If its circumference measures 6\piπ units, find its height.
Let's denote the radius of the cone as 'r' and the height as 'h'.
The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
And the formula for the circumference of the base of a cone is:
C = 2 * π * r
We know that the volume of the cone is 33π/3, so:
(1/3) * π * r^2 * h = 33π/3
Simplifying this equation, we get:
π * r^2 * h = 99π
r^2 * h = 99
We also know that the circumference of the base of the cone is 6π, so:
2 * π * r = 6π
Simplifying this equation, we get:
r = 3
Now we can substitute this value of 'r' into the equation we obtained earlier:
r^2 * h = 99
3^2 * h = 99
h = 11
Therefore, the height of the cone is 11 units.
what is the probability of being delt 4 hearts from a standard 52 card deck if only 4 cards are to be delt
The probability of being dealt 4 hearts from a standard 52 card deck if only 4 cards are to be dealt is 0.0026.
There are 52 cards in a standard deck, 13 of which are hearts.
We want to find the probability of getting dealt four hearts out of a four-card hand.
Since order doesn't matter, we will use combinations to calculate this probability.
P(A) = number of favorable outcomes / total number of possible outcomes.
There are 13 choose 4 ways to choose four hearts from the deck, and there are 52 choose 4 ways to choose any four cards from the deck.
So the probability of being dealt four hearts from a standard 52 card deck if only 4 cards are to be dealt is:
P(A) = (13 choose 4) / (52 choose 4)P(A)
= (715) / (270725)P(A)
= 0.002641056.
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Jackie purchases a monthly pass to see movies at the theater in order to buy each movie ticket at a discounted rate. The graph shows the costs for different numbers of movie tickets. Find the slope and y-intercept and their meaning.
Fill the blanks.
(A) The slope is $____________ and means that________________
(B) The y-intercept is $________ and means that________________
(A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
What is slope?
Slope is a measure of the steepness of a line. It describes the rate at which the line rises or falls as it moves horizontally, and it is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line. Mathematically, slope can be represented as:
Slope = (change in y-coordinates) / (change in x-coordinates)
To find the equation of the line passing through these points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1,30) and (3,40) to find the slope:
m = (40 - 30) / (3 - 1) = 10 / 2 = 5
Now we can use any of the given points and the slope to find the y-intercept. Let's use the point (1,30):
y = mx + b
30 = 5(1) + b
30 = 5 + b
b = 30 - 5
b = 25
So the equation of the line passing through the points (1,30), (3,40), (5,50), and (7,60) is:
y = 5x + 25
Therefore, (A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
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