Answer:
Step-by-step explanation:
no
Answer: y= mb + xe
Step-by-step explanation:
A study showed that low-intensity shock therapy reduces pain levels in patients with lupus. During each session, electrodes were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity shock therapy also reduces pain in patients suffering from bulging disks in the thoracic region of the back. Two hundred female patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 100 male and 100 female patients instead of 200 female patients, would you change the study design? If so, how would you modify your design? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points) (10 points)
Answer:
part A: The appropriate design for the study includes;Treatment used; Chamomile oil treatment
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
Step-by-step explanation:
Solve the following inequality: 20t + 9, 200 ≤ 16,000
Answer in interval notation.
Answer:
[0, 799.95]
Step-by-step explanation:
First, we need to isolate the variable by subtracting 9 from both sides of the inequality:
20t + 9 - 9 ≤ 16,000 - 9
This gives us:
20t ≤ 16,000 - 9
Next, we can divide both sides of the inequality by 20 to isolate the variable:
20t / 20 ≤ (16,000 - 9) / 20
This simplifies to:
t ≤ 799.95
Finally, we need to express the solution in interval notation. Since the value of t cannot be negative, the solution is:
[0, 799.95]
Therefore, the solution to the inequality in interval notation is [0, 799.95].
Simplify:
10 x²y³ / 2xy
Answer:
Step-by-step explanation:
An electrician needs to create a rectangular wire loop for an induction generator. The width of the circuit needs to be 7 greater than ⅔ the length. If the cross sectional area of the loop must equal 172, what are the dimensions of the loop?
To solve this problem, we need to use the formula for the area of a rectangle, which is length times width. We can set up the formula as follows:
Area = length * width
Since we know that the width is 7 greater than ⅔ the length, we can represent the width as follows:
width = ⅔ * length + 7
We can substitute this expression for the width in the area formula to get the following:
Area = length * (⅔ * length + 7)
We are given that the area of the rectangle must be 172, so we can set up the following equation:
172 = length * (⅔ * length + 7)
To solve for the length of the rectangle, we can first distribute the length on the right-hand side of the equation, like this:
172 = length * ⅔ * length + 7 * length
We can then combine like terms on the right-hand side of the equation to get the following:
172 = ⅔ * length^2 + 7 * length
To solve for the length, we can use the quadratic formula, which is as follows:
length = (-b +/- sqrt(b^2 - 4ac)) / 2a
In this case, a = ⅔, b = 7, and c = -172. Plugging these values into the quadratic formula, we get the following:
length = (-7 +/- sqrt(49 - 4 * ⅔ * -172)) / 2 * ⅔
Simplifying this expression, we get the following:
length = (-7 +/- sqrt(49 + 576)) / ⅓
We can further simplify this expression by calculating the value of the square root, like this:
length = (-7 +/- sqrt(625)) / ⅓
Simplifying again, we get the following:
length = (-7 +/- 25) / ⅓
To find the final value of the length, we need to calculate the two possible values of the square root, which are 25 and -25. Plugging these values into the equation for the length, we get the following:
length = (-7 + 25) / ⅓ = 18 / ⅓ = 6
length = (-7 - 25) / ⅓ = -32 / ⅓ = -10
Since the length of a rectangle must be positive, we can discard the negative value and only consider the value of 6. This means that the length of the rectangle is 6, and the width is ⅔ * 6 + 7 = 11. Therefore, the dimensions of the rectangle are 6 by 11.
Simplify -x-(-4x-6)=6
Answer:
To simplify the given equation, we can start by using the rules of algebra to rearrange the terms and combine like terms on both sides of the equation. This gives us:
-x - (-4x - 6) = 6
We can then distribute the negative sign on the left side of the equation to get:
-x + 4x + 6 = 6
We can then combine like terms on the left side of the equation to get:
3x + 6 = 6
We can then subtract 6 from both sides of the equation to get:
3x = 0
We can then divide both sides of the equation by 3 to get the final result:
x = 0
Therefore, the simplified form of the given equation is x = 0.
Step-by-step explanation:
find the area of the figure
The area of the figure is 84.139 square ft
How to determine the area of the figure?From the question, we have the following parameters that can be used in our computation:
Shapes = Rectangle and Semicircle
For the rectangle, we have
Length = 5 ft and Width = 14 feet
For the circle, we have
Diameter = 14 ft - 4 ft - 4 ft
Evaluate
Diameter = 6 feet
Start by calculating the radius of the semicircle
So, we have the following representation
radius = Diameter/2
This gives
radius = 6/2
Evaluate
radius = 3
The area of the shape is then calculated as
Area = Length * WIdth + πr²/2
So, we have
Area = 5 * 14 + 3.142 * 3²/2
Evaluate
Area = 84.139
Hence, the area is 84.139 square ft
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Which of the following is showing the correct ratio for Cosine of C ?
6 / 10
10 / 8
6 / 8
8 / 10
The value of Cosine of C is 8/10. So the option d is correct.
In the given question, we have to find which of the following is showing the correct ratio for Cosine of C.
The given options are:
(a) 6/10
(b) 10/8
(c) 6/8
(d) 8/10
As we know that cosine is the ration of adjacent side and hypotenuse.
From the given diagram we can see that;
Adjacent Side = 8
Hypotenuse = 10
Opposite Side = 6
Now the;
CosC = Adjacent Side/Opposite Side
CosC = 8/10
Hence, the value of CosC is 8/10. So the option d is correct.
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Challenge The members of the city cultural center have decided to put on a play once a night for a week. Their
auditorium holds 500 people. By selling tickets, the members would like to raise $2,050 every night to cover all expenses.
Let d represent the number of adult tickets sold at $6.50. Let s represent the number of student tickets sold at $3.50 each.
If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise
exactly $2,050? At one performance there were three times as many student tickets sold as adult tickets. If there were
480 tickets sold at that performance, how much below the goal of $2,050 did ticket sales fall?
There are 100 students and 400 adults.
The 480 tickets sold had a $10 fall in ticket sales.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
Let d be the number of adults and y be the number of students.
⇒ d + s = 500 ..(1)
The number of adult tickets sold at $6.50 and the number of student tickets sold at $3.50 each.
⇒ 6.5d + 3.5s = 2050 ..(2)
From equation (1) d = 500 - s
Plug the value of d in equation (2)
6.5(500 - s) + 3.5s = 2050
3250 - 6.5s + 3.5s = 2050
3250 - 3s = 2050
3s = 3250 - 2050
3s = 1200
s = 400
Plug s = 400 in d = 500 - s
⇒ d = 500 - 400 = 100
Hence, there are 100 students and 400 adults.
Now, at one performance there were three times as many student tickets sold as adult tickets.
⇒ s = 3d
3d - s = 0 ..(3)
d + s = 480 ..(4)
⇒ 4d = 480
d = 120 Adults
Plug d = 120 in equation (4)
120 + s = 480
s = 480 - 120
s = 360 Students
The money earned from these 480 people is
120 * 6.5 + 360 * 3.5 = 780 + 1260 = $2040.
$2040 - $2040 = $10
Hence, the 480 tickets sold had a $10 fall in ticket sales.
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Which of the following is the correct if clause to determine whether y is in the range 10 through 50, inclusive? (Points : 1) A) ify>=10 and y <= 50: B) if10 > y and y < 50: C) if y >= 10 or y <= 50; D) if 10,y ory.50
We follow the inclusive rule, The answer to the question is (A) that is
if y>=10 and y <=50
What do you mean by intervals?In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.
What are the symbols and their meaning of the intervals?The intervals used are:
(a , b) , All the numbers between a & b without including them.
[a, b] , All the numbers between a & b including them.
y lies in [10,50].
And since it means that it includes 10 and 50 and all the numbers between them.
The final answer is (A) that is if y>1=10 and y <=50.
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θ is an acute angle. Find the value of θ in degrees.
sec(θ)=2
The value of θ is 60°.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin, cos , tan , cosec , sec and cot
Let the angle be θ , that is;
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Thus, tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data that the angle be represented as θ
Now , we are given that the angle θ is acute
Since Acute angles measure less than 90 degrees
So , the value of θ < 90°
when the value of sec θ = 2
cos θ = 1/sec θ
, cos θ = 1/2
The value of θ when cos θ is 1/2.
when the angle θ is 60°
Therefore ,
the value of θ is 60°
sec 60° = 2
Hence , The value of θ is 60°
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Please help me on this I’m really confused on this
Answer: c = 7
Step-by-step explanation:
180 = 86 + 31 + 9c
180 = 117 + 9c
63 = 9c
7 = c
Answer:
c = 7°
Step-by-step explanation:
You want the value of c given that angles in a triangle are marked 86°, 31°, and 9c.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°. Using given angle values, this means ...
86° +31° +9c = 180°
117° +9c = 180° . . . . collect terms
9c = 63° . . . . . . . subtract 117°
c = 7° . . . . . . . . divide by 9
The value of c is 7°.
What are the missing reasons in the two-column proof?
Given: ↔MO bisects ∠PMN and ↔OM bisects ∠PON
Prove: ΔPMO ≅ ΔNMO
Triangle ΔPMO and ΔNMO are congruent, therefore ΔPMO ≅ ΔNMO.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
MO bisects ∠PMN and OM bisects ∠PON.
1.
MO bisects ∠PMN,
Reason : It is given condition.
2.
∠PMO ≅ ∠NMO
Reason : The image is symmetrical, therefore ∠PMO ≅ ∠NMO.
3.
MO = MO
Reason : In triangle, PMO and NMO the side MO is common,
Therefore, MO = MO
4.
OM bisects ∠PON.
Reason : It is given condition.
5.
∠POM = ∠NOM
Reason : The image is symmetrical, therefore ∠POM = ∠NOM.
6.
ΔPMO ≅ ΔNMO
Reason : The figure is symmetric, and triangle ΔPMO and ΔNMO are congurent.
Therefore, ΔPMO ≅ ΔNMO.
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Activity 9: 1 Challenge You! 214 3/4/2/1 4/2/3/1 1 4 Hi there! I am the MATH WIZARD, I came here to challenge you. Simplify the following expressions. If you do these correctly, I will have you as my apprentice. Good luck!
1.) 6e⁰ + (11f)⁰ - 5/g⁰
2.) (3-⁴ + 5-³)-¹
3.) (3-⁴ + 5-³)-²
4.) 5(2a-¹b³)⁰
___________
10c-⁵ d⁶ e-⁸
5.) -5(m-⁴ n-⁵)-³
____________
7(p-⁶q⁸)-⁴
6.) ( 3x-⁴ y-⁵ z-²)-²
____________
The simplification of the expressions in the question using the rules of indices are as follows;
1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2
2. (3⁻⁴ + 5⁻³)⁻¹ = [tex]49\frac{31}{206}[/tex]
3. (3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]
4.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}[/tex] = [tex]\dfrac{c^5\cdot e^8}{2\cdot d^5}[/tex]
5.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}[/tex]
What is are indices in mathematics?An index or indices is the power by which a number or variable or expression raised.
1.) 6·e⁰ + (11·f)⁰ - 5/g⁰
6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1
6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2
Therefore;
6·e⁰ + (11·f)⁰ - 5/g⁰ = 2
2.) (3⁻⁴ + 5⁻³)⁻¹
(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))
1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))
1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209
10125/206 = 49 + 31/206
(3⁻⁴ + 5⁻³)⁻¹ = [tex]49 \frac{31}{206}[/tex]
3.) (3⁻⁴ + 5⁻³)⁻²
(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)
1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)
1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)
1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)
1/((206/10125)²) = (10125)²/(206)² = 102515625/42436
102515625/42436 = 2415 32685/42436
(3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]
4.) [tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}[/tex]
[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }[/tex]
[tex]\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]
[tex]\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]
[tex]\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]
[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]
5.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}[/tex]
[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }[/tex]
[tex]\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }[/tex]
[tex]\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }[/tex]
[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }[/tex]
[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]
[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]
6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²
(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = [tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)[/tex]
[tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2[/tex]
3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴
Therefore;
(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴
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A statistics class was given a pretest on probability (since many had previous experience in some other class). Then the class was given a six-page review handout to study for two days. At the next class they were given another test. Is there sufficient evidence that the scores improved?
Answer:
No, there is not sufficient evidence that the scores improved.
Step-by-step explanation:
Just because these people were given a six-page review handout doesn't mean that:
a. They actually did any of it
b. They learned anything
c. Since the kids have other experiences in class, the scores might not have necessarily improved that much, if at all
d. They had enough time to study
e. They cared enough in the first place
Generally, there is no rock-solid evidence at all pointing to the fact that their test scores improved. While you could make the assumption assuming every kid did what they were supposed to do, there isn't enough evidence to say that the scores improved.
Tim's book collection is 12% nonfiction books. He has 36 nonfiction books in his collection.
Part A
What is the total number of books in Tim's collection? Explain your thinking.
Part B
If Tim adds 20 more nonfiction books to his collection, what will be the new percentage of nonfiction books? Explain your thinking.
a) The total number of books in Tim's collection is; 300 books
b) If Tim adds 20 more nonfiction books to his collection, the new percentage of nonfiction books is; 17.5%
How to solve Algebraic Word Problems?We are given;
Number of Non fiction books Tim has = 36
Percentage of non-fiction books = 12%
a) Let the total number of books in his collection be x. Thus;
(12/100) * x = 36
x = 3600/12
x = 300 books
b) He adds 20 more non fiction books to his collection. Thus;
New total non fiction books = 36 + 20 = 56
New total number of all books = 300 + 20 = 320
Thus;
New percentage of non fiction books = 56/320 * 100%
New percentage of non fiction books = 17.5%
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NO LINKS!! Help me with these 2 column proofs 8aa
Here is the two column proof:
Statement Reason
∠1 ≅ ∠2 and ∠2 ≅ ∠3 Given∠1 ≅ ∠3 Transitive property of congruence Proved===================================================
Statement Reason
CS = AS and AS = ST GivenCS = ST Transitive property of congruence ProvedFind the inequality represented by the graph.
Answer:
[tex]\boxed{\bf{\underline{ y\le -\cfrac{3}{2}x-2}}}[/tex]
Step-by-step explanation:
From the given graph,
[tex]\bf y-intercept :\boxed{\tt -2}[/tex]
[tex]\bf Slope:\tt \cfrac{\Delta y}{\Delta x} =\cfrac{-3}{2} =\boxed{-\cfrac{3}{2} }[/tex]
Notice that graph is shaded below (not above), so y is less than the other side of the inequality. the graph elso has a solid line (not dashed), so we are dealing with an "or equal to" inequality.
Therefore, we should use the less than or equal to symbol.
[tex]\boxed{\bf{ y\le -\cfrac{3}{2}x-2}}[/tex]
_____________________
Hope this helps!
Have a great day!
on a line chart, you can change the of the vertical axis to provide more vertical space and a more dramatic slope to the lines.
we are allowed to change the vertical axis on a line chart.
why we need to change the vertical axis?suppose we have a large range of value needed to plot along the vertical and horizontal axis, but the current line chart cannot meet this demand. in such cases, we can customize the scales to provide more vertical and horizontal spaces.
what is dramatic slope?dramatic slopes are the steep slopes of a straight line calculated by vertical and horizontal coordinate of two points laying on it. By changing the vertical axis as well as the horizontal axis we can plot a graph of a straight line more properly and finally more dramatic slope is visible there.
hence, we can change the scale values on a line chart to meet the requirement of the plot.
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can someone who loves math do this and tell me the answers or do step by step please
Answer:
Step-by-step explanation:
3.) Slope: 15x
Y-int: 120
Y=15x+120
4.) For this one i'm not sure maybe..
5.) Slope: 5x
Y-int: 250
Y=5x+250
Conrad has 6 more marbles than Rory. If r represents the number of marbles that Rory has, which expression represents the number of marbles that Conrad has?
The expression representing the situation is (r+6).
What is expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given that, Conrad has 6 more marbles than Rory and r represents the number of marbles that Rory has,
We see, Conrad has more marble than Rory and Rory has r marbles,
Mathematical can be represented as,
c = r+6
Hence, The expression representing the situation is (r+6).
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Carter has 153 songs on a playlist. He's categorized them in the following manner: 20 country, 31 blues, 8 Latin American, 17 jazz, 26 rap, 14 folk, and 37 hip hop. If Carter begins listening to his playlist on shuffle, what is the probability that the first song played is a folk song? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
the probability that the first song played is a folk song is 9.1%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Carter has 153 songs on a playlist. He's categorized them in the following manner:
20 country, 31 blues, 8 Latin American, 17 jazz, 26 rap, 14 folk, and 37 hip hop.
The number of folk songs is 14
P(folk) = number of folk songs/ total
= 14/ 153
=0.091
Hence the probability that the first song played is a folk song is 9.1%.
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Triangle ABC has sides a>b>c. If one of the angles is 60 degrees, name the angle that can be equal to 90 degrees.
Answer:
angle b
Step-by-step explanation:
let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree
Last year the cost of Tom's train ticket was £42 This year the cost of Tom's train ticket increased to £50 Write down the increase in the cost of Tom's ticket as a fraction of last year's cost. (2 marks
Answer:
19.048%
Step-by-step explanation:
The formula for the increase in cost will be :
[(New cost - Original Cost)÷Original Cost] × 100
So let's substitute values in from the question :
[(50-42)÷42] × 100
[8÷42] × 100
0.19048 × 100
19.048%
Hope this helped and have a good day
Max draws 2 rectangles each with an area of 24 square centimeters what could be the side lengths of max rectangles
Max can draw Rectangles of side lengths which are the integral divisors of 24 that can be (2,12) or (3,8) or (4,6) etc.
How to find Side Lengths of a Rectangle if Area is Known?You can calculate a rectangle's area if you know its length and width. However, because these two amounts are distinct, you can't do a reverse computation to find both of them if you only know the area. You can find both of them in the specific case where they are equal, which gives the shape of a square, and you can compute one if you know the other. If you are aware of the rectangle's perimeter as well, you can utilize that knowledge to determine two potential length and width numbers.
Calculation:Area of a Rectangle = Length × Breadth
Area= 24 square centimeters
So, Side Lengths or Breadth of the Rectangle can be the divisors of 24.
Lengths and Breadths can be (2,12) or (3,8) or (4,6) etc.
Max can draw Rectangles of side lengths which are the integral divisors of 24 that can be (2,12) or (3,8) or (4,6) etc.
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0.064 divided by 0.06
Answer: 1.06
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Directions - Match the equations for parallel lines. (Note: you will not use all choices on the right side).
The equations for parallel lines:
y = -1/2 x - 2 ----- y = -1/2 x + 6
y = 1/2 x + 4 ----- y = 1/2 x - 4
y = 2x -4 ----- y =2/1x + 2
y = 5x + 2 ----- y = 5x - 1
y = 1/5 x + 10 ---- y = 1/5 x + 3
What is slope of line?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
If an equation in the form y = mx + c then m is the slope of the line.
Equation of line slope Slope parallel line
y = -1/2 x - 2 -1/2 -1/2
y = 1/2 x + 4 1/2 1/2
y = 2x -4 2 2
y = 5x + 2 5 5
y = 1/5 x + 10 1/5 1/5
Now identify the lines from the option whose slope are -1/2, 1/2, 2, 5, 1/5.
The slope of the line y = -1/2 x + 6 is -1/2.
The slope of the line y = 1/2 x - 4 is 1/2.
The slope of the line y = 2x -4 is 2.
The slope of the line y = 5x + 2 is 5.
The slope of the line y = 1/5 x + 10 is 1/5.
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compute the arc length of the curve:
x(t)=2t^(3/2)+2, y(t)=2t-3, 0<=t<=2
The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m
What is Integration ?In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
According to the given information
We can find the length of the arc by
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]
Find the derivative of x w.r.t to t
dx/dt = [tex]3t^{\frac{1}{2} }[/tex]
Find the derivative of y w.r.t to t
dy/dt = 2
Putting the values in above equation
We get
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]
L= [tex]\int\limits^2_0 {\sqrt{9t+4} } \, dt[/tex]
L = [tex]\frac{2}{27}(9t+4)^{\frac{3}{2} }[/tex]
limit approaches from 0 → 2
Hence
The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m
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1000000000000000000000000000000x100000000000000000000000000000
Answer:
100000000000000000000000000000000000000000000000000
Step-by-step explanation:
After a dilation with a scale factor of 2 about the origin,ΔABC maps onto ΔDEF Which of the following statements is true?
2. AB=DF
m ∠B=2. m ∠E
CA≅FD
BC/EF=CA/FD
Hello, I'm pretty sure this answer is D
Answer: D) BC/EF=CA/FD
Step-by-step explanation:
multiply: 0.61 x 2.9.
Answer:
The anwser is 1.769
Step-by-step explanation:
I did this on a calculator