Answer:
statistics is defined as:
the branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.
Final answer:
Statistics is a mathematical discipline focused on data collection, analysis, interpretation, and presentation. It includes both the process of dealing with numerical data and the resulting numerical facts used to make decisions. The field consists of descriptive statistics and statistical inference, which help understand and compare data for informed decision-making.
Explanation:
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of numerical data. It encompasses the entire process from gathering the data to drawing conclusions based on the numerical information obtained. Statistics can also refer to the numerical facts themselves, which are derived from these processes. The field is divided into two key areas: descriptive statistics, which summarizes data from a sample using indexes such as mean or standard deviation, and statistical inference, which makes predictions about a population based on a sample of data.
Statistics are not confined to mere numbers; they represent a comparison and understanding of numerical data. These comparisons help us make informed decisions in various fields, from public policy to medicine. For example, statistics can tell us the percentage increase in a population over a decade, enabling policymakers to plan resources accordingly. Statistics is integral to our daily lives, even though many may not realize its pervasive influence.
Let R be the region in the first quadrant of the xy-plane bounded by the hyperbolas xyequals1, xyequals9, and the lines yequalsx, yequals4x. Use the transformation x equals StartFraction u Over v EndFraction , y equals uv with ugreater than0 and vgreater than0 to rewrite the integral below over an appropriate region G in the uv-plane. Then evaluate the uv-integral over G.
To rewrite the integral over an appropriate region G in the uv-plane, we need to use the given transformation x = u/v and y = uv. The region G is defined by certain constraints on u and v, which can be found by solving the inequalities derived from the boundaries of R in the xy-plane. Finally, we can set up and evaluate the double integral over G.
Explanation:To rewrite the integral over an appropriate region G in the uv-plane, we need to use the given transformation x = u/v and y = uv. Let's consider each boundary of R separately:
For the hyperbola xy = 1, substituting the given transformations, we get (u/v)(uv) = 1, which simplifies to u^2 = v.For the hyperbola xy = 9, substituting the given transformations, we get (u/v)(uv) = 9, which simplifies to u^2 = 9v.For the line y = x, substituting the given transformations, we get uv = u/v.For the line y = 4x, substituting the given transformations, we get uv = 4(u/v).Now, we need to find the region G in the uv-plane that corresponds to R in the xy-plane. The region G is defined by the following constraints: u^2 ≤ v, 9v ≥ u^2, uv ≤ u/v, and uv ≥ 4(u/v). Combining these constraints, we get u^4 ≤ v^2 ≤ 9u^3 and u^2 ≤ 4v. The boundaries of G can be found by solving these inequalities.
To evaluate the integral over G, we need to determine the limits of integration for u and v. Once we have the limits, we can set up the double integral of the function over G and evaluate it.
Write the expression 4^4(4^-7)(4) using a single
exponent.
4^-28
4^-4
4^-3
4^-2
Answer:
4^-2
Step-by-step explanation:
4^4(4^-7)(4) I solved this separately
256(0.00006103515625)(4) Multiply
0.015625(4) Multiply
0.0625
This decimal is equivalent to 4^-2
4^-2 = 0.0625
If this answer is correct, please make me Brainliest!
Final answer:
The expression [tex]4^4(4^-7)(4[/tex]) simplifies to [tex]4^-2[/tex] by adding the exponents of the same base, resulting in a single exponent expression.
Explanation:
To simplify the expression [tex]4^4(4^-7)(4)[/tex] using a single exponent, you'll need to apply the rules of exponents. When you have the same base being multiplied, you can add the exponents. Start by looking at the terms 4^4 and 4^-7. The rule says to add the exponents when multiplying: 4 + (-7) = -3. So those two terms combine to make 4^-3.
Next, we have the single 4, which can also be written as 4^1 since any number to the power of 1 is itself. Now add the exponents again: -3 + 1. This gives us[tex]4^-2[/tex], which is the expression simplified with a single exponent.
The correct answer to this problem is therefore [tex]4^-2.[/tex]
What is the result of adding these two equations -2x+7y=-5, -2x-4y=6
Answer:-4x+3y=1
Step-by-step explanation:
First put the equations above one another
-2x+7y=-5
-2x-4y= 6
Just add the corresponding number from the top from the one right below it
-2x plus -2x is 4x
7y plus -4y is 3y
-5 plus 6
Then bring down the equal sign
And you get
-4x+3y=1
The addition of the two equations -2x+7y=-5 and -2x-4y=6 is -4x +3y = 1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two equations are -2x+7y=-5 and -2x-4y=6. The equations can be added as below,
Write the two equations with the like terms adjacent to each other than perform the algebraic operation and get the final solution.
-2x+7y=-5
-2x-4y=6
________
-4x + 3y = 1
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The table shows transportation from five different bank accounts. Fill in the missing numbers
There is no answer, there is no table.
Can someone please answer the bottom question. I really need help. Be sure to explain because I have no idea what I’m doing
Answer:
See below.
Step-by-step explanation:
RSTV is a quadrilateral. We see that segments RV and RS are congruent. We also see that segments TV and TS are congruent. That makes quadrilateral RSTV a kite. A kite is a quadrilateral that has one set of congruent adjacent sides and a second set of congruent adjacent sides. One set of congruent adjacent sides may or may not be congruent to the second set of congruent adjacent sides. In this case they are not.
The diagonals of a kite are perpendicular which is shown in your figure with segment VS perpendicular to segment RT. The diagonals form 4 right triangles. The 4 right triangles are VRW, SRW, VTW, and STW.
Triangles VRW and SRW are congruent.
Triangles VTW and STW are congruent.
Let's work on the angles first.
Let's work on triangle VTW.
Angle VWT is a right angle.
m<VWT = 90
m<WVT = 42
m<VWT + m<VTW + m<WVT = 180
90 + 42 + m<WVT = 180
m<WVT + 132 = 180
m<WVT = 48
Triangle SWR is a right triangle.
m<RWS + m<RSW + m<SRW = 180
90 + m<RSW + 21 = 180
m<RSW + 111 = 180
m<RSW = 69
Triangles WVR and WSR are congruent with corresponding angles WVR and WSR.
m<WVR = m<WSR = 69
m<TVR = m<WVT + m<WVR
m<TVR = 48 + 69 = 117
m<TVR = 117
Now we deal with sides.
Let's look at triangle VWT.
Side VT is the hypotenuse.
m<VTW = 42 deg
VT = 15
For angle VTW, VW is the opposite leg, and VT is the hypotenuse.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
[tex] \sin \angle A = \dfrac{opp}{hyp} [/tex]
[tex] \sin \angle VTW = \dfrac{VW}{VT} [/tex]
[tex]\sin 42^\circ = \dfrac{VW}{15}[/tex]
[tex]VW = 15 \sin 42^\circ[/tex]
VW = 10
Since triangles RVW and RSW are congruent, corresponding sides VW and SW are congruent.
SW = VW = 10
Trianlge RSW is a right triangle with right angle RWS.
For angle WRS, SW is the opposite leg. RW is the adjacent leg.
[tex] \tan A = \dfrac{opp}{adj} [/tex]
[tex] \tan \angle WRS = \dfrac{SW}{RW} [/tex]
[tex] \tan 21^\circ = \dfrac{10}{RW} [/tex]
[tex] RW \tan 21^\circ = 10 [/tex]
[tex] RW = \dfrac{10}{\tan 21^\circ} [/tex]
RW = 26
We now know VW and RW. Using the Pythagorean theorem we can find RV.
(RW)^2 + (VW)^2 = (RV)^2
26^2 + 10^2 = (RV)^2
RV = 28
Perimeter:
Triangles RVT and RST are congruent, so we have:
RV = RS = 28
VT = ST = 15
perimeter = RS + RV + VT + ST
perimeter = 28 + 28 + 15 + 15
perimeter = 86
Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply
The domain is all real numbers,
The range is all real numbers greater than or equal to 1
The y-intercept is 3.
The graph of the function is 1 unit up and 2 units to the Daft from the graph of y = x2
The graph has two x-intercepts
Answer:
The domain is all real numbers
The y-intercept is 3.
Step-by-step explanation:
Let's analyze each statement separately. The function is
[tex]f(x)=(x+1)^2+2[/tex]
We have the following statements:
The domain is all real numbers, --> TRUE. The domain of a function is the set of values that the variable x can take. For this function, there are no restriction on the values that x can take, so the domain is all real numbers.
The range is all real numbers greater than or equal to 1 --> FALSE. The range of a function is the set of values that the variable y can take. For this function, we see that the factor [tex](x+1)^2[/tex] is always equal or greater than zero; this means that the minimum of the function is [tex]f(x)=2[/tex], so the range is all real numbers greater than or equal to 2.
The y-intercept is 3. --> TRUE. The y-intercept is the value of the function when x = 0. For this function, if we substitute x = 0, we find:
[tex]f(0)=(0+1)^2+2=1^2+2=3[/tex]
The graph of the function is 1 unit up and 2 units to the left from the graph of [tex]y=x^2[/tex] --> FALSE. The graph of a function is scaled n units up when [tex]g(x)=f(x)+n[/tex]; in this case, we see that the factor n in our fuction is n = 2, so the function is actually scaled 2 units up, not 1.
The graph has two x-intercepts --> FALSE. The x-intercept of a graph is the value of x when [tex]f(x)=0[/tex]. If we require [tex]f(x)=0[/tex] for our function, we get:
[tex]0=(x+1)^2+2\\\rightarrow (x+1)^2=-2[/tex]
However, this equation has no solutions: so, the graph has no x-intercepts.
The graph of the function [tex]f(x) = (x + 1)^2 + 2[/tex] has a domain of all real numbers, a range of all real numbers greater than or equal to 2, a y-intercept of 3, and is 1 unit left and 2 units upwards shifted from the base graph [tex]y = x^2[/tex]. It has one x-intercept, not two.
Explanation:The function in question is f(x) = (x + 1)2 + 2. To analyze its characteristics, we first need to look at its general shape, domain, and range. Since it is based on the parent function f(x) = x2, which is a parabola, the transformations will affect the position but not the overall shape or domain.
The domain is all real numbers because for any x-value, there is a corresponding y-value. This applies to all quadratic functions.The range is all real numbers greater than or equal to 2, not 1. The minimum point of the graph occurs when the squared term is zero, which in this case is at f(-1) = 2.The y-intercept is the value of the function when x=0. Substituting into the function gives f(0) = (0 + 1)2 + 2 = 3.The graph is a standard parabola that opens upward. It is shifted 1 unit to the left (not Daft) and 2 units upwards from the graph of y = x2.The graph has only one x-intercept (not two), which can be found by setting the function equal to zero and solving for x.
At a post office, the weight of the mail at 10.00 a.M was 80 pounds. Two hours later, the weight of the mail had increased by 30%. Find the weight of the mail at noon.
Answer: The weight of mail at noon is 104 pounds.
Step-by-step explanation:
Given that , At a post office, the weight of the mail at 10.00 A.M was 80 pounds.
Two hours later, the weight of the mail had increased by 30%.
Since , time after 2 hours of 10 A.M would be 12 P.M which is known as noon.
Mathematically , the weight of the mail at noon = (Weight at 10 AM) +30% of (Weight at 10 AM)
= 80 + 0.30(80) pounds
= 80 (1+0.30) pounds
= 80 (1.30) pounds
= 104 pounds
Hence, the weight of mail at noon is 104 pounds.
Consider this triangle with the given lengths. A triangle has side lengths 40, 9, 41. Apply the converse of the pythagorean theorem to determine if it’s a right triangle. Is the triangle a right triangle? No, 92+402=412. No, 9 squared + 40 squared not-equals 41 squared Yes, 92+402=412. Yes, 9 squared + 40 squared not-equals 41 squared
Answer:
it's C my doods
Step-by-step explanation:
Yes, 9²+40²=41²
What is Pythagoras theorem?Pythagoras theorem states that, a right-angled triangle, the square of the one side is equal to the sum of the squares of the other two sides.
Pythagorean Triples where any 2 side the sum of the squares adds up to be equal the other side.
A triangle has side lengths are 40, 9 and 41
∵ 41 is the longest side length and that makes it the hypotenuse
The square of the two other sides is 9²+40² = 1,681
Also, 41² = 1,681
As we can see, the sum of the squares equal the square of the hypotenuse
Since this triangle follows the theorem, we can conclude that the triangle is a right triangle
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Valerie has 127.00 in her wallet and earns 15.50 per hour . Which equation show this situation
Answer:
Step-by-step explanation:
Write the following expressions in standard form:
⅘ (¼ − 5)
Answer:
Step-by-step explanation:
[tex]\frac{4}{5}(\frac{1}{4}-5)=\frac{4}{5}*\frac{1}{4}-\frac{4}{5}*5\\\\=\frac{1}{5}-4\\\\=\frac{1}{5}-\frac{4*5}{1*5}\\\\=\frac{1}{5}-\frac{20}{5}\\\\=\frac{1-20}{5}\\\\=\frac{-19}{5}[/tex]
Which expressionis equivalent to 5x + 2 - x + 10?
Answer:
[tex]5x + 2 - x + 10 \\ 5x - x + 2 + 10 \\ 4x + 12 \\ = 4(x + 3)[/tex]
hope this helps you....
Select a composite number to break into factors. Continue
factoring until all factors are prime.
56
Answer:
The factors are 7 * 2 * 2 * 2
Step-by-step explanation:
Step 1: Find all of the factors
56
28 2
14 2
7 2
Answer: The factors are 7 * 2 * 2 * 2
Sam's math teacher offered after school tutoring 16 out of the 30 days
in November to help students review for the mid-term exam. Which
decimal is equivalent to the fraction of days that tutoring was offered
in November?
Answer: 1.875 days
Step-by-step explanation:
Hi, to answer this question we simple have to divide the total day of the month (30 days) by the number of days that she offers tutoring (16).
Mathematically speaking:
30 /16 =1.875 days
1.875 days is equivalent to the fraction of days that tutoring was offered in November
Feel free to ask for more if needed or if you did not understand something.
Answer:0.533
Step-by-step explanation:
Sam's mathematics teacher offered after school tutoring 16 days out of the 30 days that were in November in order to help students review for the mid-term exam.
To convert this to a decimal, we divide the number of days tutorial was offered in November by the number of days in November. This will be:
= 16/30
= 0.533
The decimal that is equivalent to the fraction is 0.533.
4. Seven times the difference of a number k and five is twenty-one
Answer:
k=8
Step-by-step explanation:
You can solve this by setting up an equation.
7*(k-5)=21
k-5=3
k=8
Hope this helps!
Identify the independent and dependent variable in your equation
Answer:
The independent variable is the variable that can be changed.
The dependent variable is wjat you measure in an experiment
If the radius is 1/2 what is the volume
Answer:
that is the answer to the question
Algebra 1 unit 7 Exam question- Will mark brainliest if answered quickly and correctly
Answer:
[tex]=50m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]
Step-by-step explanation:
[tex]\left(5m^{\frac{4}{3}}\cdot \:5n^{\frac{1}{4}}\right)\left(m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}\right)[/tex]
[tex]=m^{\frac{4}{3}}\cdot \:5^{1+1}n^{\frac{1}{4}}m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]
[tex]=m^{\frac{4}{3}}\cdot \:5^2n^{\frac{1}{4}}m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]
[tex]=5^2n^{\frac{1}{4}}m^{\frac{4}{3}+\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]
[tex]=5^2m^{\frac{4}{3}+\frac{1}{3}}\cdot \:2n^{\frac{1}{4}+\frac{1}{8}}[/tex]
[tex]=5^2\cdot \:2m^{\frac{5}{3}}n^{\frac{1}{4}+\frac{1}{8}}[/tex]
[tex]=5^2\cdot \:2m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]
[tex]=50m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]
4 divided by the sum of h and 7
Answer:
4/h+7
Step-by-step explanation:
4 is on top of H+7
Find the values of x and y using the given chord, secant, and tangent lengths.
Answer:
x = 15.65
y = 3.5
Step-by-step explanation:
Step 1
Find the equation for x and y
Equation for x is given as
x² = 7( 7+28) ..........Equation 1
14(14 + y) = x²........ Equation 2
Solving for Equation 1
x² = 7( 7+28)
x² = 7(35)
x² = 245
x = √245
x = 15.65
From Equation 1 , x² has been determined to be 245
Therefore we substitute 245 for y in Equation 2
14(14 + y) = x²........ Equation 2
14(14 + y) = 245
196 + 14y = 245
14y = 245 - 196
14y = 49
y = 49 ÷ 14
y = 3.5
The expression 60\cdot1.2^t60⋅1.2 t 60, dot, 1, point, 2, start superscript, t, end superscript models the number of nano-related patents granted in the US as a function of years since 199119911991. What does 606060 represent in this expression? Choose 1 answer:
Answer:
There were 60 nano-related patents granted in 1991
Step-by-step explanation:
Consider the effect of the transformation (x, y) → (x, 2y) on the parallelogram ABCD with vertices A(0, 0), B(1, 1), C(3, 1), and D(2, 0). Select True or False for each statement.
The transformation (x, y) → (x, 2y) doubles the y-coordinates of the parallelogram ABCD vertices, resulting in a new parallelogram with doubled height and consequently doubled area, demonstrating that the change in height is proportional to the original height.
Explanation:The question posed relates to the effect of a transformation on the coordinates of a parallelogram's vertices. Specifically, we look at the transformation (x, y) → (x, 2y), which stretches the y-coordinates of the vertices while keeping the x-coordinates unchanged. For the given parallelogram ABCD with vertices A(0, 0), B(1, 1), C(3, 1), and D(2, 0), we apply the transformation to each vertex:
Vertex A(0, 0) becomes A'(0, 0 × 2) = A'(0, 0)Vertex B(1, 1) becomes B'(1, 1 × 2) = B'(1, 2)Vertex C(3, 1) becomes C'(3, 1 × 2) = C'(3, 2)Vertex D(2, 0) becomes D'(2, 0 × 2) = D'(2, 0)The transformation doubles the height (y-coordinate) of the parallelogram, while the base (x-coordinate) remains the same. Consequently, the area of the parallelogram also doubles, confirming that the change in height is proportional to the original height. By applying the transformation to a simple geometric figure, students can visualize and understand the properties of transformations and their effects on the shapes.
find the length of side x in simplest form with a rational denominator
Given:
The figure contains a right triangle.
The two angles of the triangle are 45° each.
The length of one leg is 3 units.
The length of the hypotenuse is x units.
We need to determine the value of x.
Value of x:
The value of x can be determined using the formula,
[tex]cos \ \theta=\frac{adj}{hyp}[/tex]
where [tex]\theta=45^{\circ}[/tex], adj = 3 and hyp = x.
Substituting these values, we get;
[tex]cos \ 45^{\circ}=\frac{3}{x}[/tex]
Simplifying, we get;
[tex]x=\frac{3}{cos \ 45^{\circ}}[/tex]
[tex]x=\frac{3}{\frac{\sqrt{2}}{2}}[/tex]
[tex]x=3 \times \frac{2}{\sqrt{2}}[/tex]
[tex]x=\frac{6}{\sqrt{2}}[/tex]
Thus, the value of x is [tex]x=\frac{6}{\sqrt{2}}[/tex]
What is the answer to the image
Answer:1/4
Step-by-step explanation:there are four sides one is shaded so the answer is 1/4
The shaded area is equal to 1/4
You are considering purchasing deep-dish caramel apple pies from a local baker. You currently make a very popular deep-dish apple pie but it is labor-intensive and you want to weigh your options. Currently, it costs you $13.45 to make each pie. There is also a $0.21 labor cost per slice for your pie and each of your pies serves 8 slices. The local baker will charge you $75 for 4 pies. Each bakery-made pie serves 12 slices and will cost you $1.36 per pie in labor. Show a cost comparison for each option.
Step-by-step explanation:
your bakery1 pie in total: $13.66
1 slice: $1.70
local bakery1 pie in total: $20.11 (75+1.36×4)÷4
1 slice: $1.67
Corrine wrote temperatures in degrees Celsius and the equivalent temperatures in degrees Fahrenheit. Equivalent Temperatures Celsius –10 5 10 20 Fahrenheit 14 41 50 68 Which explains how Corrine could determine if the temperatures vary directly?
Answer:
Compare the equivalent temperatures as a ratio; if the ratios are equivalent, then the temperatures vary directly.
Step-by-step explanation:
Took the test - answer got deleted :/
Janice bought 3 new shirts. The shirts were each originally priced at $24, but she bought them each on sale for a $6 discount. Which equation can be used to find c the cost of the three shirts Janice bought ? A c=24-6 B c= (3x24) - (3x6) C c=(3x24-6
Answer:
the answer is b
Step-by-step explanation:
Nathaniel builds birds and birdhouses using Lego blocks. Let BBB represent the number of birds and HHH represent the number of birdhouses that Nathaniel can build with his Lego blocks. 43B+215H \leq 300043B+215H≤300043, B, plus, 215, H, is less than or equal to, 3000 Nathaniel wants to build 505050 birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks? Choose 1 answer: Choose 1 answer: (Choice A) A Nathaniel can build at most 111 birdhouse. (Choice B) B Nathaniel can build at most 222 birdhouses. (Choice C) C Nathaniel can build at most 333 birdhouses. (Choice D) D Nathaniel can build at most 444 birdhouses.
Answer:
(C) Nathaniel can build at most 3 birdhouses.
Step-by-step explanation:
Given that:
[tex]43B+215H \leq 3000[/tex]
where:
B represents the number of birdsH represents the number of BirdhousesNathaniel wants to build 50 birds(B) using lego Blocks, we want to determine how many birdhouses(H) he can build with the remaining Lego blocks.
If B=50
[tex]43(50)+215H \leq 3000\\2150+215H \leq 3000\\\text{Subtract 2150 from both sides}\\215H \leq 3000-2150\\215H \leq 850\\\text{Divide both sides by 215}\\H \leq 3.95[/tex]
Therefore, Nathaniel can build at most 3 Birdhouses.
Answer: 3
Step-by-step explanation:
We are given that the number of birds Nathaniel wants to build using Lego blocks is \blue{50}50start color #6495ed, 50, end color #6495ed. When we substitute \blue B = \blue {50}B=50start color #6495ed, B, end color #6495ed, equals, start color #6495ed, 50, end color #6495ed in the given inequality, we will obtain an inequality for HHH alone:
\begin{aligned}43B+215H &\leq 3000\\\\ 43(\blue {50})+215H &\leq 3000 \\\\ 215H &\leq 850\\\\ H&\leq 3 \dfrac{41}{43}\end{aligned}
43B+215H
43(50)+215H
215H
H
≤3000
≤3000
≤850
≤3
43
41
Hint #22 / 3
So HHH must be less than or equal to 3\dfrac{41}{43}3
43
41
3, start fraction, 41, divided by, 43, end fraction. However, we should remember that the number of birdhouses Nathaniel can build must be an integer.
Since 333 is the biggest integer less than or equal to 3\dfrac{41}{43}3
43
41
3, start fraction, 41, divided by, 43, end fraction, Nathaniel can build 333 birdhouses at most with the remaining Lego blocks.
Hint #33 / 3
Nathaniel can build at most 3 birdhouses.
A suburban high school has a population of 1376 students. The number of students who participate in sports is 649. The number of students who participate in music is 433. If the probability that a student participates in either sports or music is 974 /1376, what is the probability that a student participates in both sports and music
108 / 1376 is the probability that a student participates in both sports and music.
Step-by-step explanation:
It is given that,
A suburban high school has a population of 1376 students.
Let the event A be the no.of students participated in sports.Let the event B be the no.of students participated in music.The number of students who participate in sports is 649.
The number of students who participate in music is 433.
To find the probability of event A (sports) :
P(sports) = No.of students participated in sports / Total students.
⇒ 649 / 1376
∴ P(A) = 649 / 1376
To find the probability of event B (music) :
P(music) = No.of students participated in music / Total students.
⇒ 433 / 1376
∴ P(B) = 443 / 1376
From the question, we know that the probability that a student participates in either sports or music is 974 /1376.
∴ P(A∪B) = 974 / 1376
To find the probability that a student participates in both sports and music :
The formula used here is,
P(A∩B) = P(A) + P(B) - P(A∪B)
⇒ 649 / 1376 + 433 / 1376 - 974 /1376
⇒ 108 / 1376
∴ P(A∩B) = 108 / 1376
The probability that a student participates in both sports and music is 108/1376
How to determine the probability?The given parameters are:
Total = 1376
Sport = 649
Music = 433
P(Sport or Music) = 974/1376
The required probability is:
P(Sport and Music) = P(Sport) + P(Music) - P(Sport or Music)
This gives
P(Sport and Music) = 649/1376 + 433/1376 - 974/1376
Evaluate the expression
P(Sport and Music) = 108/1376
Hence, the probability that a student participates in both sports and music is 108/1376
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the width of a rectangle is 6 units less than the the length. The area of a rectangle is 7 units. What is the length of the rectangle.
Answer:
Length: 7 units
Width: 1 unit
Step-by-step explanation:
The length of rectangle is 7 units.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the length of rectangle be x.
Then, width of the rectangle = x - 6
Also, Area of rectangle = 7 units
So, length x width = 7
x(x- 6)= 7
x² - 6x = 7
x² -6x -7 =0
x² -7x + x - 7=0
x( x- 7) +1 (x- 7)= 0
(x+ 1)(x- 7)=0
x= -1 or 7.
Hence, the length of rectangle is 7 units.
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Find the tangent of ∠R.
Answer:
15/8
Step-by-step explanation:
The tangent of an angle is the opposite side over the adjacent side. In this case, the opposite side length is the square root of 17^2-8^2=15. This means that the tangent of angle R is 15/8. Hope this helps!