In 35 differnt ways (Combination) the 4 players can be selected from a team of 7.
What is permutation and Combination ?Combinations are decisions that are made by choosing some or all of a group of things, regardless of how they are arranged.
Utilizing the combinations formula, it is simple to determine how many distinct groups of r items each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.
A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. In order to determine the number of configurations for seating 3 people in 5 seats, we thus multiply the alternatives at our disposal.
Permutations are several ways to arrange things in a certain sequence. It may alternatively be stated as the linear reordering of elements in an already ordered collection.
Here we have to select 4 people from a team of 7, so its a combination
So the number of ways are = [tex]\x^{7}C\x_{4} = \frac{7!}{4!\ 3!} = 35[/tex].
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15 In circle F with m/EFG = 78 and EF = 4 units, find the length of arc EG. Round to the nearest hundredth. F G E
Length of arc EG = 5.446 degrees and EG = 0.05446 degrees while written in hundredth.
What means arc length of a circle?Arc length is defined as the distance of two points along the boundary of a circle or a section of a curve. Arc length is not a straight line.
Arc length is calculated by the following formula.
arc length in radians
s = r Ф
where, r is radius of circle or curve
Ф is the central angle in radians
arc length is degrees
s = Ф×π/180 × r
r is the radius of circle
Ф is the central angle in degrees
π = 3.142
How to calculate the arc length in the given problems?given, central angle EFG = 78 degrees.
EF = 4 units
EF is the radius of the given circle
as per the rules of a circle FG is also a radius
FG = FE = 4 units
Now arc length EG = ∠EFG × π/180 × EF
Arc length = 78 × 3.142/180 × 4
=5.446 units
hence, arc length EG = 5.446 units or 5.446 degrees
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A and B are vertical angles. A=(x+15) B=(5x−17) the measure of b
What is the inverse of 12?
The inverse of 12 as calculated by the given data is found to be 1/12.
The inverse can be found by finding its reciprocal the number ,
inverse of 1 = 1 / 12
There are two types of inverse , additive inverse and multiplicative inverse .
The additive inverse can be found by finding the negative of the number. The multiplicative inverse, often known as the reciprocal, is another inverse of a number.
The multiplicative inverse, often known as the reciprocal, is another inverse of a number. The product of a reciprocal multiplied by the original number is always 1.
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Write the following using index notation:
2 x 2 x 2
b) 3x3
3 x 3
c)
6 x 6 x 6 x 8 x 8 x 8
d)
3 * 4 * 3 x 4 * 3
Index notations are as follows:
a) 2³
b) 3²
c) 6³ * 8³
d) 3³ * 4²
What are Exponents?A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.
Let's break down the given index notation one by one:
a) 2 is taken 3 times = 2³
Similarly,
b) 3²
c) 6³ * 8³
d) 3³ * 4²
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For the interval estimation of μ when σ is assumed known, the proper distribution to use is the_____. a. standard normal distribution b. t distribution with n degrees of freedom c. t distribution with n − 1 degrees of freedom d. t distribution with n − 2 degrees of freedom
When estimating a population mean (μ) with a known population standard deviation (σ), the proper distribution to use is the standard normal distribution. So, correct option is A.
This is because the sampling distribution of the sample mean follows a normal distribution when the population standard deviation is known. The central limit theorem guarantees that the sample mean will be normally distributed with mean μ and standard deviation σ/√n, where n is the sample size.
The formula for constructing a confidence interval for μ when σ is known is:
CI = x' ± zα/2 * (σ/√n)
where x' is the sample mean, zα/2 is the z-score corresponding to the desired confidence level (α), σ is the population standard deviation, and n is the sample size.
Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can use z-scores to find the appropriate values for zα/2. This is why the standard normal distribution is used for interval estimation when σ is known.
In summary, the standard normal distribution is used for interval estimation of μ when σ is known because the sampling distribution of the sample mean is normally distributed when the population standard deviation is known.
So, correct option is A.
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Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
By the Number line, the true statements are,
⇒ 1 < 3
⇒ - 3 < 1
What is Number line?Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
We have to given that;
In Number line, Plot the numbers - 3, 1 and 3.
Now, After plotting the numbers in Number line, we get;
⇒ - 3 < 1 < 3
Thus, The correct statements are,
⇒ 1 < 3 and - 3 < 1
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Solve this problem
Step by step
The measure of the missing length of the trapezoid is equal to 3√39 units.
How to determine the missing length of a trapezoid
Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:
D = d + 2 · c
Where c is the length of the horizontal leg of the right triangle in a trapezoid.
And the missing leg can be found by means of Pythagorean theorem:
x = √(r² - c²)
Where:
r - Hypotenusec - Shortest legx - Longest legFirst, determine the length of shortest leg: (D = 40, d = 26)
40 = 26 + 2 · c
14 = 2 · c
c = 7
Second, find the longest leg by Pythagorean theorem:
x = √(20² - 7²)
x = 3√39
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What is the degree of 2 polynomial?
A polynomial with a degree of two is referred to as a quadratic polynomial.
What is a quadratic polynomial?When the highest power of a variable term in a polynomial expression equals 2, the term is considered a quadratic polynomial. The exponent of a polynomial is all that is considered when determining its degree. It does not account for the power of a coefficient or constant term.
When a quadratic polynomial is equated to 0, it generates a quadratic equation or a quadratic function. The solutions to a quadratic equation are known as its roots or zeros.
A quadratic polynomial is a second-degree polynomial with the highest degree term having the value 2 as its coefficient. A quadratic equation is written in its general form as ax² + bx + c = 0.
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im not sure how to answer thank you
The value of x in the triangle WXY is 27°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠VWY + ∠XWY = 180° (sum of angle in straight line)
6x + ∠XWY = 180°
∠XWY = 180 - 6x
∠XYW + ∠ZYW = 180° (sum of angle in straight line)
∠XYW + 4x = 180°
∠XYW = 180 - 4x
∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)
(180 - 6x) + (180 - 4x) + 90 = 180
450 - 10x = 180
10x = 270
x = 27°
The value of x is 27°
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a) What type of triangle is triangle ABC? b) Give reasons for your answer. I need the correct answer for B with Reasons Not "ab and ac are the same" any word other than the same
Answer:
Isosceles triangle
Step-by-step explanation:
Thorough explanation: Through the angles in the triangle ABC.
First, observe that angle ACD = 50 degrees (given)
Since lines AB and DE are parallel to each other,
angle BAC = angle ACD = 50 degrees (by the property of alternate angles)
It is also given that angle ABC = 80 degrees.
Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.
Angle BAC + Angle ABC + Angle ACB = 180 degrees
50 + 80 + Angle ACB = 180
Angle ACB = 180 - 50 - 80
= 50 degrees
Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)
Item 4 Greg has a piece of rope 18 ft long. He wants to cut it into two pieces so that the longer piece is 2 ft less than 3 times the length of the shorter piece. How long will each piece of rope be
The length of the shortest piece is 5, and the longest piece is 13 feet by solving the equations.
The length of the shortest piece is 5, and the longest piece is 13 feet.
the solution is as follows,
Greg has a piece of rope that is 18 ft long.
He wants to cut it into two pieces so that the longer piece is 2 ft less than three times the length of the.
Let the length of the shorter piece be x.
And the length of the longer piece is 3x -2.
Greg has a piece of rope that is 18 ft long.
Then,
longest piece+ shorter piece = 18
x + 3x -2 = 18
4x - 2 =18
4x = 18+2
4x = 20
x= 20/4
x = 5.
Therefore,
The length of the shorter piece is x =5.
And the length of the longer piece = 3x -2 = 3(5)-2 = 15-2 = 13
Hence, the length of the shortest piece is 5, and the longest piece is 13 feet.
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The rectangular floor of a classroom is 30 feet in length and 24 in width. A scale drawing of the floor has a length of 15 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answer: 54 inches squared
Step-by-step explanation:
Since it is a scale drawing, when we scale one variable up or down, we have to scale the other value the same amount because they are proportional. For example, if we divide one value by 3, we have to divide the other value by 3 also.
In this case, the real length is 30 feet, and the scale drawing length is 15 in. We divided by 2, so we have to divide the width by the same amount. 24/2 = 12 inches, so the width would be 12 inches or 1 foot.
Finding the Probability of Simple Events
Answer:
th chicken
Step-by-step explanation:
Jessica and Josh are selling entertainment books to raise money for the art room after school one book sells for $18 Jessica receive the prize for selling the most books in the school Jessica sold 13 times more books than Josh together they sold 280 books how many did each of them sell
Based on the question above, Jessica sold 260 books and Josh sold 20 books.
What is the math equation about?Let x be the number of books Josh sold
We know that:
Jessica sold 13x books
Together they sold 280 books
So we can set up an equation:
x + 13x = 280
14x = 280
x = 20
Josh sold 20 books
Jessica sold 13 * 20 = 260 books
Therefore Jessica = 260 books sold and Josh = 20 books sold.
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Which expression is equivalent to 4 - 10 (9m – 7:)
0-3 - 90m
O 42 – 54m
O 74 - 90m
O-7 - 54m
The correct choice will be 74 - 90m
What is the perimeter of a regular pentagon inscribed in a circle with radius 1 meter
Answer:
Step-by-step explanation:
The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. The length of each side of a regular pentagon inscribed in a circle with radius 1 meter can be found using the formula: side length = 2 * radius * sin(180/number of sides).
For a regular pentagon, the number of sides is 5. Plugging this into the formula gives us:
side length = 2 * 1 * sin(180/5) = 2 * 1 * sin(36) = 2 * 0.587785 = 1.175570
So the perimeter of the regular pentagon is equal to 5 * 1.175570 = 5.877849 meters.
What do you mean by equivalents?
The term equivalent means equal or interchangeable in value, quantity, significance, etc.
In math term equivalent is used for the following concepts.
expressionfractionetc.Here we have to know that the term equivalent refers to two numbers, expressions, or quantities with the same value.
Here there are many ways to express an equivalent quantity and it can be denoted either by a bar or an equivalent symbol.
Here we want to know that the equivalent can also mean some common or logical equivalence between different values or quantities.
Therefore, based on these definition we have identified that the equivalence is similar but not the same as equality.
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Is horizontal asymptote y axis?
No, horizontal asymptote is not represented by y- axis it is represented by the x -axis.
To find the location of the given horizontal asymptote first find the degree of denominator and the degree of numerator.Degree of denominator is larger than the degree of the numerator for the given exponent then it represents the horizontal asymptote x -axis When degree of denominator is more than the degree of numerator than y = 0.Horizontal asymptote of the graph is very close to the horizontal line that is x -axis.Therefore, the horizontal asymptote is not represented by the y-axis, it is represented by the x-axis.
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Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16
Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.
As per the given data the given equation is:
[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]
The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]
Your hyperbola opens left/right, because it is of form x - y.
Comparing terms, we find that
h = -4, k = 5, a = 3, y = 4
In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].
Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).
The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]
[tex]c^2=9+16=25$[/tex], so c = 5.
The coordinates of the foci are (-9, 5) and (-1, 5).
The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)
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In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for the true proportion of all individuals who are fans of the New York Yankees? A. 0.0088 B. 0.058 C. 0.063 D. 0.116 E. 0.173
The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.
The Correct option is (B).
How to find the margin of error?The formula to calculate the margin of error for the true proportion is;
M = √[p(1 - p)/n]
Given:
n= 40
p = 44/70
Now, The general formula for the margin of error would be:
z x √[p (1-p) ÷ n]
where:
z = values for selected confidence level
p = sample proportion
n = sample size
Since the confidence level is not given,
√[p (1-p) ÷ n]
=√[44/70 (1 - (44/70) ÷ 70]
=√[0.6286 (0.3714)] ÷ 70
=√0.2335 ÷ 70
= √0.0033357
= 0.05775 or 0.058
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What are the solutions of the quadratic equation 2x^2 5x 12 0?
The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.
what is a quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.
where a, b, and c are constant terms and x is the unknown variable.
Here I am using the factoring method to solve a quadratic equation.
Given quadratic equation is
[tex]2x^2 - 5x -12 = 0.[/tex]
By comparing the General form of the quadratic equation we will get
a = 2, b = -5 and c = -12.
2x^2 - (8-3)x - 12 = 0.
2x^2 - 8x + 3x -12 = 0.
2x(x-4) + 3(x-4) = 0
(x - 4) (2x + 3) = 0.
x - 4 = 0 or 2x + 3 = 0
x = 4 or x = -3/2
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x-12 = 0?
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The figure shown contains 3 squares and 1 right triangle. What is the length of the hypotenuse of the triangle? Explain how you found your answer
the length of the hypotenuse is ???? cm
In order to find the hypotenuse of the triangle
We need to find the other sides of a right triangle
Length of the 1st side of a right triangle is connected with a square with area 144[tex]cm^{2}[/tex]
Hence in order to find the side we
[tex]\sqrt{144} = side[/tex]
[tex]12 = side[/tex]
Length of the second side is connected to a small square with area 25[tex]cm^{2}[/tex]
[tex]\sqrt{25} = side[/tex]
[tex]5 = side[/tex]
Now we can find the hypotenuse of a right triangle with the phytogorean theorem
[tex]a^{2}+ b^{2} = c^{2}[/tex]
[tex]12^{2}+ 5^{2} = c^{2} \\169 = c^{2}[/tex]
[tex]\sqrt{169}= c[/tex]
[tex]13 = c[/tex]
Hence , the hypotenuse of a right triangle is 13cm
What is the answer to g=6x for x
Answer:
The answer is x=g/6
Step-by-step explanation:
When solving an equation like this, you want to move x over to the left of =, which leaves g, and 6. now always remeber that the next variable, g for instance, will be the one divided by the factor, 6
SU is a midsegment of QRT
If QR=-5v+96 and SU = 19v-38 than what is the value of X
Considering the given triangle, the information given helped to apply similar triangle principle to determine v to be 3.9
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
TS and TR , SU and QR
The solution is worked out using sides WX and XV, WY and YU
TS / TR = SU / QR
TS / TR = 1/2 since it is a mid segment
1 / 2 = (19v - 38) / (-5v + 96)
-5v + 96 = 2 * (19v - 38)
-5v + 96 = 38v - 72
96 + 72 = 38v + 5v
168 = 43v
v = 3.9
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BRAINLY GRANTED FOR CORRECT ANS PLEASE HELP
P (X)= [tex]x^3+4 x^2-3x+2[/tex] moreover, [tex]\frac{P(x)}{x - 1} = x^{2} + 5x +2[/tex] as a result, the actual claim is [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]
How do you find the probability equation?The likelihood of an event occurring is determined by probability: P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.
The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Therefore the correct answer is option A ) [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]
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Factor Completely
-3p^7+3p^3
Answer:
3p^3 (-p^4 + 1)
Step-by-step explanation:
The common factor of both -3p^7 and 3p^3 is 3p^3
Divide -3p^7 by 3p^3 and get -p^4
Divide 3p^3 by 3p^3 and get 1
So the factorisation is 3p^3 (-p^4 + 1)
A triangle has vertices at (1, 3), (2, -3), and ( -1, -1). What is the approximate perimeter of the triangle?
Answer choices
15
10
14
16
Answer:14
Step-by-step explanation:You can use distance formula to find the length of each side, and then add them together to approximate the perimeter.
The scale factor of the blueprint of a gymnasium to the actual gymnasium is 1 in15 ft . The area of the floor on the blueprint is 114 in2 . What is the area of the actual gymnasium
The area of the actual gymnasium is 25,650 square feet.
We know that the scale factor of the blueprint to the actual gymnasium is 1 in 15 ft, which means that every 1 inch on the blueprint represents 15 feet in the actual gymnasium. To find the area of the actual gymnasium, we can use the formula:
Area of actual = (Area of blueprint) x (Scale factor)²
We know that the area of the floor on the blueprint is 114 square inches, so we can plug that into the formula:
Area of actual = 114 in² x (15 ft/1 in)² = 114 in² x 225 ft² = 25,650 ft²
Therefore, the area of the actual gymnasium is 25,650 square feet.
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what is the probability that you get a total of 17 given You are playing a version of the roulette game, where the pockets are from 0 to 10 and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability that you get a total of 15 given on the first spin you spin a 2
In the roulette game, the probability that you get a total of 15 given on the first spin you spin a 2 is 8.26%
To find: the probability that you get a total of 15 in three trials
Given that you spin a 2 on the first trial.
This means, the required probability is equivalent to the probability of finding a sum of 13 in the next two trials.
In each trial, there are 11 possible outcomes as the pockets numbered from 0 to 10.
so the sample space i.e., the total number of outcomes is:
S = 11^2
S = 121
And the favourable outcomes would be,
(2, 11), (3, 10), (4, 9), (5, 8), (6, 7), (7, 6), (8, 5), (9, 4), (10, 3), (11, 2)
So, the number of favourable outcomes A = 10
Using the definition of probability,
P = A/S
P = 10/121
P = 0.0826
P = 8.26%
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The complete question is:
You are playing a version of the roulette game, wherethe pockets arefrom 0 to 10 and even numbers are red and odd numbersare black (0 isgreen). You spin 3 times and add up the values yousee. What is theprobability that you get a total of 15 given on thefirst spin youspin a 2
1/5t + 2 - 2 = 17 - 2
Answer:
[tex]t=75[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{5} t+2-2=17-2[/tex]
Lets solve for [tex]t[/tex].
Subtract 2 from 2.
[tex]\frac{1}{5} t=17-2[/tex]
Subtract 2 from 17.
[tex]\frac{1}{5} t=15[/tex]
Combine [tex]\frac{1}{5}[/tex] and [tex]t[/tex].
[tex]\frac{t}{5} =15[/tex]
Multiply both sides of the equation by 5.
[tex]\frac{t}{5}*5 =15*5[/tex]
[tex]t=75[/tex]