A group consists of five five men and eight eight women. seven seven people are selected to attend a conference.
a. in how many ways can seven seven people be selected from this group of thirteen thirteen?
b. in how many ways can seven seven women be selected from the eight eight women?
c. find the probability that the selected group will consist of all women.
a) 116 ways to select seven people.
b) ways to select 7 women.
c) The probability is 0.004662
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
a) Number of ways can seven people be selected from this group of thirteen
C( 13, 7)
= 13! /6! 7!
= 1716
b) Number of ways seven women selected from Eight women
C(8 ,7)
= 8!/ 7! 1!
= 8
c) The probability that the selected group will consist of all women
= 8 / 1716
= 0.004662
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In your notebook, draw a right angle and then draw a bisector of the right angle. Label all parts. What are some properties of the angles formed by the bisector?
Answer:
Let's consider this right triangle described in the picture.
∠ABD = ∠CBD, since BD is a bisector.
Angles ∠ADB and ∠BDC are neighbor angles and their sum is equal to 180°.
∠BDC is an exterior angle and ∠BDC=∠ABD+∠ADB.
Similarly, ∠ADB is an exterior angle and ∠ADB=∠CBD+∠BCD
Step-by-step explanation:
what two numbers multiplies to -90 and add to -8
Final answer:
The two numbers that multiply to -90 and add up to -8 are -10 and 2. This is found by factoring -90 and checking different factor pairs until the correct one is identified.
Explanation:
The student is asking for two numbers that when multiplied result in -90, and when added result in -8. This is a factorization problem that can be addressed by setting up a system of equations or by using intuition to guess and check pairs of factors. We are looking for a pair of numbers that have one positive and one negative number, because the product is negative (-90), and the sum is also negative (-8).
By listing out the factors of 90, we can test which pair of numbers, with one being negative, would multiply to -90 and add up to -8. After some trial and error, we find the pair that works are -10 and 9. -10 × 9 = -90 and -10 + 9 = -1. However, since the sum needs to be -8, then the correct pair is -10 and 2, because -10 × 2 = -20 and -10 + 2 = -8.
WILL GIVE BRAINLIEST, 15 points-The daily number of patients visiting a dentist's office during one week are 8, 41, 35, 39, 36, and 42.
Which statement is true?
The mean, median, and mode are all appropriate measures of center.
Both the mean and median are appropriate measures of center.
The median is the only appropriate measure of center.
Both the median and mode are appropriate measures of center.
Answer: The median is the only appropriate measure of center.
Step-by-step explanation:
The statement is ''Both the median and mode are appropriate measures of center''. Actually, the three, that is, the mean, media and mode can be used to measure the central of tendency. But the MEAN has a problem, it can be Skewed by large values in the distribution/data. Assuming, the days of the week when patients visiting a dentist's office are;
Monday: 8, Tuesday: 41, Wednesday: 35, Thursday: 39, Friday: 36, and Saturday: 42.
And the mean of the distribution = 33.5. Most patients visit the dentist Tuesday to Saturday, where Saturday is the highest. The data is skewed. So, the MEDIAN will do the job perfectly.
For the mode; since we do not have; (1). two highest mode with the same value in the data provided and, (2). the highest value and the second to the highest values are not too far from each other. We can use the MODE here for measuring the central tendency.
===> CONCLUSION: (1). Assuming the data fails the two condition for mode, the most correct statement will be ''The median is the only appropriate measure of center".
===> (2). Also, for this data, the MEDIAN will be the only appropriate measure of center.
Is this done correctly or incorrectly??
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What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?
y=-3x-5
y=-3x+5
y=3x-5
y=3x+5,
The equation of line passes through the points (2, -1) and (5, -10) will be;
⇒ y = - 3x + 5
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (2, -1) and (5, -10)
Now,
Since, The equation of line passes through the points (2, -1) and (5, -10)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 10 - (-1)) / (5 - 2)
m = - 9 / 3
m = - 3
Thus, The equation of line with slope - 3 is,
⇒ y - (-1)= - 3 (x - 2)
⇒ y + 1 = - 3x + 6
⇒ y = - 3x + 6 - 1
⇒ y = - 3x + 5
Therefore, The equation of line passes through the points (2, -1) and
(5, -10) will be;
⇒ y = - 3x + 5
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Sarah deposits $600 in a savings account that pays 2.5% per year. What is the minimum number of years it would take for the amount in her account to be more than $800, provided no more money is deposited in the account?
It will take at least 12 years for Sarah's $600 deposit at a 2.5% annual interest rate to grow to more than $800, assuming the interest is compounded annually.
To determine how long it will take for Sarah's $600 deposit at a 2.5% annual interest rate to grow to over $800, we can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.Since the problem doesn't specify the compounding frequency, let's assume it's compounded annually for simplicity:
[tex]A = 600(1 + 0.025)^t[/tex]. We need A to be greater than $800.
To find the minimum number of years (t), we solve for t:
[tex]800 < 600(1 + 0.025)^t[/tex]
Solving for t gives us: t > ln(800/600) / ln(1.025).
Using a calculator, we find that t > 11.89.
Therefore, it will take at least 12 years for the amount in Sarah's account to exceed $800.
Write a recursive definition for the set of odd positive integers.
Final answer:
A recursive definition for the set of odd positive integers starts with a base case of 1 and uses a recursive step where each subsequent odd integer is obtained by adding 2 to the current odd integer.
Explanation:
To write a recursive definition for the set of odd positive integers, you can define a base case and a recursive step. The base case is the smallest odd positive integer, which is 1. The recursive step will then generate the next odd integer by adding 2 to the current odd integer. Here's how you can express it:
Base case: Let O1 = 1, which establishes that 1 is the first odd positive integer.
Recursive step: For every odd positive integer On, there exists an On+1 = On + 2. This means that if you have an odd positive integer, the next one in the set can be found by adding 2 to the current one.
This definition ensures that every number generated by the recursive step will be odd since adding 2 to an odd number always results in another odd number, and starting from 1, guarantees that all numbers will be positive.
So I tried to answer this the best that I can but I keep getting wrong answers can someone help me I will award brainliest .
Identify the polynomial. x 3 y 3 monomial binomial trinomial
Answer:
x³y³ is monomial.
Step-by-step explanation:
Given :Polynomial x³y³ .
To find : Identify monomial binomial trinomial.
Solution : We have given that
Polynomial x³y³ .
Monomial : A polynomial with just one term.
Examples : 1) 3xy
2) 5y²x³ Both are monmial .
x³y³ is also a monomial because it has only one term.
Therefore, x³y³ is monomial.
a 12-ft-long ladder is leaning against a wall and makes an 80 degree angle with the ground.how high up the wall does the ladder reach, and how far is the base of the ladder from the base of the wall? round to the nearest inch.,
Answer:
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
Step-by-step explanation:
Let us draw a diagram for the given situation.
In the attached figure,
AB = the height of wall where the ladder reaches
AC = ladder
BC = distance of base of ladder from the base of the wall
In triangle ABC,
[tex]\sin C=\frac{AB}{AC}\\\\\sin80=\frac{AB}{12}\\\\AB=12\sin80\\\\AB=11.82[/tex]
And
[tex]\cos C=\frac{BC}{AC}\\\\\cos80=\frac{BC}{12}\\\\BC=12\cos80\\\\BC=2.08[/tex]
Now, 1 feet = 12 inches
Hence, 11.82 ft = 141.84 inches
and 2.08 feet = 24.96 inches
Therefore, in the nearest inches, we have
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
How do the areas of the parallelograms compare?
The area of parallelogram ABCD is 4 square units greater than the area of parallelogram EFGH.
The area of parallelogram ABCD is 2 square units greater than the area of parallelogram EFGH.
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
The area of parallelogram ABCD is 2 square units less than the area of parallelogram EFGH.
The inverse of x -> y is:
What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1
The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4
Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
This problem is about Geometric Sequence. Let's see why.
[tex]\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .[/tex]
T₁ = [tex]\frac{1}{324}[/tex]
T₂ = [tex]\frac{1}{108}[/tex]
T₃ = [tex]\frac{1}{36}[/tex]
T₄ = [tex]\frac{1}{12}[/tex]
[tex]\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }[/tex]
From the above results it can be concluded that this is Geometric Sequence.
The next number will be the fifth term and can be calculated as following.
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^{5 - 1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^4[/tex]
[tex]T_5 = \frac{1}{324} \times 81[/tex]
[tex]\large {\boxed {T_5 = \frac{1}{4} } }[/tex]
Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
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the weight of a goat increased by 12 pounds is 38 pounds.write an equation to represent the situation.
3. If the volume of a cube of wood is15.625 cm3 and its mass is 10.00 grams, show the calculation for the density of the wood. @ganeshie8 @SolomonZelman,
Answer:
The density of the wood is, 0.64 [tex]g/cm^3[/tex]
Step-by-step explanation:
Using the density formula:
[tex]\text{density} = \frac{\text{mass}}{\text{Volume}}[/tex] .....[1]
As per the statement:
If the volume of a cube of wood is 15.625 cm3 and its mass is 10.00 grams.
⇒Volume = 15.625 cubic cm and mass = 10 gram
Substitute the given values in [1] we have;
[tex]\text{density} = \frac{10}{15.625}[/tex]
Simplify:
density = 0.64 [tex]g/cm^3[/tex]
Therefore, the density of the wood is, 0.64 [tex]g/cm^3[/tex]
??? quadrilateral abcd ??? is inscribed in this circle. what is the measure of angle c? enter your answer in the box. ?? a quadrilateral inscribed in a circle. the vertices of the quadrilateral lie on the edge of the circle and are labeled as a, b, c,
d. the interior angle a is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. the angle b is labeled as left parenthesis 2 x minus 4 right parenthesis degrees. the angle d is labeled as left parenthesis 3 x plus 9 right parenthesis degrees.
Answer:
∠C = 107°
Step-by-step explanation:
Quadrilateral ABCD is inscribed in a circle, and a quadrilateral inscribed in a circle is known as cyclic quadrilateral.
So, ABCD is cyclic quadrilateral.
∠A = 2x + 3
∠B = 2x - 4
∠D = 3x + 9
Also. the sum of opposite angles of the cyclic quadrilateral is supplementary.
⇒ ∠B + ∠D = 180
⇒ 2x - 4 + 3x + 9 = 180
⇒ 5x = 175
⇒ x = 35
Now, ∠A = 73
Also, ∠A + ∠C = 180
⇒ ∠C = 180 - 73
⇒ ∠C = 107°
Removing which point from the coordinate plane would make the graph a function of x?
(–4, 3)
(–2, 1)
(0, 4)
(1, 1)
The points at which the quadratic equation intersects the x-axis are referred too
Which situation best represents a proportional relationship?
a. sandra sold 2 bracelets for $3 and 3 bracelets for $6.
b. jeff ran 4 miles in 20 minutes and 6 miles in 24 minutes.
c. lamont packed 27 glasses in 9 cases and 81 glasses in 27 cases.
d. fernanda placed 8 pencils in 2 boxes and 16 pencils in 8 boxes?
4. Name a pair of corresponding angles
1. Angle 1 and angle 6
2. Angle 2 and angle 6
3. Angle 3 and angle 5
4. Angle 4 and angle 5
~
5.Use the figure. Assume that lines JL and MP are parallel
If m angle 4 =105°, then what is m angle 8?
1. 105°
2. 75°
3.175°
4.25°
For the given case the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°. The correct option is (1).
What are parallel lines?The parallel lines are a group of straight lines that never intersect with one another. The distance between two parallel is always the same.
The given problem can be solved as follows,
(4) The pair of angles can be named as below,
(1) The angles ∠1 and ∠6 are called consecutive angles.
(2) The angles ∠2 and ∠6 are called corresponding angles.
(3) The angles ∠3 and ∠5 are called consecutive interior angles.
(4) The angles ∠4 and ∠5 are called alternate interior angles.
(5) The measure of ∠8 is given as below,
Since ∠4 and ∠8 are corresponding angles.
∠4 = ∠8 = 105°.
Hence, the names of the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°.
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9x^2 - 8x - 1 = 0
What are the x intercepts?
a shop made a profit of £23500 in 2009. in 2010 the profit increased to £28000.work out the percentage increase in profit, to the nearest 1%
PLZ SOMEONE HELP ME ON THIS
MATH HELP LEASE WILL GIVE BRAINLIEST!!!
What is the value of θ for the acute angle in a right triangle?
sin(θ) = cos(58°)
Question 4 options:
32°
58°
122°
29°
Which of the following are characteristics of the graph of the quadratic parent function?
A. It has one intercept.
B. It opens down.
C. It has a vertex at (0, 0).
D. It is U-shaped.
Answer:
The correct options are A, C and D.
Step-by-step explanation:
The quadratic parent function is
[tex]f(x)=x^2[/tex]
The properties of quadratic parent function are:
1. It has one intercept, i.e, x- and y-intercept are at origin.
2. It has a vertex at (0, 0).
3. It is U-shaped.
4. Each image y has two preimage, except 0.
5. It opens up.
From the given option one the option B is incorrect because the quadratic parent function opens upward.
Therefore the correct options are A, C and D.
can someone check my work. I don't know what I did wrong
1.
(05.08 MC)
Given the equation 1 over x−1 + 2 over x =x over x−1
Part A: What values of x that would make the equation no solution? Why?
Part B: What is the solution of the equation. Show all of your steps.
Max and Maggie have to clean the house. It takes Max 10 hours to clean the house, while Maggie can complete the task in 6 hours. How long will it take for them to work together? Explain each step in solving this equation.
Answer:
a
Step-by-step explanation:
write 4x - 2y = -8 in slope-intercept form