Answers
The angle measures of w and x are given as follows:
w = 51º.x = 78º.How to obtain the angle measures?In this problem we have an isosceles triangle, meaning that two of the side lengths, along with two of the angle measures, are congruent.
The congruent side lengths are given as follows:
SR and RQ.
Hence the congruent angle measures are given as follows:
w -> opposite to SR.51º -> opposite to RT.Hence angle w is given as follows:
w = 51º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle x is given as follows:
x + 2 x 51 = 180
x = 180 - 102
x = 78º.
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Related Questions
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
Answer:
39 1/3 = 118/3 square units
Step-by-step explanation:
You want the area under the curve y = -x² +9x on the interval [3, 5].
IntegralThe fundamental theorem of calculus tells us the integral of the function will be its anti-derivative. That is, for f(x) = -x² +9x, we want the function F(x) whose derivative is f(x). The reverse of the power rule for derivatives can be used:
[tex]F(x)=-\dfrac{x^3}{3}+9\dfrac{x^2}{2}[/tex]
AreaThe area of interest is ...
F(5) -F(3) = -1/3(5³ -3³) +9/2(5² -3²) = -98/3 +72
F(5) -F(3) = 39 1/3
The area under the curve between x=3 and x=5 is 39 1/3 square units.
george and jenna each completed a 12 miles run. this graph shows the total distance in miles that genna ran over time
Answers
In the first hour of their run, Jenna ran 1 mile more than George.
Given graph shows the data on Jenna's running status.
It shows that Jenna ran 12 miles in 2 hours of time.
Jenna's running status in the first one hour = 12/2 = 6 miles.
Given that George ran at a constant of 5 miles per hour.
To find out how many miles will Jenna ran more than George in the first one hour = 6 -5 = 1 mile.
From the above analysis, we can conclude that the Jenna will run 6 miles in the first one hour and George will run 5 miles in the first one hour. So, Jenna will run 1 mile more than George.
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Given question is not having enough information, the complete question is attached below,
Given f(x)=x2−4‾‾‾‾‾‾√ and g(x)=3x2, what expression represents (f∘g)(x)?
Enter your answer, in simplest form, in the box.
(f∘g)(x)=
Answers
The value of (f∘g)(x) is 3x² - 2.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here, we have
Given: f(x) = √x²-4 and g(x) = 3x²
We have to find the value of (f∘g)(x).
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(3x²)
f(3x²) = √9x⁴- 4
f(3x²) = 3x² - 2
Hence, the value of (f∘g)(x) is 3x² - 2.
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Find the 50th partial sum of the arithmetic sequence
-6, -2, 2, 6, ...
Answers
The 50th partial sum of the given arithmetic sequence is 4600
Calculating partial sum of an arithmetic sequenceFrom the question, we are to calculate the 50th partial sum of the given arithmetic sequence
The given arithmetic sequence is
-6, -2, 2, 6, ...
To find the 50th partial sum of the sequence, we will find the sum of the first 50 terms in the sequence.
The sum of n terms of a sequence is given by the formula,
S = n/2(a + l)
Where a is the first term
and l is the last term
l is given by
l = a + (n - 1)d
Where d is the common difference
In the given series
a = -6
d = -6 -(-2) = -6 + 2 = 4
Thus,
l = -6 + (50 - 1)4
l = -6 + 49×4
l = -6 + 196
l = 190
Then,
S = 50/2(-6 + 190)
S = 25(184)
S = 4600
Hence,
The sum is 4600
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Please find the answer for both questions nicely
Answers
Answer: d) the amount of clay for each student. 8
Step-by-step explanation: For the sketch, draw 8 pieces of paper being divided evenly. For the expression write 2 divided by 1/4 = 8.
A rectangular paperboard measuring 26in long and 16in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Answers
The perimeter of the paperboard that remains after the semicircle is removed is 93.12 inches
How to solve for perimeterInformation given in the problem includes:
A rectangular paperboard measuring 26in long and 16in wide
information for the semicircle are
Width = 16 inches
Radius = 16 / 2 = 8 inches
Length = 26 inches
Circumference of the semi circle is calculated using the formula
= π * radius
Where the radius is 8 inches and π = 3.14.
Substituting in to the formula and solving for the circumference of the semicircle which same as perimeter of the semicircle gives:
= 8 x 3.14
= 25.12
The perimeter would be
26 inches + 26 inches + 25.12 inches + 16 inches
= 93.12 inches
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
The frequency table that summarizes the data by the biologist and the additional plants is c. third table.
How to find the frequency table?From the data by the biologist and the additional plants, we see that there are 11 plants with flowers and 7 with caterpillars.
The number of flowering plants with caterpillars is 6 plants. Those without flowers would then be:
= 11 - 6
= 5 plants
This is shown by the second frequency table.
In conclusion, the correct frequency table showing the data by the biologist is the second frequency table.
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Calculate the height of the pole
Answers
Step-by-step explanation:
See image
There were 230{,}600230,600230, comma, 600 jobs available in the field of radiology in the year 201420142014. Each year, that number is expected to grow by 0.9\%0.9%0, point, 9, percent.
Write a function that gives the expected number j(t)j(t)j, left parenthesis, t, right parenthesis of jobs in radiology ttt years from the year 201420142014.
Do not use commas in your answer.
Answers
The formula for the expected number of jobs in radiology t years from the year 2014 can be written as:
j(t) = 230600*(1+0.009)^t
We can implement this formula as a Python function:
```python
def expected_jobs(t):
return int(230600*(1+0.009)**t)
```
Note that we use the `int` function to round down the result to the nearest integer, as the number of jobs is always a whole number. Also, we do not include commas in the result, as requested.
PLEASE HELP ME! I WILL BE GIVING 50 POINTS!
Answers
Answer: B
Step-by-step explanation:
Ex: Shortest to smallest.
What are the ordered pair solutions for this system of equations? y = -x² + 2 y = x First, set the equations equal to each other and move everything to one side. A:-x²+x+2=0 C: -x² + 2 = X B:x² + x 2 = 0 D: x² + x + 2 = 0 -
Answers
To find the ordered pair solutions for the system of equations y = -x² + 2 and y = x, we can set the two equations equal to each other:
-x² + 2 = x
Now we can rearrange this equation into standard quadratic form by moving everything to one side:
-x² + x + 2 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = -1, b = 1, and c = 2
Plugging these values into the formula, we get:
x = (-1 ± √(1 - 4(-1)(2))) / 2(-1)
x = (-1 ± √9) / (-2)
x = (-1 ± 3) / (-2)
So the solutions for x are x = -1 and x = -2.
To find the corresponding values of y, we can plug these values of x into either of the original equations. Let's use y = x:
When x = -1, y = -1
When x = -2, y = -2
Therefore, the ordered pair solutions for this system of equations are (-1, -1) and (-2, -2).
The graph shows a proportional relationship. Which equation matches the graph? A: y=1/3x B: y=x C: y=3x D: y=9x
Answers
The equation that represent the graph is C) y=3x.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here let us take the two points [tex](x_1,y_1)=(1,3) , (x_2,y_2)=(3,9)[/tex].
Now using slope formula then,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> m = [tex]\frac{9-3}{3-1}=\frac{6}{2}=3[/tex].
Now using equation formula then,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-3=3(x-1)
=> y-3 = 3x-3
=> y=3x.
Hence the equation that represent the graph is C) y=3x.
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The diameter of the lead in a pencil p must be within 0.01 millimeters of 1 millimeter
Answers
The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. In the form of inequality, this can be expressed as 0.01<p<1.
A mathematical expression with values that on the left and right are not equal is referred to as having an inequality. In essence, an inequality examines any two values as well as demonstrates whether one is bigger than, less than, or neither greater nor less than the comparable quantity. Numbers are compared using inequalities to determine the range of quantities that fall inside the parameters of a variable. The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. This can be expressed as 0.01<p<1 inequality.
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Your question is incomplete but most probably your full question was,
The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. Express this statement of an inequality.
A farmer sells four of his farm products, Maize, potatoes, carrots and tomatoes in each of the two
towns in Rwanda ( Huye and Muhanga) to three classes of customers: Consumers, wholesalers
and retailers in bags as given below:
HUYE
Product
Maize Potatoes Carrots Tomatoes
Consumers 4 6 7 4
Retailers 3 2 1 6
Wholesalers 4 3 5 3
MUHANGA
Product
Maize Potatoes Carrots Tomatoes
Consumers 4 5 3 6
Retailers 7 8 4 4
Wholesalers 2 4 0 1
In order to sell his products in the towns, a farmer pays a commission to salesman, town managers
and Division Manager as shown below.
Salesman
Town
manager
Division
manager
Huye 6% 5% 2%
Muhanga 4% 3% 3%
The selling price per bag is given as follows
Products
Selling price per bag in
Rwf
Maize 200
Potatoes 1,000
Carrots 500
Tomatoes 700
Required: ---------------- 2 Marks per Each
a) Find the total sales in units by product and customer type.
b) Determine the difference between the two towns in sales (in Units) by product and
customer type.
c) Calculate the total sales in Rwf by each town.
d) Find the sales in Rwf by customer type for each town.
e) Compute the amount of commission to be paid by type of commission and type of
customer.
Answers
a) To find the total sales in units by product and customer type, we need to multiply the number of bags sold by the selling price per bag. The table below shows the calculations:
Town Product Consumers Retailers Wholesalers
Huye Maize 800 600 800
Potatoes 6,000 2,000 3,000
Carrots 3,500 500 2,500
Tomatoes 2,800 4,200 2,100
Muhanga Maize 800 1,000 0
Potatoes 5,000 8,000 4,000
Carrots 1,500 2,000 0
Tomatoes 4,200 2,800 700
b) To determine the difference between the two towns in sales (in Units) by product and customer type, we subtract the sales in Muhanga from the sales in Huye. The table below shows the calculations:
Town Product Consumers Retailers Wholesalers
Maize 0 -400 800
Huye Potatoes 0 -1,000 0
Carrots 2,000 0 2,500
Tomatoes -1,400 1,000 1,400
Total 600 -400 4,700
Product Consumers Retailers Wholesalers
Maize 0 400 0
Muhanga Potatoes 0 6,000 1,000
Carrots -2,000 -500 0
Tomatoes 1,400 -1,400 -700
Total -600 4,500 300
c) To calculate the total sales in Rwf by each town, we need to add up the sales in units for each town and product and then multiply by the selling price per bag. The table below shows the calculations:
Town Total sales in Rwf
Huye 24,400
Muhanga 23,700
d) To find the sales in Rwf by customer type for each town, we need to multiply the number of bags sold by the selling price per bag and then add up the sales for each customer type. The table below shows the calculations:
Town Customer Maize Potatoes Carrots Tomatoes
Huye Consumers 800 6,000 3,500 2,800
Retailers 600 2
If I was of any help to you, consider giving my solution a 5-star rating.
Good luck to you friend!
| Town/Customer | Maize | Potatoes | Carrots | Tomatoes |
|---------------|-------|----------|---------|----------|
| Huye Consumers | 4 | 6 | 7 | 4 |
| Huye Retailers | 3 | 2 | 1 | 6 |
| Huye Wholesalers | 4 | 3 | 5 | 3 |
| Muhanga Consumers | 4 | 5 | 3 | 6 |
| Muhanga Retailers | 7 | 8 | 4 | 4 |
| Muhanga Wholesalers | 2 | 4 | 0 | 1 |
b) The table below shows the difference between the two towns in sales (in Units) by product and customer type:
| Customer | Maize | Potatoes | Carrots | Tomatoes |
|----------|-------|----------|---------|----------|
| Consumers | 0 | 1 | 4 | -2 |
| Retailers | 4 | 6 | 3 | 2 |
| Wholesalers | 2 | -1 | 5 | 2 |
c) The total sales in Rwf by each town are as follows:
- Huye: 4(200) + 6(1000) + 7(500) + 4(700) + 3(200) + 2(1000) + 1(500) + 6(700) + 4(200) + 3(1000) + 5(500) + 3(700) = 30,600
- Muhanga: 4(200) + 5(1000) + 3(500) + 6(700) + 7(200) + 8(1000) + 4(500) + 4(700) + 2(200) + 4(1000) + 0(500) + 1(700) = 46,800
d) The sales in Rwf by customer type for each town are as follows:
| Town/Customer | Consumers | Retailers | Wholesalers |
|---------------|-----------|-----------|-------------|
−3z−z :Give answer, please
Answers
Answer:
-4z
Step-by-step explanation:
Simply add the z, which is a variable together.
Answer:
-4z
Step-by-step explanation:
Find the value of x, y, and z in the parallelogram below.
Answers
The values of x , y and z in the parallelogram are 12, -20 and -33 respectively
How to find the angles of a parallelogram?A parallelogram is a quadrilateral with opposite side equal to each other and opposite sides parallel to each other.
The opposite angles of parallelogram are equal . Consecutive angles in a parallelogram are supplementary .
Therefore,
-4y + 5 = 85
-4y = 85 - 5
-4y = 80
divide both sides by -4
y = 80 / -4
y = - 20
Therefore, let's find x and z as follows:
8x - 1 + 85 = 180
8x = 180 - 84
8x = 96
divide both sides by 8
x = 96 / 8
x = 12
Let's find z
- 3z - 4 + 85 = 180
-3z = 180 - 81
-3z = 99
divide both sides by -3
z = 99 / -3
z = -33
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How do you graph 2x^2 -5x + 5 = 3 ?
Answers
(1. 5,0 ) , (1 , 0 ) are the values of x in linear equation.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
2x² -5x + 5 = 3
2x² -5x + 5 - 3 = 0
2x² -5x + 3 = 0
2X² - (2+ 3)X + 3 = 0
2X² -2X - 3X + 3 = 0
2x(x - 1 )-3(x - 1 ) = 0
(2x - 3) (x - 1 )
x = 3/2 , 1
x = 1. 5 , 1
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A quantity with an initial value of 480 grows exponentially at a rate such that the quantity doubles every 6 minutes. What is the value of the quantity after 0.2 hours, to the nearest hundredth?
answer 1920
Answers
The value of quantity after 0.2 hours is, 960
Given that;
A quantity with an initial value of 480 grows exponentially at a rate such that the quantity doubles every 6 minutes.
We know that;
The exponential growth function is
A = A₀ (1 + r)ⁿ
Where, A= The number of quantity after t days
A₀ = initial number of quantity
r = rate of growth
n = time in minutes
A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 0.2 hours = 12 minutes
And, A = 2 x 480 = 960
A₀ = 480
n = 12 minutes
r = ?
⇒ A = A₀ (1 + r)ⁿ
⇒ 960 = 480 (1 + r)¹²
⇒ 2 = (1 + r)¹²
⇒ [tex]r = \sqrt[12]{2} - 1[/tex]
Now, to find the quantity after 12 minutes, we plug A = 830, t = 12 minutes in exponential function;
⇒ A = A₀ (1 + r)ⁿ
⇒ [tex]A = 480 (1 + \sqrt[12]{2} - 1)^{12}[/tex]
⇒ A = 480 (2)
⇒ A = 960
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For # 1 - 3 Identify each of the following numerical values as
either: (P) Parameter or (S) Statistic
1. of a company's employees the opinion of just
those that were there on time one morning about what they
thought of a new training program.
2. in a study abour a small company of 25
employees, the range of their employees salaries
3. in a study about the value of American homes in
2012, the average decrease of all the homes sold in Gwinnett
Answers
Answer:
S - S - P
Step-by-step explanation:
(S) Statistic - The opinion of just those employees who were there on time one morning about a new training program would be a statistic as it represents a sample of the entire population of employees in the company.
(S) Statistic - The range of employees' salaries in a study about a small company with 25 employees would be a statistic as it represents a characteristic of a sample of employees from the company.
(P) Parameter - The average decrease of all the homes sold in Gwinnett in a study about the value of American homes in 2012 would be a parameter as it represents a characteristic of the entire population of American homes in Gwinnett.
Randy and Brenda organize one of their family reunions and have developed the budget shown in the circle graph.
If the total budget for the family reunion is $1,200, then how much will be spent on food and drinks?
A $360
B $660
C $540
D $420
Answers
Answer:
C $540
Step-by-step explanation:
Food: .30 × $1,200 = $360
Drinks: .15 × $1,200 = $180
-------
$540
Use the following amortization chart:
Selling price
of home
$ 74,000
Down payment
$ 5,000
Principal
(loan)
$ 69,000
Rate of
interest
5.08
Years
30
Payment per $1,000
$ 5.3682
Monthly mortgage payment
$ 370.41
What is the total cost of interest?
Note: Do not round intermediate calculations. Round your answer to the nearest whole dollar.
Answers
Answer:
Step-by-step explanation:
To find the total cost of interest, we first need to find the total payment over the life of the loan:
Total payment = Monthly payment x Number of payments
Total payment = $370.41 x (30 x 12)
Total payment = $133,347.60
Next, we need to subtract the principal (loan) amount to find the total interest paid:
Total interest = Total payment - Principal
Total interest = $133,347.60 - $69,000
Total interest = $64,347.60
Rounding to the nearest whole dollar, the total cost of interest is $64,348.
If x = 3 units, y = 5 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
Answers
The calculated value of the area of the rhombus is 35 sq units
Finding the area of the rhombusFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
x = 3, y = 5 and h = 4
Using shape decomposition, we have the following
Shapes = Rectangle and 2 triangles
So, the area is
Area = Rectangle + 2 triangles
Using the area formulas, we have
Area = 1/2 * xy + 1/2 * xy + hy
substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 3 * 5 + 1/2 * 3 * 5 + 4 * 5
Evaluate
Area = 35
Hence, the area is 35 sq units
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Find the perimeter of quadrilateral PQRS.
Perimeter =
(50 POINTs will give BRAINIEST FOR EFFORT)
Answers
The perimeter of the quadrilateral PQRS is calculated as:
= 180 units.
How to Find the Perimeter of the Quadrilateral?Recall that if two tangents meet outside a circle, their length will be the same based on the tangents theorem.
Therefore, note that every line segments that appear tangent and intersect each other outside the circle have the same length.
Thus, we have:
Perimeter of the quadrilateral PQRS = 52.5 + 37.5 + 23 + (37.5 - 23) + 27.1 + (52.5 - 27.1)
Perimeter of the quadrilateral PQRS = 180 units.
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Solve for x. Enter the solutions from least to greatest.
(x - 10)² - 1 = 0
lesser x =
greater x =
Answers
Answer:
lesser x = 9
greater x = 11
Step-by-step explanation:
(x-10)² - 1 = 0
(x-10)² = 1
(x-10) = +- root1 (positive and negative root1)
So (x-10) = +1 and (x-10) = -1
Firstly
X - 10 = 1
X = 11
Secondly
X - 10 = -1
X = 9
So you have x = 9, and x = 11
The smaller one is the lesser x (9)
The larger one is the greater x (11)
HELP PLEASEE!!!
Whoever answers right gets brainliest!!
Answers
The average rate of change of the given function between the two given values is: 0.82
How to find the average rate of change of a function?The Average Rate of Change of a function is one that is defined as the average rate at which one quantity is changing with respect to another thing changing. Thus, an average rate of change function is basically a process that helps to calculate the amount of change in one item divided by the corresponding amount of change in another.
It is given by the formula:
f'(x) = [f(b) - f(a)]/(b - a)
We are given the function:
f(x) = √(3x - 11)
Thus from x1 = 4 to x2 = 6, we will have:
f(4) = √(3*4 - 11) = 1
f(6) = √(3*6 - 11) = √7
Thus:
f'(x) = ((√7) - 1)/(6 - 4)
f'(x) = 0.82
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A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area?
A. 80
B. 90
C. 100
D. 16
Answers
The wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.
Define the capture-recapture method?The basic idea behind this method is that if we capture a random sample of animals from a population, tag them, and release them back into the population, then later capture another sample of animals, the ratio of tagged to untagged animals in the second sample can be used to estimate the total population size.
To estimate the total population of wild hogs in the area, we can use the capture-recapture method.
In this case, the wildlife group tagged and released 20 wild hogs, and later counted 8 wild hogs out of the 40 they saw. We can set up a proportion to estimate the total population size:
(Tagged hogs in first sample) / (Total population size) = (Tagged hogs in second sample) / (Number of hogs in second sample)
Putting the values,
⇒ 20 / x = 8 / 40
Simplifying and solving for x, we get:
⇒ x = (20 × 40) / 8 = 100
⇒ x = 100
Therefore, the wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.
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A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 7 freshmen, 8 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
Answers
The problem can be solved using combinations. We need to choose 2 freshmen from 7, 3 sophomores from 8, 4 juniors from 7, and 5 seniors from 7. The number of ways to do this is:
C(7,2) * C(8,3) * C(7,4) * C(7,5) = 21 * 56 * 35 * 21 = 2,756,040.
Therefore, there are 2,756,040 ways to form the dance committee.
The number of ways to choose 2 freshmen from 7 is 7C2 = 21.
The number of ways to choose 3 sophomores from 8 is 8C3 = 56.
The number of ways to choose 4 juniors from 7 is 7C4 = 35.
The number of ways to choose 5 seniors from 7 is 7C5 = 21.
To find the total number of ways to choose the committee, we multiply these numbers together:
21 x 56 x 35 x 21 = 2,849,680
Therefore, there are 2,849,680 ways to choose the dance committee.
Classify the following triangle as right or not. Explain why it is or is not.
24
27
15
Answers
A right triangle is a triangle that has a right angle (90 degrees).
To check if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
If we apply this theorem to this triangle, we get:
24^2 + 15^2 = 576 + 225 = 801
27^2 = 729
Since 801 is not equal to 729, this triangle does not satisfy the Pythagorean theorem and is not a right triangle.
Which of the following probability models would the probability P(C) = 1/3 complete?
a P(A) = 1/9 P(B)= 1/2
b P(A) = 1/9 P(B)= 2/9
c P(A) = 1/6 P(B)= 3/9
d P(A) = 2/9 P(B)= 8/18
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The 7th term of the binomial expression given can be found to be 8.136 × 10^7 × x^(-4)
How to find the term ?To find the 7th term of (3x - 4/x²)¹⁴, we can use the binomial theorem, which states that for any positive integer n and any real numbers a and b:
(a + b)ⁿ = ∑(C(n, k) x a^(n-k) x b^k)
Using the binomial theorem formula, the 7th term can be calculated as follows:
Term_7 = C(14, 6) x (3x)^(14-6) x (-4/x²)^6
First, let's find C(14, 6):
C(14, 6) = 14! / (6! x (14-6)!)
C(14, 6) = 14! / (6! x 8!)
C(14, 6) = 3003
Now, we can put everything together:
Term 7 = 3003 x (3x)^8 x (4096 / x¹²)
Term 7 = 8.136 × 10^7 × x^(-4)
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