a) 17210368 different ways can the program select which students will answer the five questions
b) 11,793,600 different ways.
What is Permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given:
Each of the 28 students in her class is equally likely to be chosen every time she runs the program.
a) The number of ways can the program select which students will answer the five questions
= [tex]28^5\\[/tex]
= 17210368
b) using Permutation
[tex]P^{28}_2[/tex] = 28! / (28-5)!
= 28! / 23!
= 28 x 27 x 26 x 25 x 24 x 23! / 23!
= 11,793,600
So, there are 11,793,600 different ways.
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7. In the first picture of two intersecting lines, what is the m ∠2? How do you know?
8. In the second picture of parallel lines cut by a transversal, which angle is supplementary to ∠8? How do you know?
9. The third picture shows parallel lines cut by a transversal. What is the m ∠2? How do you know?
10. Use the fourth picture of parallel lines cut by a transversal. What is the value of x?
7. m<2 = 138° based on the definition of vertical angles.
8. m<3 is supplementary to angle 8
9. The measure of angle 2 = 50°
10. The value of x = 20
What is a Supplementary Angle?A supplementary angle is a pair of angles whose sum is equal to 180 degrees. In other words, two angles are supplementary if they add up to a straight angle.
For example, if one angle measures 70 degrees, its supplement would be 180 - 70 = 110 degrees.
7. m<2 = 138° (reason: vertical angles are equal).
8. m<3 is supplementary to angle 8 because angle 3 and 5 are supplementary, and angle 5 is congruent to angle 8.
9. 5x + 55 = 2x + 100 (corresponding angles are equal)
Find x:
5x - 2x = -55 + 100
3x = 45
x = 15
m<2 = 180 - (5x + 55) (linear pair is equal to 180 degrees)
Plug in the value of x
m<2 = 180 - (5(15) + 55)
m<2 = 180 - 130
m<2 = 50°
10. 45 + 5x + 35 = 180 (supplementary angles)
5x + 80 = 180
5x = 180 - 80
5x = 100
x = 20
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Identify the change in the parent function that will produce the related function shown as a dashed line.
f(x)= |x|
Answer:
f(x)= (X+5)^2
Step-by-step explanation:
pls, tell me if wrong have a good day/night<3
1. Find the new value after the old value of 56 is increased by 8%.
Answer:
60.48
Step-by-step explanation:
Answer:51.52
Step-by-step explanation:
Given AABC with AB contained in the line 2x + 3y = 5. if AABC is dilated to get AA'BC_
which of the following lines could contain A'B'?
2z - 3y = 10
3z-2y = 10
2z+ 3y = 10
3z +2y=10
When triangle ABC is dilated to triangle A'BC then the line A'B' has the equation 2z+ 3y = 10.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.
Given that the triangle ABC is dilated to get the triangle A'BC.
If the triangle is dilated then, AB is parallel to A'B'.
So, the slopes of the two line are equal.
The equation of the AB is 2x + 3y = 5.
Converting into the standard equation of line:
y = - 2/3 x + 5/3
The slope of the line is -2/3.
From the given options, the line that has slope -2/3 when converted to standard form is:
2z+ 3y = 10
Hence, when triangle ABC is dilated to triangle A'BC then the line A'B' has the equation 2z+ 3y = 10.
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Calculate the area of a rectangular room that is 72 feet wide and 39 feet long.
Answer: 2808 ft.
Step-by-step explanation:
72(39) = 2808
Answer:
Area for a rectangle is Length * Width or A=l*w
Length= 72ft
width= 39ft
72*39= 2808
The area of the rectangular room is 2808
Step-by-step explanation:
Hope this helps!! :))) Mark me brainliest! :))
Solve the inequality –(2 + 2x) – 2 > 6 for x.
Answer:
x<-5
Step-by-step explanation:
-(2+2x)-2>6
-(2+2x)>8
2+2x<-8
2x<-10
x<-5
CAN SOMEONE HELP WITH THIS QUESTION?✨
The differentiation of the f(x) = g(x)/h(x), using the quotient rule, indicates that the value of f'(2) = 20/81
What is the quotient rule?The Quotient Rule for finding the derivative of a ratio of two functions, [tex]f(x) = \frac{g(x)}{h(x)}[/tex] that are differentiable is presented as follows;
[tex]f'(x) = \frac{h(x) \cdot g'(x) - g(x) \cdot h'(x)}{h(x)^2}[/tex]
The equation of the lines are found as follows;
The points on the line g(x) are; (1, 2), and (3, 6)
Therefore, we get;
Slope of the line = (6 - 2)/(3 - 1) = 2
Equation of the line is; y - 2 = 2·(x - 1) = 2·x - 2
y - 2 = 2·x - 2
y = 2·x - 2 + 2 = 2·x
The equation of the line is presented as follows;
g(x) = 2·x
Points on the graph of the function h(x) when x = 2 are; (2.5, 5), and (0, 2.5)
Slope of the graph of h(x) when x = 2 is; (2.5 - 5)/(0 - 2.5) = 1
The equation of the line is therefore; y - 5 = 1·(x - 2.5) = x - 2.5
y - 5 = x - 2.5
y = x - 2.5 + 5 = x + 2.5
h(x) = x + 2.5
f(x) = g(x)/h(x)
The value of f'(x) using the quotient rule, is therefore;
f'(x) = (h(x)·g'(x) - g(x)·h'(x))/(h(x))²
g'(x) = 2
h'(x) = 1
Therefore;
f'(x) = ((x + 2.5)×2 - 2·x × 1)/(x + 2.5)² = (2·x + 5 - 2·x)/((x + 2.5)²)
(2·x + 5 - 2·x)/((x + 2.5)²) = 5/(x + 2.5)²
f'(2) = 5/(2 + 2.5)² = 20/81
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mr. hollens give away $800 per month. He has determind that this is 16% if his buget. About how much is his overall budget
Answer:
5000
Step-by-step explanation:
800/16% = 5000
The water level is a number that indicates whether the level is above or below normal using positive or negative values. After a heavy storm, the water level of a river is −3.7 feet. This level is 1/2 times 2.5 feet more than the previous water level.
What was the previous water level?
A. -18.5
B. -9.9
C. -4.9
D. -4.3
Note: I think it is -4.9. If you have the actual right answer please leave it down below. Thanks.
Answer:
I also believe it is -4.9 but I may be mistaken
Step-by-step explanation:
Tanya drove 312 hours and used 13 tank of gas.
For how long could Tanya drive using 12 tank of gas?
Enter your answer as a mixed number in simplest form in the box.
hours please
Assuming you meant 3/12, 1/3 and 1/2. The answer would be 5[tex]\frac{1}{4\\}[/tex].
Answer:
[tex]288\frac{0}{13}[/tex]
Solution :We can use the proportional method in this question
This case is a direct proportion
What is Direct Proportion?Direct proportion is a type of proportionality relationship. For direct proportion, as one value increases, so does the other value and conversely, as one value decreases, so does the other value. The symbol ∝ represents a proportional relationship.
We put the variable as x that represents the hour
We put it into a fractional form
[tex]\frac{312}{13} = \frac{x}{12}[/tex]
Cross Multiplying
[tex]312X12 = 13x[/tex]
[tex]3744 = 13x[/tex]
[tex]\frac{3744}{13} = x[/tex]
[tex]288\frac{0}{13} = x[/tex]
To begin a bacteria study, a petri dish had
2700
bacteria cells. Each hour since, the number of cells has increased by
17%
.
Let
t
be the number of hours since the start of the study. Let
y
be the number of bacteria cells.
Write an exponential function showing the relationship between
y
and
t
The exponential equation is y = 2700 ( 1 + 0.17 )ⁿ , where n = t , the number of hours since the start of the study
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the exponential equation be represented as y
Now , the number of bacteria cells = y
The number of hours since the start of the study = n = t
The initial number of bacteria = 2,700 cells
The percentage of increase in the cells = 17 %
So , The exponential growth formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
Substituting the values in the equation , we get
y = 2700 ( 1 + 0.17 )ⁿ
On simplifying the equation , we get
y = 2700 ( 1.17 )ⁿ
where n = t , the number of hours since the start of the study
Hence , the equation is y = 2700 ( 1.17 )ⁿ
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PLEASE HELP ME ASAP!! THATS ALL I NEED
Randy needs to buy school supplies. He needs a headset that costs $30.00. He also needs notebooks that cost $3.00 each.
Part 1
Complete the table to determine his total cost for a given number of notebooks.
Format your response using 2 decimal places and NO symbols. Example: 25.00
The total cost for a given number of notebooks is 30 + 3x
How to determine the total cost for a given number of notebooksFrom the question, we have the following parameters that can be used in our computation:
Headset = $30.00
Notebook = $3.00
The total cost for x number of notebooks can be calculated as follows:
$30.00 + (3.00 * x)
So, we have
Total Cost = 30 + 3x
The response in two decimal places is Total cost = 30.00 + x * 3.00
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what the number 125% of 280
Answer:350
Step-by-step explanation: 280/4=70
280+70=350
Answer:
350
Step-by-step explanation:
The percentage is converted to decimal place and then multiplied by 280
[tex]280(\frac{125}{100} )=280(1.25)=350[/tex]
Hope this helps.
An isosceles trapezoid ABCD has two parallel sides AB and CD and mzA = 65°. Select All the correct statements.
The sum of measures of angles B and A is 130 degrees.
The measure of angle D is 115 degrees.
The sum of measures of angles D and C is 180 degrees.
The sum of measures of angles D and B is 130 degrees.
The sum of measures of angles B and C is 180 degrees.
The statement "the sum of measures of angles B and A is 130 degrees" is correct. Therefore, option A, B and E are the correct answer.
What is an isosceles trapezoid?An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure. In other words, if two opposite sides (bases) of the trapezoid are parallel, and the two non-parallel sides are of equal lengths, then it is an isosceles trapezoid.
Given that, an isosceles trapezoid ABCD has two parallel sides AB and CD and m∠A = 65°.
Correct statements are
The sum of measures of angles B and A is 130 degrees.
The measure of angle D is 115 degrees.
The sum of measures of angles B and C is 180 degrees.
Therefore, option A, B and E are the correct answer.
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Check each value and decide if it is a factor of 50 or not: 15, 2, 5, 3, 20, 50, 25, 10
Answer:
3 and 20 are NOT factors of 50.
15, 2, 5, 50, 25, and 10 are factors of 50.
Step-by-step explanation:
Hope it helps! =D
Convert the following temperatures from Fahrenheit to Celsius or vice versa.
a)
C = 23.8°C
b)
F = 113°F
c)
F = -4°F
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
a) 75°F
b) 45°C
c) -20°C
Conversion formulas:
C = (F - 32) / 1.8
F = 1.8C + 32
Now,
75°F
C = (F - 32) / 1.8
C = (75 - 32) / 1.8
C = 23.8°C
45°C
F = 1.8C + 32
F = 1.8 x 45 + 32
F = 113°F
-20°C
F = 1.8C + 32
F = 1.8 x (-20) + 32
F = -4°F
Thus,
The temperature conversion is given above.
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Plssss I need help with this math thing
The required volume of the given right rectangular prism is 2x³ - 4x² cubic units.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
From the figure,
Volume = length × width × height
= [2x - 4] × x × x
= [2x³ - 4x²]
Thus, the required volume of the given right rectangular prism is 2x³ - 4x² cubic units.
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A lumber yard has scrap wood for sale. One employee recorded the measurements for the lengths of 55 different wood boards. The median length was recorded as 58.37 inches and the IQR was recorded as 19.66 inches. Someone discovers the measuring tape used started at 2 inches instead of 0. This means that each piece of wood is actually 2 inches shorter than the value recorded by the employee. What is the updated median? Report your answer to two decimal places.
The updated median is 56.37 and the updated IQR is 17.66.
What is median of data?The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.
Given that, one employee recorded the measurements for the lengths of 55 different wood boards.
Median =58.37 and IQR=19.66
Someone discovers the measuring tape used started at 2 inches instead of 0.
The interquartile range is given by the difference between the 75th percentile(value that is greater than 75% of the measures) and the 25th percentile.
This means that each piece of wood is actually 2 inches shorter than the value recorded by the employee.
This means that the length of each wood is less than 5. However, the difference between the 75th percentile and the 25th percentile will stay the same, since both were subtracted by 2.
So, IQR=19.66-2 =17.66
Therefore, the updated median is 56.37 and the updated IQR is 17.66.
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Describe and correct the error in finding the measure of the exterior angle.
I have attached the diagram
The correct value of the measure of the exterior angle is 72 degrees
How to find the exterior angles?You should understand that when one side of a polygon is produced, the angle so formed is called an exterior angle
Note also that two opposite interior angles equal to one exterior angle
This implies that
x+30=2x-12
Collecting like terms
x-2x=-12-30
-x=-42
the value of x is 42
Then substitute x for the exterior angle
2(42)-12
84-12 = 72
The exterior angle is 72 degrees
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How do you do this? Please tell me thank you a lot.
The answer is 506 not to sure since I haven't done this in a while
Answer:
506
Step-by-step explanation:
According to the order of operations(or PEMDAS), you would first evaluate the exponent in the problem: [tex]8^3[/tex]. [tex]8^3[/tex] is equivalent to [tex]8*8*8[/tex], which is just 512. Therefore, the equation would now be 512 - 9 * 2 ÷ 3
Next step would be to do out the multiplication and division left to right. First is 9 * 2 which is 18. Then that is divided by three to get 6. The equation would now be 512 - 6.
512 - 6 is just 506.
A cuboid has the total surface area 1168 cm². If it's length and breadth are 16 cm and 14 cm respectively, what it's height?
A cuboid has 6 faces and the formula for its total surface area is:
2lw + 2lh + 2wh, where l is the length, w is the breadth, and h is the height.
Given the total surface area of 1168 cm² and the length and breadth being 16 cm and 14 cm, respectively:
2(16)(14) + 2(16)h + 2(14)h = 1168
Expanding the expression:
448 + 32h + 28h = 1168
Combining like terms:
60h = 720
Dividing both sides by 60:
h = 12 cm
So the height of the cuboid is 12 cm.
Write an expression equivalent to 4x-2x+4-1.
Answer:
2x+3 i think
Use formula to find the area of the figure
The area of the figure in this problem is given as follows:
A. 30 in².
How to obtain the area of the figure?The area of a triangle is given by half the multiplication of the base length by the height of the triangle.
Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:
4² + x² = 6²
x² = 36 - 16
x² = 20
x = square root of 20
x = 4.47.
For a right triangle, one side is considered the height of the other, hence the sides are:
4 in.4.47 + 8 = 12.47 in.Hence the area of the triangle is then obtained as follows:
Area = 0.5 x 4 x 12.47
Area = 25 in².
Which is closest to 30 in².
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K
The perimeter of a rectangular sports court is 148 feet. After a game, a player's coach estimates that the athlete has run
a total of 353 feet, which is equivalent to four times the court's length plus seven times its width. What are the
dimensions of the sports court?
The length is
feet.
Answer: Let's call the length of the rectangular court "L" and the width "W". Then, the perimeter of the court is 2 * (L + W) = 148 feet, so 2 * L + 2 * W = 148 feet.
And, according to the coach's estimate, the athlete ran a total of 4 * L + 7 * W = 353 feet.
We can use these two equations to find the dimensions of the court. Solving the first equation for W:
W = (148 - 2 * L) / 2.
Substituting this expression for W into the second equation:
4 * L + 7 * (148 - 2 * L) / 2 = 353
Expanding and simplifying the right side of the equation:
4 * L + 74 - 7 * L = 353
-3 * L = -279
L = 93 feet.
Finally, using the expression for W from the first equation:
W = (148 - 2 * L) / 2 = (148 - 2 * 93) / 2 = 32 feet.
So the dimensions of the sports court are 93 feet by 32 feet.
Step-by-step explanation:
if 2x-17=13. then x=?
Answer:
x=15
Step-by-step explanation:
2x-17=13
2x=30
x=15
Hope this helped! :)
Answer:
15
Step-by-step explanation:
2x - 17 = 13
Add 17 to both sides:
2x = 30
Divide both sides by 2:
[x = 15]
Equivalent ratio 72:64=9:_
Answer:
9:8
Step-by-step explanation:
We know that 72:64
If you multiply 9 by 8 you get 72, so you know that the answer will have to be simplified by 8.
64/8 = 8
Therefore your answer for this will be 9:8
the function has an average rate of change of
On solving the provided question, we can say that Therefore, the function has an average rate of change of -1.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The function has an average rate of change of -1.
R = 4-5/1-0
R = -1
Therefore, the function has an average rate of change of -1.
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The answers pleaseee I’ll give you points
Answer:
7. √149 ft or 12.2 ft
8. 5√2 m or 7.07 m
9. √36.75 in. or 6.06 in.
Step-by-step explanation:
7.
a² + b² = c²
7² + 10² = x²
49 + 100 = x²
x² = 149
x = √149
x ≈ 12.2
Answer: √149 ft or 12.2 ft
8.
perimeter = 20 m
side = perimeter/4 = 5 m
a² + b² = c²
5² + 5² = x²
25 + 25 = x²
x² = 50
x = 5√2
Answer: 5√2 m or 7.07 m
9.
a² + b² = c²
3.5² + x² = 7²
12.25 + x² = 49
x² = 49 - 12.25
x² = 36.75
x = √36.75 = 6.06
Answer: √36.75 in. or 6.06 in.
Answer:
7. 12.2 ft
8. 7.07 m
9. 6.06 in
Step-by-step explanation:
You want the hypotenuse of at right triangle with legs 7 and 10 ft, the diagonal of a square with perimeter 20 m, and the altitude of an equilateral triangle with side length 7 inches.
Pythagorean theoremThese problems all make use of the Pythagorean theorem, which tells yo the relation between sides a, b and hypotenuse c of a right triangle is ...
a² +b² = c²
7. LeashThe length of the leash (c) is ...
c² = (7 ft)² +(10 ft)² = 149 ft²
c = √149 ft ≈ 12.2 ft
The leash is about 12.2 feet long.
8. SquareEach side of the square is 1/4 of the perimeter, so is 5 m. The diagonal is the hypotenuse of a right triangle with legs that length. Its measure is ...
c = √(5² +5²) = 5√2 ≈ 7.07 . . . . meters
The length of the diagonal is about 7.07 meters.
9. AltitudeThe altitude of an equilateral triangle is a perpendicular bisector of one side. Its length is ...
b = √(c² -a²)
b = √(7² -3.5²) = √36.75 ≈ 6.06 . . . . inches
The altitude of the triangle is about 6.06 inches.
__
Additional comment
The triangles of problems 8 and 9 are known as the two "special" right triangles.
The side lengths of an isosceles right triangle (angles 45°-45°-90°) have the ratios 1 : 1 : √2.
The side lengths of a triangle with angles 30°-60°-90° have the ratios 1 : √3 : 2.
That is, the diagonal of the square is √2 times its side length, and the altitude of the equilateral triangle is (√3)/2 times is side length.
It can be useful to remember these triangles and their side ratios.
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The temperature fell from 0Degrees Fahrenheit to 6 and three-fifthsDegrees Fahrenheit below 0Degrees Fahrenheit in 2 and one-fifth hours. What was the temperature change per hour?
A. -3
B. -4 2/5
C. 3
D. 4 2/5
If a cubic polynomial has zeros of 3, -2, 0, write the polynomial in standard form.
The polynomial in standard form is x³ + 2x² - 3x² - 6x = 0.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The cubic polynomial has zeros of 3, -2, and 0.
This means,
x = 3
x - 3 = 0 _____(1)
x = -2
x + 2 = 0 ______(2)
x = 0 ______(3)
Now,
The zeroes can be written as,
x (x - 3) (x + 2) = 0
x (x² + 2x - 3x - 6) = 0
x³ + 2x² - 3x² - 6x = 0
Thus,
x³ + 2x² - 3x² - 6x = 0 is the standard form of the polynomial equation.
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