Answer:
1 - cos² 15° - cos² 75° can be simplified as follows:
Using the identity cos² x = 1 - sin² x, we can write the expression as:
1 - (1 - sin² 15°) - (1 - sin² 75°)
= sin² 15° + sin² 75° - 1
Using the identity sin 2x = 2sin x cos x, we can write sin 15° and sin 75° in terms of sin 30° and sin 45°:
sin 15° = sin (30° - 15°) = (1/2) * sin 30°
sin 75° = sin (45° + 30°) = sin 45° + sin 30°
Substituting these values in the above expression, we get:
sin² 15° + sin² 75° = (1/4) * sin² 30° + sin² 45° + sin 30° * sin 45°
= (1/4) * (2 * (1/2)²) + (2 * (1/2) * (1/2)) + (1/2) * (1/2)
= (1/4) + 1/2 + 1/4 = 1
So, 1 - cos² 15° - cos² 75° = sin² 15° + sin² 75° - 1 = 1 - 1 = 0.
Step-by-step explanation:
WHICH OF THE FOLLOWING ARE POLYNOMIAL FUNCTION
8Y=10X3-4
One example of a polynomial function is given as follows:
p(x) = x^3+4x^2-3x+2
What are the conditions for a polynomial function?There are two conditions for a polynomial function, and they are listed as follows:
Variable x is present only in the numerator of the function.The definition of the function contains only numeric non-negative exponents.For the example, we have that the exponents are 3, 2, 1 and 0, while it contains only a numerator.
Missing InformationThe problem is incomplete, hence the general procedure to identify a polynomial function was given.
More can be learned about functions at brainly.com/question/24808124
#SPJ1
Lamar drinks 8 fluid ounces of water with breakfast, 6 fluid ounces of water with his vitamins, 16 fluid ounces of water with his lunch, 16 fluid ounces of water with his dinner, and 32 fluid ounces of water from a bottle he carries throughout the day. Write and evaluate a numerical expression for the amount of water in fluid ounces that he drinks in a week.
The required numerical expression for the amount of water in ounces that he drinks in a week is 7× (8+6+16+16+32) ounces and the value is 546 ounces.
Lamar drinks water with,
Breakfast = 8 ounces
Vitamins = 6 ounces
Lunch = 16 ounces
Dinner = 16 ounces
Bottle = 32 ounces
To find A numerical expression for the amount of water in ounces that he drinks in a week.
One day consumption of water by Lamar is
We know that,
1 week = 7 days
One day consumption of water = 78 ounces
1 week (7 days) consumption of water = 7× One day consumption of water
= 7× (8+6+16+16+32) ounces
= 7×78 ounces
= 546 ounces
Therefore, the required numerical expression for the amount of water in ounces that he drinks in a week is 7× (8+6+16+16+32) ounces and the value is 546 ounces.
For more such questions on Numerical expressions
https://brainly.com/question/29239473
#SPJ4
How do you find the intervals on which the function is continuous given y=2(x+4)2+8?
The interval of continuity of the function is continuous given y = 2 (x + 4 ) 2 + 8 is (-∞, ∞).
Function Continuity IntervalsA function is continuous at a point if the function value exists and is finite at that point, and the limit of the function as the input approaches that point from the left and right side is equal to the function value at that point. In other words, the function has no sudden jumps or discontinuities at that point.
In the case of the function y = 2(x + 4)² + 8, the function is defined and continuous for all real numbers x. There are no values of x for which the function is undefined or has a discontinuity, so the function is continuous for all values of x, meaning that the interval of continuity is (-∞, ∞).
Learn more about Function Continuity Intervals here:
https://brainly.com/question/29207581
#SPJ4
14) Determine the base and height of the given parallelogram, and then find the area
The base of the given parallelogram is 11. 8 cm and the height is 6. 5 cm.
The area of the parallelogram is 76. 7 cm ²
How to find the area of a parallelogram ?The base is the dimension of the parallelogram that is shown either at the top or bottom of the shape. In this case, it is 11. 8 cm. The height is the distance from the top to the bottom which is 6. 5 cm in this case.
The area of a parallelogram is:
= Base x Height
= 11. 8 x 6 . 5
= 76. 7 cm ²
Find out more on the area of a parallelogram at https://brainly.com/question/10744696
#SPJ1
multiple QUESTIONS PAY 100 with brainiest
Question 1(Multiple Choice Worth 2 points)
(Circumference MC)
The circumference of a circle is 98.596 millimeters. What is the radius of the circle? Use 3.14 for π.
197.2 mm
49.3 mm
31.4 mm
15.7 mm
Question 2(Multiple Choice Worth 2 points)
(Circumference LC)
What is the circumference of a circle with a radius of 14 feet? Use 22 over 7 for π.
2,464 feet
616 feet
88 feet
44 feet
Question 3(Multiple Choice Worth 2 points)
(Circumference MC)
The diameter of a hat is 4.7 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
1.50 inches
7.38 inches
17.34 inches
14.76 inches
Question 4(Multiple Choice Worth 2 points)
(Circumference MC)
Two restaurants offer customers large pizzas using different measurements for diameter.
Restaurant 1: One large 14-inch pizza for $12.99
Restaurant 2: One large 36.83-centimeter pizza for $12.99
If 1 inch = 2.54 centimeters, what is the length of the crust around the larger pizza, using π = 3.14?
115.65 inches
22.77 inches
43.96 inches
45.53 inches
Question 5(Multiple Choice Worth 2 points)
(Circumference LC)
What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 3 inches
9.42 inches
18.84 inches
28.26 inches
88.74 inches
Question 6(Multiple Choice Worth 2 points)
(Circumference LC)
What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 8 yards
8π yards
4π yards
64π yards
25.12π yards
Question 7(Multiple Choice Worth 2 points)
(Circumference MC)
A soda company would like to replace the label on a can of soda with a radius of 4 and one fourth cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
187 over 14 cm
187 over 7 cm
187 over 56 cm
187 over 28 cm
Answer:
1. D
2. C
3.D
4.D
5.C
6. A
7.B
Round to 2 decimal places *
1 point
An architect is designing a building topped with a hemispherical dome. She
creates a scale model of the building using a scale of 0. 25 inch : 1 foot. In
the scale model, the diameter of the dome is 23. 75 inches.
What will be the circumference, in feet, of the actual dome?
The circumference of the dome will be 149.15 feet or 47.5π feet
A scale is defined as the ratio of the dimensions of an object that is represented as a draft to the real or true dimensions of the object being drafted.
The figure on the left of the ratio sign can represent the size and dimensions of the model with respect to the actual size or dimensions of the object.
On the other way, the figure on the right-hand side represents the actual dimensions and size of the real object.
So, if an object is being drawn with the ratio, of 1cm: 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always represent 1cm in the drawing.
If the object is being drawn by a scale of 5cm: 1cm then the actual size of the object will be increased. After that for every 1cm in the actual dimensions of the object, it can be a 5cm representation in the drawing.
Now, draws a scale of 0.25 inches: 1 foot. If the diameter of the dome is 23.75 inches, then the actual diameter of the dome is:
0.25 inches ------- 1 foot
23.75 inches -------? feet
= 23.75/0.25 × 1
d= 95 feet
so, the real diameter of the dome is 95 feet.
The dome is a hemisphere that is half of a sphere. So, the formula for finding the circumference of a sphere is πd, then the hemisphere will be πd/2. As we know the diameter is 95 feet, and the circumference of the hemisphere =
(π × 95)/2
=47.5π feet
Or
if the value of π = 3.14, then the circumference is calculated as (3.14 × 95)/2 = 149.15 feet
Therefore, the circumference of the dome is 149.15 feet or 47.5π feet.
To know more about circumference:
https://brainly.com/question/15223629
#SPJ4
anet wants to solve the equation y + StartFraction y squared minus 5 Over y squared minus 1 EndFraction = StartFraction y squared + y + 2 Over y + 1 EndFraction. What should she multiply both sides of the equation by?
y
y2 – 1
y + 1
y2 + y + 2
y² - 1 should be multiplied on both sides to solve the equation.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
(y² - 5) / (y² - 1) = (y² + y + 2) / (y + 1)
This can be written as,
y² - 1 = (y + 1) (y - 1)
So,
Multiplying y² - 1 on both sides.
(y² - 1) x (y² - 5) / (y² - 1) = (y² - 1) x (y² + y + 2) / (y + 1)
(y² - 5) = (y² + y + 2) (y - 1)
y² - 5 = y³ + y² + 2y - y² - y - 2
y² - 5 = y³ + y - 2
y³ - y² + y - 2 + 5
y³ - y² + y + 3
Thus,
Multiplying y² - 1 on both sides will solve the equation.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Lamar drinks 8 fluid ounces of water with breakfast, 6 fluid ounces of water with his vitamins, 16 fluid ounces of water with his lunch, 16 fluid ounces of water with his dinner, and 32 fluid ounces of water from a bottle he carries throughout the day. Write and evaluate a numerical expression for the amount of water in fluid ounces that he drinks in a week.
Solve the system of equations for a and b:
The solution to the system of equations in this problem is given as follows:
a = 327.9.b = 0.71.How to solve the system of equations?The system of equations for this problem is defined as follows:
42 = ab^6.15 = ab^9.From the first equation, we have that:
ab^6 = 42
a = 42/(b^6)
a = 42b^(-6).
Replacing on the second equation, we have that the value of b is obtained as follows:
15 = 42b^(-6) x b^9
15 = 42b³
b = (15/42)^(1/3)
b = 0.71.
Then the value of a is obtained as follows:
a = 42 x (0.71)^(-6)
a = 327.9.
More can be learned about a system of equations at https://brainly.com/question/30584901
#SPJ1
If the point (1,a) lies on the line y = 3x - 5, what is the value of a?
Answer:
a = - 2
Step-by-step explanation:
Since the point (x, y) = (1, a) lies on the line, substituting this value of x = 1 should give the corresponding value of y which is a
y = 3x - 5
At (1, a)
a = 3(1) - 5
a = 3 - 5
a = - 2
Answer
What conversion factor fraction is used to convert feet to inches?
OA. 10 inches/1 foot
OB. 1 foot/12 inches.
OC. 1 inch/10 feet
OD. 12 inches/1 foot
SUBMIT
if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is ______.
Answer: Observational
Step-by-step explanation:
If it is a experiment then you can conclude that a variable caused a response
In statistics, correlation refers to the degree to which two variables are related or associated with each other. When the correlation between two variables is close to 1.0, it indicates a strong positive relationship between them. However, it is important to note that this strong correlation does not necessarily imply a cause-and-effect relationship between the two variables, especially in a study where certain conditions may not be met.
A study is a systematic investigation aimed at acquiring knowledge and understanding of a particular phenomenon or subject matter. In order to establish a causal relationship between two variables, certain conditions need to be met, such as the establishment of a temporal sequence, a clear association between the variables, and the elimination of any confounding variables that may influence the outcome. These conditions are essential for any study seeking to establish a cause-and-effect relationship between variables.
In the absence of these conditions, even if the correlation between two variables is close to 1.0, it cannot be concluded that the explanatory variable causes changes in the response variable. This is because correlation does not imply causation. Correlation simply indicates the strength of the association between two variables, but it does not provide information about the direction or the underlying mechanisms of the relationship.
For instance, consider a study examining the relationship between smoking and lung cancer. The study finds a strong positive correlation between smoking and lung cancer, indicating that smokers are more likely to develop lung cancer than non-smokers. However, this correlation alone does not necessarily prove that smoking causes lung cancer. There may be other factors such as air pollution, family history, or genetics that could influence the development of lung cancer.
In summary, the correlation between two variables is a measure of the strength of the association between them. A high correlation does not necessarily imply a cause-and-effect relationship between the variables, especially in a study where certain conditions may not be met. It is important to consider these conditions and rule out other factors that could influence the outcome before drawing any conclusions about the causal relationship between two variables.
For more such questions on Correlation.
https://brainly.com/question/2307214#
#SPJ11
Five students came for after-school tutoring. Lin’s teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems to one of the students. 27 problems were assigned in all. write an equationfor the story the find the number of problems originally assigned by the teacher.
Step-by-step explanation:
you add all the numbers then you can get the answer
Please help me with this Question, EXPLAIN and answer.
p.s I know that the answer is 0.99 but I still need the explanation. :)
AnswerStep-by-step explanation:
.99 is right, you already know.
So first,
8 Down arrow 2
means sqrt8
The 8 goes inside the sqrt and the 2 goes outside (its called an index) but we like never write that 2. Its just a normal square root. If you are using a calculator (I think practically, you must use a calculator) you can find sqrt8. Then
take
sqrt8 UpArrow 6
means (sqrt8)^6
this is 8^3 or on the calculator 512.
Next,
512 SideArrow 500
means 500/512
this is .9765625
Lastly,
.9765625 DownArrow 4
means
4throot(.9765625)
Your calculator might have a 4throot button, but you can use 1/4 power instead because all roots can be written like fraction powers.
When .9765625 is in your calculator screen you can just use the ^ button or x^y button to raise it to the 1/4 power. (Use .25 for 1/4 or use parenthesis on the (1/4) )
(.9765625)^.25
~= 0.99
see image.
find the coordinate of the image of the following
[tex]d( - 5 [/tex]
The coordinate of the image of the point (-3/2, -1/2) under reflection in the x-axis is (-3/2, 1/2).
What is image of a point ?When we want to reflect a point with respect to x-axis, the value of ordinate is negated. Reflection with respect to x-axis does not alter the value of abscissa but the ordinate value changes.
(i) The image coordinates of the point (2, -5) under reflection in the x-axis are (2, 5). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).
(ii) The image of the point (-3/2, -1/2) under reflection in the x-axis has the coordinates (-3/2, 1/2). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).
(iii) The image coordinates of the point (-7, 0) under reflection in the x-axis are (-7, 0). This signifies that the point's x-coordinate remains constant while its y-coordinate remains constant (zero).
To learn more about image of points, visit
brainly.com/question/26642069
#SPJ1
The complete question is: 1. Find the co-ordinates of the images of the following points under reflection in the x- axis:
(i) (2, -5)
(ii) (-3/2, -1/2)
(iii) (-7, 0)
ben and chris start at the same time from places 96miles apart to cycle toward each other, ben at 16mph and chris at 12mph. if ben rests for 1/2 hour on the way, after how many hours will they meet?
Ben and Chris will meet after 3.5 hours.
What is the LCM?The least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Given:
Ben and Chris start at the same time from places 96 miles apart to cycle toward each other,
Ben at 16mph and Chris at 12mph.
The LCM of 12 and 16 is,
= 48.
So, they will meet after 3.5 hours.
Therefore, they will meet after 3.5 hours.
To learn more about the LCM;
https://brainly.com/question/20739723
#SPJ1
how many times is the letter f (any case) in the following? if fred is from a part of france, then of course fred's french is good.
The count of letter f (any case) in ' if fred is from a part of france, then of course fred's french is good', is 8.
A word, phrase, or sentence in which no letter of the alphabet appears more than once is known as a heterogram (from the prefix hetero-, meaning "different," and the suffix -gram, meaning "written"). The same idea has also been denoted by the phrases isogram and nonpattern word.
Language on Vacation: An Olio of Orthographical Oddities, written by Dmitri Borgmann in 1965, mentions the idea, however he refers to it as an isogram. Borgmann asserts that he "introduced" the term "isogram" in a 1985 essay. Although he uses the term "isogram" in the paper itself, he also offers the name "asogram" to prevent confusion with lines of constant value like contour lines.
Learn more about Letter problem:
https://brainly.com/question/27175717
#SPJ4
Find the sum of the squares of the solutions of $x^2-13x+4=0$.
The sum of the squares of the solutions of the mentioned equation is 161.38.
The solution of the given quadratic equations can be calculated through factorization. So, rewriting the equation to factorize it.
x² - 13x + 4 = 0
Based on Dharacharya formula, stated as -
x = - b ± ✓b² - 4ac/ 2a, we get the roots -
x = 12.7 and 0.3
Now, the next formula to solve will be -
x = 12.7² + 0.3²
Taking the square of each number
x = 161.29 + 0.09
Performing addition on Right Hand Side of the equation
x = 161.38
Thus, the required answer is161.38.
Learn more about quadratic equation -
https://brainly.com/question/1214333
#SPJ4
The diameter, D, of a sphere is 8.6 cm . Calculate the sphere's volume, V .
Use the value 3.14 for π , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Evaluate 64 divided [4 multiply (27 — 5 exponand 2)]
Before solving this expressions, you must understand the PEMDAS rule.
Parentheses.Exponents.Divide.Multiply.Addition.Subtraction.This rule must be used to solve this problem.
Answer Step by StepQuestion: 64 ÷[4 ×(27 - 5²)]
According to PEMDAS rule, we start with parentheses.
Step 1: 27-5². 5² = 5x5 = 25. 27 - 25 = 2.The equation is now 64 ÷[4×(2)]
2. Step 2: [4×2] = 4×2 = 8.
The equation is now 64 ÷ 8.
3. Step 3: 64 ÷ 8 = 8.
The answer to 64 ÷[4 ×(27 - 5²)] = 8.
ConclusionThis concludes solving 64 ÷[4 ×(27 - 5²)]. If this helps you, please leave a heart and stars to rate this answer. Leave a comment if you have questions or concerns.
Julie bought g gallons of gasoline for $2.75 per gallon and c cans of oil for $3.35 per can. If she bought 8.4 gallons of gasoline and 7 cans of oil, how much did she spend in all?What expression can be used to determine the total amount julie spent on gasoline and oil?
Answer: The amount Julie spent on gasoline can be calculated as g * $2.75 = 8.4 * $2.75 = $23.10.
The amount Julie spent on oil can be calculated as c * $3.35 = 7 * $3.35 = $23.45.
So, the total amount Julie spent on gasoline and oil can be calculated as $23.10 + $23.45 = $46.55.
The expression to determine the total amount Julie spent on gasoline and oil can be written as g * $2.75 + c * $3.35.
Step-by-step explanation:
The Brunsons had a new concrete patio installed in the shape of a semicircle as shown.
Mr. Brunson wants to cover the patio with concrete sealer. What is the area he will need to cover with concrete sealer? Use 314 for R. Round to the nearest hundredth
if necessary.
Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.
What is area of a circle ?
Area of circle can be defined as product of pi and square of radius .
To find the area of the semicircle, we need to use the formula for the area of a circle, but divide it by 2 since we only have half of a circle. The formula for the area of a circle is:
A = πr²
where A is the area of the circle, and r is the radius.
In this case, we have a semicircle, so we need to use half of the formula:
A = (πr²)/2
We are given that R = 314, so we can substitute that into the formula:
A = (π(314)²)/2
Using a calculator and rounding to the nearest hundredth, we get:
A ≈ 49106.15
Therefore, Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.
To learn more about Area of circle from given link.
https://brainly.com/question/28642423
#SPJ1
g/16 = 16 step by step
Answer:
Below
Step-by-step explanation:
There is only ONE step
g/16 = 16 multiply both sides of the equation by 16
g = 256 Done.
The graph shows a figure and it’s image after a transformation how would you describe this as a rotation
This graph is the rotation of 90° counterclockwise about the origin.
What is Rotation?Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.
We have the three points of the figure in graph as P(-2, 3), T(-3, 5) and J(-4, 4).
A point (x, y) after the rotation of 90° counterclockwise would be the point (-y, x).
P(-2, 3) after the rotation of 90° will be (-3, -2), which is the point P'.
T(-3, 5) after the rotation of 90° will be (-5, -3) which is the point T'.
J(-4, 4) after the rotation of 90° will be (-4, -4) which is the point J'.
Hence the image of the figure is the transformation of rotation of 90° counterclockwise.
Learn more about Rotation here :
https://brainly.com/question/12091224
#SPJ1
Your question is incomplete. The graph of possible figure is given below.
A wheel of cheese has a radius of 7 inches and a height of 3 inches. What is the approximate surface area of this wheel of cheese? Use 3.14 for pi.
The approximate surface area of this wheel of cheese is 437.6 square inches.
As per the given data, a wheel of cheese has a radius of 7 inches.
Radius r = 7 inches.
Also, a wheel of cheese has a height of 3 inches.
Height h = 3 inches
Also, given to consider the value of pi as 3.14.
π = 3.14
Here we have to determine the total surface area (TSA)of the wheel of cheese.
Since the cheese is a cylinder shaped thing.
The formula for the total surface area (TSA) of the wheel:
TSA = 2πr (r + h)
Substituting the values of the variables into the formula, we have
= 2 (3.14)(7)(7 + 3)
= 2 (21.88)(10)
= 2 (218.8)
= 437.6 square inches.
Therefore the total surface area is 437.6 square inches.
For more questions on surface area
https://brainly.com/question/22716390
#SPJ4
ABC Bank is offering to double your money! They say that if you invest with them at 6% interest compounded annually they will double your money. If you invest $500 in the account, how long will it take to double your money.
The number of years that it takes to double your money will be 12 years.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
They say that if you invest with them at 6% interest compounded annually they will double your money. If you invest $500 in the account. Then the equation is given as,
$1,000 = $500 x (1 + 0.06)ⁿ
2 = (1.06)ⁿ
ln 2 = n ln 1.06
n = ln 2 / ln 1.06
n = 11.90
n ≈ 12 years
The number of years that it takes to double your money will be 12 years.
More about the compound interest link is given below.
https://brainly.com/question/25857212
#SPJ1
WILL GIVE BRAINILEST
Answer:
1b
Step-by-step explanation:
The giant kangaroo rat is an endangered species native to California. Each decade, researchers at a nearby university estimate the giant kangaroo rat population in the San Joaquin Desert. The most recent estimate, conducted this year, concluded that there are about 73,000 giant kangaroo rats in the desert. The population is expected to decrease by a factor of 1 3 each decade. Write an exponential equation in the form y=a(b)x that can model the estimated population of giant kangaroo rats in the San Joaquin Desert, y, in x decades.
The exponential equation for the decay of the Kangaroo is written as [tex]y = 73000(\dfrac{1}{3})^x[/tex].
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 most recent estimate, conducted this year, concluded that there are about 73,000 giant kangaroo rats in the desert. The population is expected to decrease by a factor of 1/3 each decade.
The exponential expression can be written as:-
[tex]y = 73000(\dfrac{1}{3})^x[/tex]
To know more about an expression follow
https://brainly.com/question/20359553
#SPJ1
there are 7 train stations. one way ticket indicates a departing station and an arriving station. how many tickets are needed?
There are 7 train stations. One way ticket indicates a departing station and an arriving station. Total 42 tickets are needed.
There are 7 train stations.
One way ticket indicates a departing station and an arriving station.
We have to determine how many tickets are needed.
A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here.
In permutation, the elements must be arranged in a specific order, whereas in combination, the order of the elements is irrelevant.
Generally A permutation is the configuration of objects in a specific manner or order. When dealing with permutation, one should consider both selection and arrangement.
From the question;
n = 7
r = 2
[tex]^{n}P_{r}=\frac{n!}{(n-r)!}[/tex]
[tex]^{7}P_{2}=\frac{7!}{(7-2)!}[/tex]
[tex]^{7}P_{2}[/tex] = 7!/5!
[tex]^{7}P_{2}[/tex] = (7 × 6 × 5!)/5!
[tex]^{7}P_{2}[/tex] = 7 × 6
[tex]^{7}P_{2}[/tex] = 42
To learn more about permutation link is here
brainly.com/question/1216161
#SPJ4
400 students are asked how they travel to school.
45% of the students take the bus to school.
The remaining students travel by car or walk to school.
20 more students walk than travel by car.
How many students walk to school?
Answer:
120 student
Step-by-step explanation:
We know
45% of the students take the bus to school
100% - 45% = 55%
So, 55% travel by car or walk to school
400 x 0.55 = 220 students
So, 220 student travel by car or walk to school
We know
20 more students walk than travel by car
220 - 20 = 200 students
200/2 = 100 students
100 + 20 = 120 students
So, 120 students walk to school