There are 120 different ways the people can line up
How to determine the number of ways?The number of people that arrived is:
n = 5
Take the factorial to calculate the number of ways they can line up
n! = 5!
Expand
n! = 5* 4 * 3 * 2 * 1
Evaluate
n! = 120
Hence, there are 120 different ways the people can line up
Read more about permutation at:
https://brainly.com/question/11732255
#SPJ1
can you show me how can i solve sin(pi/2-x)=1/2??
By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and
[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].
What are trigonometric Identities?Trigonometric Identities exist as the equivalencies that apply trigonometry operations and have true for all the values of variables shown in the equation. There exist different trigonometric identities concerning the side length as nicely as the angle of a triangle.
How to simplify the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]?
Given:
[tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]
General solution for [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]
then from the general equation, we get
[tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] and
[tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]
Solve [tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] then [tex]$x= -2n\pi +\frac{\pi}{3}[/tex]
Solve [tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]then [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]
Therefore, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]
Radians, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]
Degree, [tex]$x = 60 \degrees- 360\degree n[/tex], [tex]$x = -60\degree- 360\degree n[/tex]
By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and
[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].
To learn more about trigonometric Identities refer to:
https://brainly.com/question/7331447
#SPJ9
someone help for easy points
Answer:
First one
Step-by-step explanation:
First one ....pick a point ....say C for 'x' add 8 for y subtract 3 and you will be at C'
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height(y), in mm, to which it grows:
Y=2+4x
What does the y- intercept of this function represent?
the original height of the plant was 2mm. The correct option is the second one.
What does the y-intercept of the function represent?
We know that the function:
y = 2 + 4x
Represents the height of a plant in mm, as a function of x, the hours kepts in sunlight.
The y-intercept is the value that y takes when we evaluate in x = 0.
So, the y-intercept is the height of the plant when it is exposed to zero hours of light.
In this case:
y = 2 + 4*x
Evaluating in x = 0
y = 2 + 4*0 = 2
This means that the original height of the plant was 2mm. The correct option is the second one.
If you want to learn more about y-intercepts:
https://brainly.com/question/1884491
#SPJ1
Following the recommended steps for solving equations, what should be your first step in solving the given
equation?
2x-3-4x-2x = -6
A. add 3 to both sides
B. subtract 4x from 2x
C. add 6 to both sides
D. add 4x to 2x
Answer:
The first step in solving the equation should be to add 3 to both sides.
Step-by-step explanation:
Adding 3 to both sides will cancel out the -3 on the left hand side of the equation, leaving only the 2x term. On the right hand side, adding 3 will cancel out the -6, leaving only 0. This will give you the equation 2x = 0, which is much easier to solve.
For the function q(x) =10 times rootindex 5 startroot x minus 2 endroot, what is the inverse function?
Hence, the inverse of the given function is [tex]{(\frac{x}{10})}^5 - 2[/tex]
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.
How to solve?given function,
q(x) = 10[tex]\sqrt[5]{x-2}[/tex]
say y=q(x)
now we have,
y = 10[tex]\sqrt[5]{x-2}[/tex]
[tex]\frac{y}{10}[/tex] = [tex]\sqrt[5]{x-2}[/tex]
raising to 5th power on both sides,
[tex](\frac{y}{10})^5[/tex] = x - 2
x = [tex](\frac{y}{10})^5[/tex] + 2
[tex]q^{-1}(x) =[/tex] [tex]{(\frac{x}{10})}^5 - 2[/tex]
to learn more about functions: https://brainly.com/question/25638609
#SPJ4
. Describe the transformation of the function, y = x + 4, from y = x.
There are two interpretations we could go for:
Adding 4 to the end means we add 4 to each y coordinate (since y = x). This shifts the entire line 4 units upReplacing x with x+4 means the xy axis is shifted 4 units to the right. If the line y = x is held completely still while the axis moves, then it gives the illusion the line is moving 4 units to the leftCheck out the diagram below.
Point A on the red line y = x has two locations it could end up. If we follow method 1, then point A shifts upward to point B. Do this to every point on the red line and the entire red line shifts up 4 units.
Or if you decide to shift 4 units to the left (method 2), then point A moves to point C's location. Doing this to every point on the red line shifts the entire line 4 units to the left.
Using the image, find the distance between the points given on the graph. Distance =√
Answer:
I think 5m is the correct answer
Answer:
Hello! The answer to your question is [tex]\sqrt{29}[/tex], or approximately 5.39.
Step-by-step explanation:
(Two methods)
Method 1:
To solve this problem, we will use the Pythagorean theorem. To create the triangle, you can connect all the points with lines. This will leave you with the base of the triangle as 2 and the leg as 5. We do not know the hypotenuse. Now, we can use the Pythagorean theorem formula:
[tex]a^2 + b^2 = c^2[/tex]
[tex]\sqrt{2^2 + 5^2 } \\= \sqrt{4 + 25} \\= \sqrt{29}\\or 5.39[/tex]
Now, we can substitute our values:
Method 2:
To solve this problem, we will use the distance formula:
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
Our points are:
A(-3, 1) and B(-1, -4)
Now, we substitute our values into the distance formula provided:
[tex]\sqrt{(-1 - (-3))^2 + (-4 - 1)^2} \\= \sqrt{(-1 + 3))^2 + (-5)^2} \\= \sqrt{(2)^2 + (-5)^2} \\= \sqrt{4 + 25} \\= \sqrt{29} \\or 5.39[/tex]
The number is between 8,500 and 8,800.
When multiplied by 8, the result is a whole number.
The digit in the hundreds place is ¾ the digit in the thousands place.
The sum of all digits in the number is 26.
The digit in the hundredths place is 200% of the digit in the tenths place.
There are no zeros in the decimal places.
Your first job is to post at least two numbers that do NOT work.
Explain why they do not work.
Post your best guess for a number that works (or a number that almost works)
choose the equation below that represents the line passing through the point (-2,-3) with a slope of -6
The equation of the line is: y + 3 = -6(x + 2) [point-slope form] or y = -6x - 15 [slope-intercept form].
How to Write the Equation of a Line?Given a point (-2, -3) and a slope (m) of -6, you can write the equation of the line in point-slope form by substituting (a, b) = (-2, -3) and m = -6 into y - b = m(x - a):
y - (-3) = -6(x - (-2))
y + 3 = -6(x + 2) [point-slope form]
Rewrite in slope-intercept form as:
y + 3 = -6(x + 2)
y + 3 = -6x - 12
y = -6x - 12 - 3
y = -6x - 15 [slope-intercept form]
Learn more about the equation of a line on:
https://brainly.com/question/13763238
#SPJ1
Calculate the volume of a cylinder of radius 5cm and height 14cm (take pie 22/7)
Answer:
Volume of a cylinder = 1,100cm³
Step-by-step explanation:
Volume of a cylinder = πr²h
Given
π = 22/7
r = 5cm
h = 14cm
Substitute the given information in the problem.
Volume of a cylinder = 22/7 × (5cm)² × 14cm
Volume of a cylinder = 22/7 × 25cm² × 14cm
Volume of a cylinder = 1,100cm³
Erica earned a total of $15,450 last year from her two jobs. the amount she earned from her job at the store was $1250 more than four times the amount you earn from her job at the college how much. how much does he earn from her job at the college
If Erica earned a total of $15450 last year from both the jobs then he earns $2840 from college if she earned 1250 more than four times the amount from college from store.
Given Total amount earned=$15450,Amount earned from store is 1250 more than 4 times earned from college.
Amount from store forms an equation.
let the amount earned from college is x.
According to question:
Amount earned from store=4x+1250
Amount earned from college=x
Total amount earned=4x+1250+x
5x+1250=15450
5x=15450-1250
5x=14200
x=14200/5
x=2840
Put the value of x in 4x+1250 to get amount earned from store=4(2840)+1250=$12610.
Hence the amount earned by Erica from college is $2840.
Learn more about equation at https://brainly.com/question/2972832
#SPJ4
A house has increased in value by 37% since it was purchased. If the original value was $720, 000, what is the value after the increase? A house has increased in value by 37 % since it was purchased . If the original value was $ 720 , 000 , what is the value after the increase ?
Answer:$986,4000
Step-by-step explanation:
A pair of dice are tossed twice.Find the probability that both rolls give at most a sum of 8.
the probability that in bot rolls we have a sum of, at most, 8, is:
P = 47/ 1,296 = 0.036
How to find the probability?The pair is tossed twice. A pair of dice has 36 possible outcomes, so if we toss twice the pair, the total number of outcomes is:
36*36 = 1,296
Now if we define the outcomes as:
{dice 1 (roll1), dice2(roll1), dice 1 (roll2), dice2(roll2) }
The outcomes that give at most a sum of 8 are:
{1, 1, 1, 1}
{2, 1, 1, 1} ( 3 permutations)
{2, 2, 1, 1} ( 6 permutations).
{2, 2, 2, 1} ( 3 permutations)
{3, 1, 1, 1} ( 3 permutations)
{3, 2, 1, 1} ( 12 permutations)
{3, 3, 1, 1} (6 permutations)
{4, 1, 1, 1} (3 permutations)
{4, 2, 1, 1} (6 permutations)
{5, 1, 1 , 1} (3 permutations)
{2, 2, 2, 2}
These are all the outcomes that give a sum of, at most, 8.
If we add all the outcomes we get 47 outcomes.
Then the probability that in bot rolls we have a sum of, at most, 8, is:
P = 47/ 1,296 = 0.036
If you want to learn more about probability:
https://brainly.com/question/25870256
#SPJ1
what are the coordinates of the point hat is 2/3 of the way from A to B?
Answer:
A. (2,3)
It is rather simple the 9 points between a and B 2/3 of that is 6
Given: AD ~ BC and AD
BC
Prove: ABCD is a parallelogram.
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
.
Step-by-step explanation:
A parallelogram has two pairs of parallel lines so if AD // BC and that AD//BC, Then it is indeed a parallelogram
please helpppppppppp thanks!
Answer:
First one is false. (You are correct)Second is true. (a will be greater than 0)Third is also false. (a can't be equal to 0)Hope it helps!!
Answer:
[tex]a < 0[/tex] False
[tex]|a| > 0[/tex] True
[tex]|a|=0[/tex] False
________________________________________________
a is on the right side of 0,
which means a is positive.
The absolute value is the distance to zero (always positive)
Which means the absolute value of a is also positive.
[tex]a < 0[/tex] is wrong because a is positive
[tex]|a| > 0[/tex] is correct because a is larger than 0
[tex]|a|=0[/tex] is wrong because [tex]a[/tex] ≠ [tex]0[/tex]
________________________________________________
Hope this helps :)
[tex]\frac{n}{4} =\frac{k}{x} / n = 15/ k = 60[/tex]
Using proportions, the value of x is given as follows: x = 16
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
We are given this following proportion:
[tex]\frac{n}{4} = \frac{k}{x}[/tex]
In this problem, we have that n = 15 and k = 60, hence:
[tex]\frac{15}{4} = \frac{60}{x}[/tex]
Applying cross multiplication:
15x = 60 x 4
Simplifying by 15:
x = 4 x 4
x = 16.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Use the function below to find F(3).
Answer: B
Step-by-step explanation:
Plug in x for 3. Then solve.
4*(1/3)^3
4*1/9
4/9
write this ratio as a fraction in simplest form without any units. 3 pounds to 54 ounces
The ratio of the measurements written as a fraction is 8/9.
What are the ratios written as fraction?A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.
In order to convert the ratio to fraction, the units of measurements have to be the same. So, pounds would be converted to ounces.
3 x 16 = 48 ounces
48 / 54 = 8/9
To learn more about fractions, please check: https://brainly.com/question/25779356
#SPJ1
factor the following expression
28w^(4)x^(2)y^(7)+12w^(9)x^(8)
The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)
What is an Expression ?An expression is defined as a mathematical statement consisting of variables , constants and mathematical operators.
The expression given is
28w⁴x²y⁷+12w⁹x⁸
Factors of the given expression will be the common terms in both the terms
w⁴x² is common in the variable term
The HCF of 28 and 12 is 4
4w⁴x² (7y⁷ + 3w⁵x⁶)
The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)
To know more about Expression
https://brainly.com/question/14083225
#SPJ1
Dante wrote several equations and determined that only one of the equations has infinitely many solutions. which of these equations has infinitely many solutions? 6 (x 3) x = 7 x 2 1 6 (x 3) x = 7 x 5 6 (x 3) x = 6 x 3 15 6 (x 3) x = 7 x 9 9
Among all the given equations 6(x+3)+x=7x+9+9 is having many solutions.
Given Equations :
6(x+3)+x=7x+2+1
6(x+3)+3=7x+5
6(x+3)+x=6x+3+15
6(x+3)+x=7x+9+9
We have to find the equation having many solutions.
The equation whose both sides are equal to each other is supposed to have many solutions. For determining all equations needs to be solved.
Equation 1
6(x+3)+x=7x+2+1
6x+18=7x+3
No the above equation is not having many solutions.
Equation 2
6(x+3)+3=7x+5
6x+18+3=7x+5
6x+21=7x+5
No the above equation is not having many solutions.
Equation 3
6(x+3)+x=6x+3+15
6x+18+x=6x+18
7x+18=6x+18
No the above equation is not having many solutions.
Equation 4
6(x+3)+x=7x+9+9
6x+18+x=7x+18
7x+18=7x+18
Yes the above equation is having many solutions.
Hence the equation which is having many solutions is 6(x+3)+x=7x+9+9.
Learn more about equations at https://brainly.com/question/2972832
#SPJ4
The options given in the question are wrong and the correct options are as under:
1) 6(x+3)+x=7x+2+1
2)6(x+3)+x=7x+5
3)6(x+3)+x=6x+3+15
4) 6(x+3)+x=7x+9+9
What is the definition of quantum physics?
Answer:
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space.
50 POINTS, I NEED IT QUICK PLSS
The thing that's wrong with the equation is that 2 shouldn't be multiplied by 4 but should have been added.
How to illustrate the information?From the information given, it can be seen that the equation is:
(3x²)(-2x⁴) = 3(-2)x² × x⁴ = 6x^8
Based on the information above, this calculation is incorrect. The correct calculation will be:
(3x²)(-2x⁴) = 3(-2)x² × x⁴
= -6x^6
Therefore, the multiplication should be an addition of the power.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Practice Problems
1. The absolute value of a number is its distance from 0 on the
number line (no sign, just value). Compare the absolute value of
7 and -7.
Answer: The absolute values of 7 and -7 are equal because they are both a distance of 7 units from 0 on the number line.
A 16 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 6 feet from the base of the tree. The base of the tree and the ground form a right angle. What is the distance, in feet, between the ground and the top of the ladder? Round your answer to the nearest tenth.
Answer:
14.8 feet
Step-by-step explanation:
since this is creating a right triangle you can use the Pythagorean theorem which is a^2 + b^2 = c^2, and by plugging in the one leg length and the hypotenuse length you get 14.8324 which rounds up to 14.8
The distance between the ground and the top of the ladder is 14.8 feet.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Given:
Hypotenuse= 16 foot,
Base = 6 feet
Using Pythagoras theorem,
H² = B² + P²
16² = 6² + P²
256 = 36 +P²
P² = 256-36
P= 14.83 feet
Hence, the distance between the ground and the top of the ladder is 14.8 feet.
Learn more about Pythagoras theorem here:
https://brainly.com/question/21926466
#SPJ2
Find f(5) for f(x)=1/4(2)^x
A. 2
B. 4
C. 32
D. 8
Step-by-step explanation:
The value of X is given so put the value of X in 1/4 (2)^x
a student was given the following daigram and asked to prove that <1= <2 what would be the reason for the final step in the proof given line A and Line B are parallel prove <1=<2
The correct option based on the paralel line given is that the corresponding angles are congruent.
How to illustrate the information?Given that a student was told to consider the diagram and asked to prove that angle 1 ≅ angle 2.
We are to find the reason for the second step in the following proof. Since lines A and B are parallel and cut by a transversal, so angles 1 and 3 are corresponding angles. That is, ∠1. ≅ ∠3
Also, angles 2 and 3 are vertically opposite angles, so ∠2 ≅ ∠3.
And, therefore we get ∠1 ≅ ∠2.
Thus, the reason in the second step will be angles 1 and 3 are corresponding angles and corresponding angles are congruent.
Learn more about parallel lines on:
https://brainly.com/question/2141319
#SPJ1
The function g(x)=8(4x) is reflected across the x-axis to create f(x) What is the equation of f(x)?
Answer:
g(x)=-32x
Step-by-step explanation:
When something is reflected over the x-axis. The x doesn't change, it's the y that changes. So let's just generally say you have the point (x, y). Reflecting this over the x-axis means the y is changing, so it becomes (x, -y). And since the g(x) represents the y, you multiply the entire thing by -1. So the new equation becomes: g(x) = -(8(4x)) = -8(4x) = -32x. So the equation is g(x) = -32x or -8(4x) if you want to leave it like how it was before.
Using the model from the example above, where f(x)=10001+999e−0.6030x, estimate the number of cases of flu on day 15. Remember that answers should be rounded to the nearest whole number.
The number of cases of flu on day 15 will be 1001 flus
Exponential functions are expressed as y = ab^x
Given the expression below
[tex]f(x)=10001+999e^{-0.6030x}[/tex]
In order to determine the number of cases of flu on day 15, we will substitute x = 15 into the expression to have:
[tex]f(x)=10001+999e^{-0.6030(15)}\\f(x)=10001+999e^{-9.045}\\f(15) = 10001+0.11786\\f(15) \approx 10001[/tex]
Hence the number of cases of flu on day 15 will be 1001 flus
Learn more on exponential function here: https://brainly.com/question/2456547
#SPJ1
Answer:
Step-by-step explanation:
Evaluate the function for the value x=15.
f(x)f(15)f(15)=10001+999e−0.6030x=10001+999e−0.603(15)≈894.565217
Rounded to the nearest whole number, there will be 895 cases on day 15.
The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of length fraction 1 over 7 unit and width fraction 1 over 2 unit?
fraction 1 and 1 over 7 units
fraction 1 and 2 over 7 units
fraction 4 over 9 unit
fraction 2 over 9 unit
The perimeter of the rectangle is 1 1/7 units
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is given as:
P = 2(l + w)
Given the following
length. = 1/7 units
width = 1/2 units
Substitute
P = 2(1/7 + 1/2)
P = 2(9/14)
P = 9/7 = 1 1/7
Hence the perimeter of the rectangle is 1 1/7 units
Learn more on perimeter of rectangle here: https://brainly.com/question/19819849
#SPJ1