Answer:
To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed, we can use the formula for permutations:
Step-by-step explanation:
Number of permutations = (number of choices for the first digit) x (number of choices for the second digit) x (number of choices for the third digit)
In this case, we have 6 choices for each digit, since we are allowed to repeat the digits. Using the formula, we get:
Number of permutations = 6 x 6 x 6 = 216
Therefore, there are a total of 216 three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed.
However, not all of these will be even. For a number to be even, the last digit must be even, so the last digit can only be 2, 4, or 6. This means that there are 3 choices for the last digit.
Therefore, the total number of even 3-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 366=108.
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CIRCUMFERENCE OF A CIRCLE
Examples
(i) Find the circumference correct to 1 decimal place.
C = 2tr
5m
Answer:
31.4 m
Step-by-step explanation:
(i) Find the circumference correct to 1 decimal place.
The formula is given as:
C = 2πr
Radius = 5m
Hence,
C = 2 × π × 5m
C = 31.415926536 m
Therefore, the circumference of a circle to 1 decimal place = 31.4 m
please help: If ray AD bisects ∠BAC, find each measure:
∠DAC=
∠BAC=
PL=
BD=
∠DAC = 28°
∠BAC = 56°
PL = 20
BD = 31
What is Bisection?Bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
An angle bisector divides an angle into equal angles. If the angle is p°, the two angles made will be (p/2)°. This angle bisector passes through the vertex of an angle.
Example: Consider an Angle ∠ABC = 90°. An angle bisector will cut it into two equal angles of 45° each.
Given, AD bisects ∠BAC
MP = 20
DC = 31
∠BAD = 28°
AD bisects ∠BAC
⇒ ∠BAD = ∠DAC
⇒ ∠DAC = 28°
∠BAC = ∠BAD + ∠DAC
∠BAC = 28° + 28°
∠BAC = 56°
Since, In a figure, sides opposite to the equal angles are also equal
∠BAD = ∠DAC
⇒ BD = DC
⇒ BD = 31
⇒ BD = 31
By the figure,
∠MAP = ∠BAD and ∠PAL = ∠DAC
⇒ ∠MAP = ∠PAL
⇒ MP = PL
⇒ PL = 20
Hence, by the above calculation the measure of ∠DAC = 28°,
∠BAC = 56°, PL = 20, BD = 31.
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A recipe for 3 people uses 150 g of flour. How much flour is needed to
make the same recipe for 6 people? Give your answer in grams (g).
600 g flour is needed to make the recipe which needs 150 g flour for 3 people, for 6 people.
Given that a recipe for 3 people uses 150 g of flour.
We know that the relation between quantity of flour and number of people for whom recipe will be prepared is directly proportional.
So if the number of people will increase so the quantity of flour will be needed more.
The flour needed to make the recipe for 1 people is = 150/3 = 50 g.
The flour needed to make the recipe for 6 people will be = 50 * 6 = 300 g.
Hence 600 g flour is needed to make the same recipe for 6 people.
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The number of plants in a terrarium is given by the function P(c) = -1.2c2 + 4c + 12 where c is the number of mg of plant food added to the terrarium. The amount of plant food that produces the highest number of plants is _____ mg (round to the nearest hundredth).
Answer:
15.33mg
Step-by-step explanation:
Given the number of plants in a terrarium is given by the function
P(c) = -1.2c^2 + 4c + 12
At the hihest number of plants produced, dP(c)/dc = 0
dP(c)/dc = --2.4c + 4
0 = -2.4c + 4
2.4c = 4
c = 4/2.4
c = 1.67
To get the highest number of plant produced, we will substitute c = 1.67 into the original function
P(c) = -1.2c^2 + 4c + 12
P(1.67) = -1.2(1.67)^2 + 4(1.67) + 12
P(1.67) = -3.34668 + 18.68
P(1.67) = 15.33332
Hence the amount of plant food that produces the highest number of plants is 15.33mg (round to the nearest hundredth).
The N71-90 virus will give an infected person a mild rash on their arms once the person has 1 billion of the virus cells in their body. After an initial infection with just one cell, each virus cell will divide into two cells every four hours. After 30 divisions there are 1,073,741,824 cells and the rash starts. Once the rash starts, the immune system kicks in and kills all of the virus cells within an hour. The number of virus cells in the body can be determined using the function where h is the number of hours after infection. If Jolene is infected by one virus cell, how many virus cells will she have after 12 divisions
Jolene will have 4096 virus cells in her body after 12 divisions
Why should we call viruses a cell?Viruses are something more than living or dead, they are both. Maybe we need a new classification of life for them, a life that lives when the environment is favorable and hibernate when it is not.
The function provided to determine the number of virus cells in the body after h hours is 2^h. To find the number of virus cells after 12 divisions, we can plug in 12 for h in the function.
2^12 = 4096.
So, Jolene will have 4096 virus cells in her body after 12 divisions.
Please note that Jolene would not develop a rash after 12 divisions as it would take 30 divisions (120 hours) for the rash to appear.
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A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If X machines are made, then the unit cost is given by the function C(x)=0.6x^2-168x+30,389. What is the minimum unit cost?
Do not round your answer.
Answer: [tex]\$18,629[/tex]
Step-by-step explanation:
Given
The unit cost is given by
[tex]C(x)=0.6x^2-168x+30,389[/tex]
find the derivative of the unit cost and equate it to zero to obtain the minimum value
[tex]C'(x)=0.6\times 2x-168\\\Rightarrow 0.6\times 2x-168=0\\\Rightarrow 1.2x=168\\\\\Rightarrow x=\dfrac{168}{1.2}\\\\\Rightarrow x=140[/tex]
Substitute 140 for [tex]x[/tex] in the cost function, we get
[tex]C(140)=0.6[140]^2-168(140)+30,389\\C(140)=11,760-23,520+30,389\\C(140)=\$18,629[/tex]
Help will mark brainliest if correct!
Write an equation for the line in slope-intercept form.
Answer:
y=4x+2
Step-by-step explanation:
The slope of the line is 4 and the y-intercept (b) is 2.
Hope this helped :)
Mi Morgan i a cience teacher he found that 30% of her 120 tudent are athlete and Mr. Gregory i a math teacher he found that 27 or 15% of hi tudent are athlete
Of the part, the whole, and the percent, a. the exact number of students that are athletes is unknown to Ms. Morgan, which is 36, and b. the total strength of the students is unknown to Mr. Gregory which is 180.
Here we need to know 3 things- the total no. of students each teacher has, the percentage of athletes, and no. of students that are athletes.
a)
As we can see in the case of Ms. Morgan, we know the total strength of the students and the percentage of the students that are Athletes. Hence what we don't know here is the exact number of students that are athletes.
Hence we need to find 30% of 120
= 30/100 X 120
= 36 students.
b)
Here, in Mr. Gregory's case, we know the percentage and the actual number of students that are athletes. Hence, here we don't know the total strength of the students Mr. Gregory has.
Total strength = no. of athletes X 100/percent of athletes
= 27 X 100/15
= 180 students.
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Complete Question
Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his students, are athletes. a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value. b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.
What is the expression 6k + 50.5 equal to? How do you write this equation?
Answer:
[tex] \huge\green{ \mid{ \underline{ \overline{ \tt ♡ ANSWER ♡ }} \mid}}[/tex]
[tex]6k + 50.5 = 0 \\ 6k = - 50.5 \\ k = \frac{ - 50.5}{6} \\ k = - 8.4166..[/tex]
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Identify the applications that involve percentages. SELECT ALL THAT APPLY.
Commission
Original Sale Price
Retirement
Sales Tax
Loans
Income
Income Tax
here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.
How do equations function?To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.
so we have,
John had paid $8.00 an hour and waits tables
Therefore,
In 29 hours, he earns -
[tex]= 40 X 8\\= 320 $[/tex]
Via tups, he earned 210.50$
So, in total he earns
[tex]= 320 + 210.50\\= 530.50 $[/tex]
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Find the area of the kite.
6
2
10
16
A=
square units
Answer:
72
Step-by-step explanation:
The area of a kite is half the product (multiplication) of the diagonals.
Each diagonal has length 12, so A = (1/2)(12)(12) = (1/2)(144) = 72.
Note: You can also find the area by finding the areas of the 4 right triangles. By the way, the diagonals are perpendicular, so all 4 triangles are right triangles.
Area of a small triangle: Area = (1/2)(base)(height) A = (1/2)(2)(6) = 6.
Area of a larger triangle: A = (1/2)(10)(6) = 30
Total area: 2 small triangles plus 2 larger triangles A = 2(6) + 2(30) = 72
GUYS AND GIRLS PLEASE HELP
Answer:
i do not know the answer sorry
Write the expression as the
sine or cosine of an angle.
cos 3x cos x - sin 3x sin x
The solution of the expression will be Cos(3x+x).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Cos 3x os x - Sin 3x Sin xThe solution will be calculated by using the formula:-
Cos(A+B) = (CosA CosB - SinA SInB)
Cos(3x+x). = Cos 3x os x - Sin 3x Sin x
Therefore the solution of the expression will be Cos(3x+x).
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Make q the subject of the formula 2(q + p) = 1 + 5q Give your answer in the form ap-b where a, b and c are all positive integers.
[tex]2(q+p)=1+5q\implies 2q+2p=1+5q\implies 2q+2p-5q=1 \\\\\\ 2q-5q=1-2p\implies q(2-5)=1-2p\implies -3q=-2p+1 \\\\\\ q=\cfrac{-2p + 1}{-3}\implies q=\cfrac{2}{3}p-\cfrac{1}{3}[/tex]
Answer:
Step-by-step explanation: 2(q+p)=1+5q
2q+2p=1+5q
2q-5q=1-2p
-3q=1-2p/:(-3)
q=-1/3+2/3 p
ewan has 48 tiles and 16 blue tiles.
what is the ratio of white tiles to the number of blue tiles?
give the ratio in the simplest form.
Answer:
3 white to 1 blue
Step-by-step explanation:
16 x 3= 48
So each 3:1
How do you find the missing angle of a triangle with all sides?
The missing angle of a triangle where only the measure of all sides are given can be calculated by using the Cosine Law .
What is Law Of Cosine ?
The law of cosine is also known as Cosine Rule. This law is useful in finding the missing information of any triangle.
For example, if you know the lengths of three sides of a triangle , this rule helps to find the angle between the two sides of the triangle.
Let a , b and c be the sides of the triangle and let A , B and C be the angle corresponding to the respective sides .
Then by the Cosine Law the angles are represented as : [tex]CosA = \frac{b^{2} +c^{2} -a^{2} }{2bc}[/tex] ;
[tex]CosB = \frac{c^{2} +a^{2} -b^{2} }{2ac}[/tex] ; [tex]CosC = \frac{a^{2} +b^{2} -c^{2} }{2ab}[/tex] .
Therefore , The Law Of Cosines is used to find the missing angle .
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heyy! i’ll give brainliest please help.
Answer: D
Step-by-step explanation:
Answer:
It would be answer c.
Step-by-step explanation:
When elevation is higher, there is less air pressure, which causes air molecules to spread out, and when its spreads out temperature decreases.
At a lower altitude, it is more humid because air molecules are more compact, which causes the temperature to be warmer, so the answer is c.
How do you tell if a graph is linear quadratic or exponential?
A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.
To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.
For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:
y = mx + b
3 = m*2 + b
7 = m*5 + b
Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.
A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.
For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:
y = ax^2 + bx + c
6 = a*1^2 + b*1 + c
13 = a*2^2 + b*2 + c
24 = a*3^2 + b*3 + c
Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.
An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.
For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:
y = a*b^x
16 = a*b^2
24 = a*b^3
Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.
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The foundation for a new high school building is rectangular in shape, and the area is [tex]5x^3 + 4x^2 - 10x - 8[/tex] square meters. Factor by grouping to find expressions for the dimensions of the building
The dimensions of the building are (x² - 2)(5x + 4). The result is obtained by using the expression for the dimensions.
How to factor by grouping?Grouping is a specific technique used to factor polynomial equations. You can use it with quadratic equations and polynomials that have four terms. The method is slightly different.
Here is how to factor by grouping:
Look at the equation and find the master product (ac).Find the factors of ac that the sum is equal to b.Split the center term into two factors.Group the terms to form pairs.Factor out each pair and factor out the shared parentheses.The area of the new high school building in a rectangular shape is 5x³ + 4x² - 10x - 8. Factor by grouping to find the dimensions!
Follow the steps on how to factor by grouping.
5x³ + 4x² - 10x - 8
= (5x³ + 4x²) - (10x - 8)
= x²(5x + 4) - 2(5x - 4)
= (x² - 2)(5x + 4)
Hence, the dimensions of the building are (x² - 2)(5x + 4).
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What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created
Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
As we know that,
(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.
(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.
Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
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Please help me with the question!
Answer:
i think 45 but im not to sure
Step-by-step explanation:
Answer:
c i think or it might be a
Step-by-step explanation:
Frankie enlarged the size of a rectangle to a height of 20 cm. What is the new width if it was originally 2 cm wide and 4 cm tall
Answer: 10
Step-by-step explanation:
4 to 20 which is times by 5 so 2 times by 5 is 10
Marking brainliest help please
Answer:
maybe the answers are: no, yes, yes.
Step-by-step explanation:
not too sure but I hope this helps and is right :)
i am incredibly sorry if my answers are wrong!
Answer:
A. No B. Yes C. Yes
Step-by-step explanation:
A. No
B. Yes
C. Yes
(PLEASE HELP AS SOON AS POSSIBLE)
Answer:
G
Step-by-step explanation:
The origin in a graph is the point (0, 0) where x and y are both 0. If you move 4 units left, x is -4. And if you go down 2 units, y is -2. So the ordered pair would be (-4, -2)
opt G. (-4,-2)
I don't know...
If a car's gas tank has 15 gallons of gas in it, and the gauge says the tank is 75% full, then how many gallons can the entire tank hold?
12
20 gallons
24
11.25
Answer:
20 gallons
Step-by-step explanation:
set up proportion
15/x=75/100
cross multiply
75x=1500
x=20 gallons
Find the area. The figure is not drawn to scale. Show work
Answer:
13.8 square feet
Step-by-step explanation:
To find the area of a triangle you use the formula a = 1/2 bh
a = 1/2 (6.9) (4) = 13.8
(simplier to understand) a = 1/2 (6.9) (4) = 27.6 divided by 1/2 = 13.8
A population of 210,000 people is increasing by 15% each year. How much will the population be in 5 years?
According to the compound interest formula, the population is 5 years is 422,385.
The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Here we have given that the population of 210,000 people is increasing by 15% each year.
And then while looking into the given question, we have identified that the value of
interest rate = 15%
principal count = 210,000
time period = 5
Here we have to convert R as a percent to r as a decimal, then we get
=> r = R/100
=> r = 15/100
=> r = 0.15 rate per year,
Now, we have to solve the equation for A
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Apply the values on it , then we get,
[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]
When we simplify this one then we get
[tex]A = 210,000.00(1 + 0.15)^5[/tex]
Therefore, the value of A is 422,385.
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En un garaje hay 31 vehículos entre automóviles y motocicletas. Se cuentan 98 ruedas en total. ¿Cuántos automóviles y cuántas motocicletas hay?
Answer:
129
Step-by-step explanation:
The graph represents an object that is shot upwards from a tower and then falls to the ground. The independent variable is time in seconds and the dependent variable is the object’s height above the ground in meters.
A How tall is the tower from which the object was shot?
B When did the object hit the ground?
C Estimate the greatest height the object reached and the time it took to reach that height. Indicate this situation on the graph.