There are 24 ways for Alice, Bob, and Charlie to buy pets and leave the store satisfied. They could each buy a puppy, a kitten, and a hamster, or they could each buy a different combination of the three types of pets.
How many different pet options can Alice, Bob, and Charlie choose from before feeling satisfied?Alice, Bob, and Charlie can leave the pet store satisfied in 12 different ways.This can be shown using a combination equation, where n = the number of items (in this case, pets) and r = the number of selections (in this case, 3): C(n,r) = n! / (r! × (n - r)!). In this equation, n = 29 (15 puppies + 6 kittens + 8 hamsters) and r = 3 because Alice, Bob, and Charlie each have to select one pet.When plugging these numbers into the equation, the result is C(29,3) = 29! / (3! × (29 - 3)!) = 29! / (3! × 26!) = 8649 / 514880 = 12 different ways. Alice, Bob, and Charlie can each select a puppy, a kitten, and a hamster and leave the store satisfied in 12 different ways.Alice, Bob, and Charlie can buy pets and leave the store satisfied in 6 ways. Step 1: Alice can buy a puppy, Bob can buy a kitten, and Charlie can buy a hamster. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 2: Alice can buy a kitten, Bob can buy a hamster, and Charlie can buy a puppy. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 3: Alice can buy a hamster, Bob can buy a puppy, and Charlie can buy a kitten. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 4: Alice can buy a puppy, Bob can buy a hamster, and Charlie can buy a kitten. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 5: Alice can buy a kitten, Bob can buy a puppy, and Charlie can buy a hamster. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 6: Alice can buy a hamster, Bob can buy a kitten, and Charlie can buy a puppy. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. In sum, Alice, Bob, and Charlie can buy pets and leave the store satisfied in 6 ways. Each person can buy a different kind of pet and the store will still have the same number of pets afterwards.To learn more about the combination theory refer to:
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Solve for x in this triangle. Round your answer to the nearest tenth. 17 х° 6
Answer:
x ≈ 70.6°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{6}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to the nearest tenth )
A sequence of 3 transformations is applied to the L-shaped
figure to produce the image shown on the coordinate plane.
The 3 transformations, in no particular order, are:
A) translation 9 units to the left and 4 units down
B) reflection in the x-axis
C) rotation of 90 degrees counter-clockwise rotation about
the origin
What is the correct order in which to apply these
transformations in order to produce the given image?
Answer:
BCA
Step-by-step explanation:
How do you tell if a system of equations has no solution or infinitely many?
If you solve the equation and get the same number as yourself, there are infinite solutions, and if you get the wrong equation, there is no solution.
Without graphing, how can you determine if a system of equations has one solution or an infinite number of solutions?You can see that both slopes are the same (-3). This shows that the lines are parallel without creating a graph. Therefore, the system of equations cannot be solved.
What distinguishes infinitely many solutions from zero? If the equation is wrong, the system has no solution. If the equation statement is true, there are infinitely many solutions.
A linear algebra problem is a linear system of n equations with n unknown variables. A system may have one solution, no solution, or an infinite number of solutions.
solution - all linear equations intersect or intersect at some point in space
No Solution - System is inconsistent and not all linear equations intersect or intersect.
Infinitely many solutions - some linear equations are the same line in space, some variables are unbounded.
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20, 70, 110, 140, 160, ___ what’s the next sequence?
Answer:
D (i hope)
Step-by-step explanation:
When you minus the highest to the lowest it is added by 10 so
160-140= 20
140-110=30
110-70= 40
70-20= 50
I had added 10 to 160 and got 170
Listen ducky:
160-140=20
140-110=30
110-70=40
70-20=50
20+30+40+50+10 (we need to add 10 on every part because of the question), so 10+10+10+20+30+40+50=170
The answer is D, my dear duck
Kira needs 3,000 milligrams of zinc for a science experiment.
Which expression can be used to determine how many grams of zinc she needs?
A.
1000
÷
3000
B.
1000
×
3000
C.
3000
÷
1000
D.
3000
×
100
Answer:
3 grams
Explanation: To solve you have to divide the mass value by 1000.
3000/1000=3 Grams
I hope this helps :)
Find the surface area and round to the nearest hundredths place when necessary.
Answer:
Let's find the area of 1 triangle (this may not be the formula but I'm doing it in a more easier way).
20(base) x 10.5(height) = 210
210 divided by 2 ( x 1/2) = 105
Since there are 4 sides we must multiply the area of 1 triangle four times! Since there are 4 sides of triangles.
105 x 4 = 420
Oh and I almost forgot! We need to find the area of the square below!
20 x 20 = 400!
Now we add both areas of all the triangles and the area of the bottom square:
420 + 400 = 820 in2 is your answer. (we use the unit 2 since we are finding areas and adding them up)
Formula of a triangle:
BH x 1/2
B(base) x H(height) x 1/2 (basically just dividing by 2)
Find the final price or each product after sales tax is applied. Round to the nearest cent. Potted Plant: $17.29 Sales Tax: 3%
Answer:
17.81 would be your answer.
Step-by-step explanation:
You would do 17.29 x 1.03 to get the price after sales tax is added which would be 17.81
Think back to the pyramids in Egypt. For a Social Studies project, you created a scale figure of one pyramid. The dimensions are shown. How much paint will you need to paint the entire pyramid for your project?
The surface area of the pyramid is 568 square inches.
What is the surface area of a square pyramid?The surface area of the square pyramid is defined as the total area covered by the surfaces required to make the square pyramid. The area is the space occupied by the square pyramid in two-dimensional planes.
The formula to calculate surface area will be calculated by the formula below,
SA=B+12(P × l)
Here, B is the area of the base, P is the perimeter of the base, and l is the slant height.
SA = ( 8 x 8 ) + 12 ( 8 x 4 + 10 )
SA = 64 + 12 ( 32 + 10 )
SA = 64 + 12 x 42
SA = 568 square inches
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NEED HELP ASAP!!! GIVING BRAINLIEST
Answer:
Step-by-step explanation:
Can anyone me help PLEASE
Answer: (0, 1), (2,3), (x,x), (-5,x) (I put x's in for the missing numbers)
Step-by-step explanation: Hope this helps!!
Here is the graph:
If you vertically stretch the exponential function, f(x) = 2%, by a factor of 3,
what is the equation of the new function?
A. g(x) = • 2*
B. g(x) = 3.2%
C. g(x) = 2.3%
D. g(x) = 23x
If you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x
Exponential functionThe standard exponential function is expressed as:
y = ab^x
The value of x determines the nature of a graph whether vertical or horizontal stretch.
If x > 1, it is a vertical stretch
Given the function f(x) = 2^x, if you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x
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PLEASE HELP ASAP
Combine like terms
8x + 3 - 5x + 9
Answer: B
Step-by-step explanation: [tex]8x-5x=3x\\3+9=12\\[/tex]
Hope this helps any
Answer:
B. 3x+12
Step-by-step explanation:
8x+3-5x+9
First combine the x. So, 8x-5x=3x
Next combine the 3 and the 9. So, 3+9=12
After you combined like terms your equation now looks like: 3x+12
Hope it helped you.
what are the leading coefficient and degree of the polynomial? 3u-5u^6+9u^3.
HELP!
Answer:
-5, 6
Step-by-step explanation:
Since 6 is the highest power, it is the degree, and so we also take the coefficient of that term.
HELP PLEASE 10 POINTS!
pls explain
a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
Answer:
a) 400% b) 1/4 c) 64
Step-by-step explanation:
Answer:
a. 400%
b. 25
c. 64
Step-by-step explanation:
a. 160 ÷ 40/100
160 × 100 / 40
4 × 100 = 400%
b. 40 ÷ 160%
40 ÷ 160/100
40 × 100/160 = 25
c. 40% × 160
40/100 × 160
4 × 16 = 64
can someone help me with this but please with details on how u got the answer:
The function’s average rate of change over the interval from x: 1 to x:2 is:
The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
We have the interval from x = 1 to x = 2.
To find the function’s average rate of change over the interval from x = 1 to x = 2 is:
We interpreted the interval in the coordinate form.
The curve from (1, 2) to (2, 0) is a straight line.
And the slope of the line is the average rate of change of the function.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (0-2) / (2-1)
m = -2/1
m = -2
Therefore, the average rate of change is -2.
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m∠A =
, m∠B =
, m∠C =
Rhombus ABCD has a diagonal BD¯¯¯¯¯.
m∠ADB=(6x−7)°
m∠CDB=(5x+5)°
What is the m∠ADC ?
Enter your answer in the box
The function f is defined by f(x) = x^2 + 3x - 10. If f(x-2) = x^2 + bx + c, what are the values of b and c?
______________________________
When you put the answer could you put the steps that you took, so I could use it on other problems
Thanks
Distributive Property
Factoring
FOIL (First Outside Inside Last)Functions
Function NotationApplicationStep 1: DefineLet's organize what is given to us in the problem.
We are given a function f, defined as f(x) = x² + 3x - 10.
We are asked to find the values of b and c in f(x - 2) = x² + bx + c.
Step 2: SolveIn order to solve the question, we first must find the full function of f(x - 2):
[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]
∴ [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]
Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:
[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]
∴ we have found the values of b and c.
Answer∴ the value of b is equal to -1 and the value of c is equal to -12.
___
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___
Topic: Algebra I
Unit: Factoring
Simplify using only positive exponents:
(2h^7v^-3)/(5h^-4v^5)^-5
Therefore the expression simplified using only positive exponents is 10h^4v^22.
Define positive exponents.An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.
Define multiply and divide.A mathematical procedure called multiplication shows how many times a number has been added to itself. The multiplication symbol (x) or (*) are used to denote it. A mathematical process that shows how many equal amounts add up to a given number is called division.
To simplify the expression using only positive exponents, we need to make sure that all the exponents are positive.
We can simplify the expression:
(2h^7v^-3)/(5h^-4v^5)^-5
= (2h^7v^-3)/(1/(5h^-4v^5)^5)
= (2h^7v^-3) * (5h^4v^25)
= 10h^4v^22
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help meeee i keep confusing myselffff
Answer:
Its D
Step-by-step explanation:
Learning
Diagnostic
Analytics
See your levels
Miss Wu has 535 gold stickers. She wants to give the same number of stickers to each of her
8 students. If she gives away as many stickers as she can, how many stickers will be left
over?
stickers
Submit
rostimonials Contact us rooms of sorton erivacy polley
Please help quick
Answer:
13
Step-by-step explanation:
Speedometer readings for a motorcycle at 12-second intervals are given in the table.
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.
ft
(b) Give another estimate using the velocities at the end of the time periods.
ft
(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
O (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
O (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t.
O (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
(a) The distance traveled by motorcycle is 1548 ft.
(b) The distance traveled by motorcycle is 1512 ft.
(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.
Given table is:
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:
12(30 + 28 + 25 + 21 + 25)
=12 × 129
= 1548 ft
The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:
12(28 + 25 + 21 + 25 + 27)
=12 × 126
= 1512 ft
The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.
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Please help with the attached question :))
Answer:
6.5 cm
Step-by-step explanation:
Given the perimeter is 33 cm
Sum the 4 sides and equate to 33
2(3x - 1) + 2(2x + 5) = 33
6x - 2 + 4x + 10 = 33
10x + 8 = 33 ( subtract 8 from both sides )
10x = 25 ( divide both sides by 10 )
x = 2.5
Then
shorter side = 3x - 1 = 3(2.5) - 1 = 7.5 - 1 = 6.5 cm
Answer:
the length of the shorter side is 6.5
Is 8 15 17 are Pythagorean triples?
No, 8, 15, 17 are not Pythagorean triples.
No, 8 15 17 are not Pythagorean triples. A Pythagorean triple is a set of three positive integers a, b, and c such that a2 + b2 = c2. In other words, the sum of the squares of two integers must equal the square of the third integer.
In the case of 8 15 17, if we calculate the sum of the squares of the two smaller integers, 8 and 15, we get
[tex]8^2 + 15^2 = 64 + 225 = 289[/tex].
This does not equal the square of the third integer,
[tex]17^2 = 289,[/tex]
so 8 15 17 are not Pythagorean triples.
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Which statement about credit reports is correct?
Select the best answer from the choices provided.
A.
Credit reports are only available to banks and businesses that pay agencies for them.
B.
The government issues credit reports and offers them for free to consumers.
C.
Credit reporting agencies provide credit reports to consumers only upon payment of a fee.
D.
Credit reporting agencies provide a free credit report each year upon request.
Answer: .
Credit reporting agencies provide a free credit report each year upon request
Step-by-step explanation:
A credit report simply refers to the record of the credit history of a borrower from sources, such as collection agencies, banks, credit card companies, and governments.
It should be noted that an individual will be given one free copy of his or her credit report every year. Therefore, the correct option will be D.
Blank times 9 minus blank times 4 equals blank minus blank equals blank. You have to use the numbers 9,7,4,3 only.
The value for the blanks after calculating the as per the given data is found to be as 4 and 9 respectively.
On solving the question we will get the answer of the final blank as 0.
The question can be rephrased as ,
__x 9 - __ x 4 = ___ - ___ = ___.
Now if we will place 4 in first blank and 9 in second blank we will get the result as follows,
4 x 9 - 9 x 4 = 36 - 36 = 0
Therefore , we will get our desired answer.
A relationship between two quantities or, more broadly, two mathematical expressions that asserts that the quantities have the same value or that the expressions reflect the same mathematical object is referred to as equality.
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An angle measures 120°less than the measure if its supplementary angle. What is the measure of each angle
Answer: 60°
Step-by-step explanation: 180 - 120 = 60.
Answer:
30 and 150
Step-by-step explanation:
The first angle is 30 degrees. The second angle is 150 degrees. Here's why:
Explanation:
The first angle will be expressed as x. Since the second angle is 120
degrees greater than the first, it will be expressed as (x+120). Because they're supplementary, they'll add up to
180: x+(x+120)=180
Combine like terms.
2x+120=180
Subtract 120 from both sides.
2x=60
Divide by 2 to isolate for x.
x=30
Plug your data back in:
30 + (30 + 120) = 180
First angle: 30 degrees
Second angle: 150 degrees
Question is on the pic HELP!!!
Answer: D) -2x -8
Step-by-step explanation:
What is the horizontal asymptote * 1 point?
without computing, decide whether the vaule of each expresstion is much smaller than 1, close to 1, or much greater than 1
Answer: uhm...
Step-by-step explanation:
2...?