The number of different meals possible is 96, computed using combinations.
The combination is a method of choosing a number of articles from a larger set of articles in no particular order.
In the question, we are asked about the different dinner meals possible when a dinner meal is made up of an appetizer, a main course, a dessert, and a drink.
The choices for the appetizer are soup or salad, so the number of ways of choosing an appetizer = 2C1 = 2.
The choices for the main course are chicken, fish, steak, or lobster, so the number of ways of choosing a main course = 4C1 = 4.
The choices for the dessert are ice cream, pie, sorbet, or pastry, so the number of ways of choosing a dessert = 4C1 = 4.
The choices for the drink are coffee, tea, or milk, so the number of ways of choosing a drink = 3C1 = 3.
The total number of ways is the product of all of them.
Therefore, the total number of ways = 2*4*4*3 = 96.
The number of different meals possible is 96, computed using combinations.
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CD player: $142.00
Sales tax: 5.5%
The total amount paid by a customer who purchased a CD player at $142.00 and sales tax of 5.5% is $149.81
Sales taxCost of CD player = $142.00Sales tax = 5.5%Amount of sales tax = 5.5% of $142.00
= 5.5/100 × 142
= 0.055 × 142
= $7.81
Total amount paid by customers = Cost of CD player + Amount of sales tax
= $142.00 + $7.81
= $149.81
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I have 4 times as many 10 cent stamps as 3 cent stamps. I have one less 2-cent stamp than
The value of the stamp collection in terms of b is; 45b + 43 cents
How to solve algebra word problems?
We are given;
If there are x 3-cent stamps, then there are 4x number 10-cent stamps
So the number of 2-cent stamps is 1 less than 3 cent stamps and that will be x - 1, 2 cent stamps
Number of 2 cents stamps = b
Thus; x - 1 = b
x = b + 1
The value of the stamp collection is as follows;
x number of 3 cents stamps = 3(b + 1) = 3b + 3 cents
4x number of 10 cents stamps = 10(4(b + 1)) = 10(4b + 4) = 40b + 40
The value of the 2 cents stamp = 2b cents
Total value is;
2b + 40b + 40 + 3b + 3 = (45b + 43) cents
Complete Question is;
I have 4 times as many 10-cent stamps as 3-cent stamps. I have one less 2-cent stamp than 3 cent stamp. If I have b2-cent stamps, what is the value of my stamp collection in terms of b ?
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Solve each triangle - find any missing side and angle measures. Round answers to the nearest tenth.
The sides of the right-angle triangle will be 16 units and 20.30 units. And the missing angle will be 52°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The side AC will be
tan 38° = 12.5 / AC
AC = 15.999
AC ≈ 16 units
Then the side AB will be
AB² = 12.5² + 16²
AB = 20.30 units
We know that the angle sum is 180 degrees. Then we have
∠A + ∠B + ∠C = 180°
38° + ∠B + 90° = 180°
∠B = 52°
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Question 2 of 18
For which pair of functions is the vertex of g(x) 4 units to the right of the
vertex of f(x)?
A. f(x) = x² and g(x) = x² + 4
B. f(x) = x² and g(x) = (x − 4)²
C. f(x)=x² and g(x) = (x+4)²
D. f(x) = x² and g(x) = x² - 4
Answer:
B
Step-by-step explanation:
g(x)=(4-4)²
g(x) =0
and f(x)=x²
f(x)=0²
To prove that ΔAED ˜ ΔACB by SAS, Jose shows that StartFraction A E Over A C EndFraction = StartFraction A D Over A B EndFraction.
Triangle A E D is shown. Line segment B C is drawn from side A D to A E to form triangle A C B.
Jose also has to state that
The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.
What other congruence statements must Jose state?It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.
It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.
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ayuda necesito resolver este problema con procedimiento ;)
[tex]x^3-2x^2+x-1[/tex] is one of the prime factors of the polynomial
How to factor the expression?The question implies that we determine one of the prime factors of the polynomial.
The polynomial is given as:
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1[/tex]
Expand the polynomial by adding 0's in the form of +a - a
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^7 - 4x^6 +x^6 + 2x^5 -2x^5- 3x^4 + 4x^4 + 2x^3 -6x^3+2x^3- x^2 -3x^2 +4x^2-2x+2x-1[/tex]
Rearrange the terms
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^5 - 3x^4 + 2x^3 - x^2 + 2x^7 - 4x^6 + 4x^4 -6x^3+4x^2-2x+x^6-2x^5+2x^3-3x^2+2x-1[/tex]
Factorize the expression
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^2(x^6-2x^5+2x^3-3x^2+2x-1) + 2x(x^6-2x^5+2x^3-3x^2+2x-1) + 1(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]
Factor out x^6-2x^5+2x^3-3x^2+2x-1
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x^2+2x + 1)(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]
Express x^2 + 2x + 1 as a perfect square
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]
Expand the polynomial by adding 0's in the form of +a - a
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^4-x^3 +x^3-2x^3-x^2 -2x^2 +x+x - 1)[/tex]
Rearrange the terms
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^3-x^4-2x^3-x^2+x+x^3-2x^2 +x - 1)[/tex]
Factorize the expression
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3(x^3-2x^2+x-1) -x(x^3-2x^2+x-1)+1(x^3-2x^2+x-1))[/tex]
Factor out x^3-2x^2+x-1
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3 -x+1)(x^3-2x^2+x-1)[/tex]
One of the factors of the above polynomial is [tex]x^3-2x^2+x-1[/tex].
This is the same as the option (c)
Hence, [tex]x^3-2x^2+x-1[/tex] is one of the prime factors of the polynomial
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Ruby is at a family reunion and would like
to know the average age of everyone
present. Here are the ages of everyone at her
reunion:
35, 2, 7, 33, 25, 70, 75, 40, 42, 12, 15, 7, 44,
20, 25, 3, 65, 62
What is the mean?
Round to the nearest whole number.
Answer:
32
Step-by-step explanation:
To find the mean of the data set, you find the sum of the data set, and divide it by how much data you have in the data set. In this case you have 18 people (amount of data in the data set) and the sum is 35+2+7+33+25+70+75+40+42+12+15+7+44+20+25+3+65+62 = 582. So divide these two values: [tex]\frac{582}{18} = 32.\overline{33} \approx 32[/tex]
Answer:
32.33
Step-by-step explanation:
how many 4-digit positive intergers have four different digits where the leading digit is not zero, the interger is amultiple of 5 and 5 is the largest digit
The 4-digit positive integers have four different digits where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit is 108.
[tex]5*4*3*1+4*4*3*1=60+28=108[/tex]
Positive integers are the numbers we use to depend: 1,2, 3,4, 1 , 2, three, four, and so forth. Numbers with a fractional component not identical to zero and poor numbers are excluded from a fixed of high-quality integers. The operations of addition, subtraction, multiplication, and division can be finished with tremendous integers.
Positive integers are definitely your counting numbers. wonderful integers are in reality a part of a larger institution of numbers referred to as integers. Integers are all of the whole numbers, each advantageous and poor. by complete numbers, we imply numbers without fractions or decimals.
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We make four cases based on where the multiple of the 5 digits (0 or5) is. The number has to end with either 5 or 0 since it's a multiple of5. In all but the last case, 5 and 0 are used at the end and in another spot that separates the cases.
Case 1: The first digit can't be 0 so it must be 5. There are 4.3 to choose the middle two digits. After that, the last digit has to be 0, so there are a total of 1.4.3.1=12 numbers.
Case 2: The second digit can be 5, leaving 2 choices. The first and third numbers can be chosen in 4.3 ways, like last time. The last digit has to be 0 or 5, but not the one we already used. There are a total of 4.2.3.1=24 numbers.
Case 3: There are the same choices, but the digits 0 and 5 are at the last and second-to-last spots. So there are 4.2.3.1 =24 numbers again.
Case 4: There are 4.3.2 ways to choose the first three numbers. There has to be a 5 in the number because the largest digit is 5. Coincidentally, there are 4.2.3.1 numbers again.
There are a total of 12 + 24.3= (D)84 numbers.
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1. Try It #1 A company sells doughnuts. They incur a fixed cost of $25,000 for rent, insurance, and other expenses. It costs $0.25 to produce each doughnut.
a. Write a linear model to represent the cost C of the company as a function of x, the number of doughnuts produced.
Answer:
In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.
It is required to represent the cost C of the company as a function of x, the number of doughnuts produced.
To do so, multiply the expense of each doughnut by the number of doughnuts then add the fixed expenses of the doughnut selling company to find the total cost of the company.
Step-by-step explanation:
The expense of each doughnut is $0.25.
The expenses for x doughnuts are $0.25x.
The fixed cost is $25000.
The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C = 0.25x + 25000.
The total cost of the company is, C = 0.25x + 25000.
Help me please I would really be happy
The polynomial is not a perfect square trinomial. This is false..
How to illustrate the information?It should be noted that a perfect squares trinomial is the algebraic expression which has the form of ax² + bx + c.
The equation given is 9x² - 30x + 25. This will be expanded as:
9x² - 30x + 25.
9x² - 15x - 15x + 25
3x(3x - 5) - 5(3x - 5)
= (3x - 5)(3x - 5)
In this case, 9x² - 30x + 25 is a perfect square binomial of 3x - 5 and not a trinomial.
Therefore, the correct option is false.
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A worker has four different job offers, each with a contract for six years. assuming the job descriptions are identical, which offer will allow the worker to earn the most over six years?
Assuming the salary is included in the job descriptions, then they all pay the same amount for the same length of time, meaning he will earn the same amount at any of the jobs. This looks like a trick question.
The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as _____. Group of answer choices risk analysis regression analysis data mining decision tree analysis
The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis
Risk analysis is define as the the process of identifying and analyzing potential issues that could negatively impact key business initiatives or projects. This process is done in order to help organizations avoid or mitigate those risks.
So, The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis
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use the distrubutive property to simply -9(n-4)
Answer:
The distrubutive property
-9(n-4)
=-9n+36
-2x+9x^6+1-9x^2 how do you answer this question in descending order
Answer:
9x ^ 6 -9x ^ 2-2x + 1
Step-by-step explanation:
Helpp guys thank youu
1. if we add something in x then it will also add up in value of y
2. x by 5 times then y value increases by 3*5 = 15 times
3. if x is added with 5 then y value increases by 8.
What is Algebra?
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
As, per the first part
y=x
So, if we add something in x then it will also add up in value of x.
In second part,
y=3x
If x by 5 times then y value increases by 3*5 = 15 times
In third part, if x is added with 5 then y value increases by 8.
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How many passwords are there that start with a letter, contain only numbers and upper and lowercase letters, and are exactly 6 characters long
There are 1,86,78,66,560 possinbe passwords.
The easiest way to count the acceptable passwords is to note that there are 36^6 six-character strings made up of upper-case letters and digits, and 26^6 of them are made up entirely of letters, so there are 36^6 − 26^6 that include at least one digit.
⇒ 36^6 - 26^6
⇒ 2,17,67,82,336 - 30,89,15,776
⇒ 1,86,78,66,560
The answer is 1,86,78,66,560.
A password occasionally called a passcode, is a secret fact, generally a string of characters usually used to confirm a person's identity.
Historically, passwords we're expected to be memorized, but the large range of password-included offerings that common characters get entry to can make memorization of unique passwords for each service impractical.
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A boat is 400 feet away from one dock and 500 feet away from the another dock. the angle between the paths is 45°. what is the approximate distance between the docks?
Answer:
The approximate distance between the docks is 357 feet
Step-by-step explanation:
Let the distance between docks be d.
This is the opposite side to 45° angle of triangle with other sides 400 ft and 500 ft.
Use the law of cosines to find the value of d:
[tex]d = \sqrt{400^2+500^2-2*400*500*cos45} =357[/tex] (rounded)Which congruence criteria cab be used directly from the information about triangles jhk ghl to prove hk and ghl
Triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and angles. The ratio of their corresponding sides are also to be proportional.
Given triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.
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the question is on the image
by the way the 20cm is meant to be 15cm
Answer:
2.36 liters
Step-by-step explanation:
The volume Janet wants is 1/3 of 1/2 of the volume of a sphere with radius 15 cm. The formula for the volume of a sphere is given.
ApplicationThe water volume is ...
V = (1/3)(1/2)(4/3π)(15 cm)³ = 750π cm³ ≈ 2356 cm³
There are 1000 cm³ in 1 liter, so Janet needs about ...
2356 cm³/(1000 cm³/L) = 2.356 L
Janet should put about 2.36 liters of water in the fish tank.
Answer:
it is all I could.
Hope it helps
Which of the following represents a function?
(5, 1), (5, 2), (5, 3), (5, 4)
(-5, 6), (-5, 6), (-5, -6), (-5, -6)
(8, 3), (8, 3), (-8, -3), (-8, -3)
(3, 9), (-7, 1), (6, 12), (3, -9)
Answer:
(8,3),(8,3),(-8,-3),(-8,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x=8, then y=3, and if x=-8, then x=-3.
In the other sets of ordered pairs, however, one x-value has more than one possible y-value. Let's use the first set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
If 3x + 2y = 1 and
2x + 7y = 3
How do you find x and y step by step?
Step-by-step explanation:
there are 2 main approaches (in their core they are the same, of course, but they look different) :
1. use one equation to express one variable by the second, and then use this in the second equation to solve for the remaining variable. with that you go back into the first equation and solve for the first variable.
2. multiply both equations by certain factors as needed, then add both results, so that there is one summary equation with only one variable, and then solve for it. then use that in one of the original equations and solve for the second variable.
using 1.
3x + 2y = 1
3x = 1 - 2y
x = (1 - 2y)/3
2x + 7y = 3
2(1 - 2y)/3 + 7y = 3
2(1 - 2y) + 21y = 9
2 - 4y + 21y = 9
17y = 7
y = 7/17
x = (1 - 2y)/3 = (1 - 2×7/17)/3 = (1 - 14/17)/3 =
= (17/17 - 14/17)/3 = 3/17 / 3 = 1/17
using 2.
multiply first equation by 2, the second by -3
6x + 4y = 2
-6x - 21y = -9
----------------------
0 -17y = -7
-17y = -7
17y = 7
y = 7/17
and so on (as under 1.).
Step-by-step explanation:
First, you can multiply the both equation by one of the coefficient of either X or Y as shown above.
Secondly, after doing that you can multiply one of the equations by the negative sign in order for one of the coefficient to cancel out.
From there you can find X
After getting X , you can put the answer you get into any equation of your choice. collect like terms and then you'll find Y.
Hope this helps. If you don't understand use the picture if the solving above for better explanation. Thanks
What numbers go in the sqaures?
On the first two pairs you need to write 3 and 4, and 6 and 2.
On the second page we have:
1) 4
2) 2 and 7
3) 1
4) 1 and 3
5) 3.
What numbers go in the squares?
a) Here we just need to use scientific notation.
For the first case, the numbers that go in the exponent boxes are the same ones that go in the example, which are 4 in the first one and 2 on the second one.
Then, if we want the difference to be 29,400, then we can use 3 on the first box and 6 on the second. OR, because this is an absolute value, we can just invert those.
This is:
6 and 2 on the first two squares, and 3 and 4 on the second two squares.
b) Here we want to make perfect squares.
For example, on the first case we have:
x*2*2
We need to find the value of x such that this is a perfect square. Notice that we can rewrite this as:
x*2*2 = x*4
Then it only is a perfect square if x = 4.
For the second case:
14*x*y
This is only a perfect square if x*y = 14
Then we can use x = 2 and y = 7.
With similar reasoning, on the next box we have:
2*8*x
2*8 = 16, is already a perfect square, so x = 1.
The next one is:
x*3*y
Here we can define x = 3 and y = 1, so we get a perfect square.
Finally:
3*x
Here the only possible value of x is 3.
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whats the vertex-? Would it be -1???
Answer:
last option : vertex is 2, -1 . axis of symmetry is x = 2
Answer:
D
(2 -1)
*(^_^)*
...............
Can a point of inflection exist where f''(x)=DNE?
Yes, a point of inflection exists where f''(x) = DNE.
We know that the point of inflection, also known as the inflection point, is where the function's concavity changes. Changing the function from concave down to concave up, or vice versa, means that. In other words, an inflection point is a location at which the rate of slope change from an increasing to a decreasing manner, or vice versa, occurs. There is no doubt that those points are neither local maxima nor minima. They are called stationary points.
Let's take an example [tex]f(x) = x^{\frac{1}{3} }[/tex]
Here, [tex]f'(x)=\frac{1}{3x^{\frac{2}{3} } }[/tex]
and [tex]f''(x)=-\frac{2}{9x^{\frac{5}{3} } }[/tex]
Clearly f''(x) = DNE at x = 0. We are going to check if x = 0 is a point of inflection or not.
At x = -1, (left side of 0), [tex]f''(-1)=-\frac{2}{9(-1)^{\frac{5}{3} } }=\frac{2}{9} > 0[/tex] (concave up)
At x = 1, (right side of 0), [tex]f''(1)=-\frac{2}{9(1)^{\frac{5}{3} } }=-\frac{2}{9} < 0[/tex] (concave down)
Then by the definition, we can conclude that x = 0 is a point of inflection.
Therefore, a point of inflection exists where f''(x) = DNE.
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The mean GPA for 127 residents of the local apartment complex is 1.6. What is the best point estimate for the mean GPA for all residents of the local apartment complex
By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.
The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation ;
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
The sample of 112 residents has a mean GPA of 1.7.
By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.
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someone please help me
Answer:
20 sq in
Step-by-step explanation:
formula is (base * height)/2 so plug it in:
5*8=40
40/2=20
20 sq in
A polygon has 15 sides.
(b) If the sum of seven of the exterior angles is 200°, find the sum of the
eight interior angles not adjacent to these exterior angles.
Answer:
The sum of the eight interior angles not adjacent to these exterior angles is 1280°.
=================
Given A 15-sided polygon with sum of 7 exterior angles 200°.To find The sum of the 8 interior angles, remote to known 7 angles.SolutionWe know that:
sum of all exterior angles of a polygon is 360°.sum of each interior and exterior angle pair is 180°.So the sum of the 8 exterior angles is:
360° - 200° = 160°Sum of both interior and exterior angles of 8 angles:
180°×8 = 1440°Sum of those 8 interior angles is:
1440° - 160° = 1280°What is the solution to the system of equations {−2x+4y=1−4x+3y=12
The solution to the system of equation is ( -4.5 , -2)
What is a system of Equation ?A system of equation is a set of equations that have a common solution.
The set of equation given are
-2x +4y = 1
-4x +3y = 12
To find the solution , Elimination Method will be used
Multiplying equation 1 by 2 and then
Subtracting equation 1 by 2
-4x +8y = 2
-4x +3y = 12
+ - -
5y = -10
y = -2
Substituting this value to determine the value of x
-2x -8 = 1
-2x = 9
x = -4.5
Therefore the solution to the system of equation is ( -4.5 , -2)
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30 POINTS JUST ANSWER
The slope of line AB, BC, CD and AD are 1, -1/6, 2, -4/6 respectively. Quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C
How to determine the slopeFormula for slope is given as;
Slope = [tex]\frac{y2 -y1}{x2 -x1}[/tex]
A(-4 -1)
B(-1 2)
C(5 1)
D(1 -3)
a. Slope of line AB = [tex]\frac{2- (-1)}{-1 (-4)}[/tex] = [tex]\frac{2+ 1}{-1 + 4}[/tex] = [tex]\frac{3}{3}[/tex] = 1
b. Slope of line BC = [tex]\frac{1-2}{5-(-1)}[/tex] = [tex]\frac{-1}{6}[/tex]
c. Slope of line CD = [tex]\frac{-3 - 5}{1-5}[/tex] = [tex]\frac{-8}{-4}[/tex] = 2
d. Slope of line AD = [tex]\frac{-3 (-1)}{1 -(-4)}[/tex] = [tex]\frac{-4}{5}[/tex]
Quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C
Thus, the slope of line AB, BC, CD and AD are 1, -1/6, 2, -4/6 respectively.
and quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C
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Suppose there are 1,000 total sales representatives in the midwest and northeast regions, with 500 sales re
region. describe the best way for the sales director to include 200 sales representatives, with an equal num
region and an equal number in each group, while yielding valid conclusions in the study.
Making 20 groups of 10 is the sampling strategy that can be used to select 200 sales representatives.
What is sampling?
Sampling is the phrase used to describe a statistical procedure in which a predetermined number of observations are chosen from a larger population. More precisely, sampling can be described as the process of choosing a portion of a statistical population in order to estimate the characteristics of the entire population. Samples that are representative of the population under study are sought for by statisticians.
Making 20 groups of 10 is the most effective way of sampling that can be employed here for the sales director to incorporate 200 sales representatives in this situation, with an equal amount of representatives from each region.
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