Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.
The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
4 toppings are chosen from a set of 12, hence the number of ways is given by:
[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
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What is 9 lbs 6 oz converted to ounces?
Answer:
150 ounces
Step-by-step explanation:
Sum, difference, and product..help!
The sum of the function will be (r – s)(x) = –2x² + x – 3, The difference of the function will be (r – s)(x) = –2x² + x – 3, and The product of the function will be (r × s)(x) = 2x³ – 6x².
The complete question is attached below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The functions are given below.
r(x) = x – 3
s(x) = 2x²
The sum of the function will be
(r + s)(x) = x – 3 + 2x²
(r + s)(x) = 2x² + x – 3
The difference of the function will be
(r – s)(x) = (x – 3) – 2x²
(r – s)(x) = –2x² + x – 3
The product of the function will be
(r × s)(x) = (x – 3) (2x²)
(r × s)(x) = 2x³ – 6x²
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If the sides of a square are increased by 2 inches, the area becomes 25 squares inches. Find the length of sides of the original square.
You know that the sides of a square are increased by 2 inches: the expression should be written as (x+2)
The area is 25 square inches
The area of a square is s×s or s²
so it can be solved as:
(x+2)²=25
[tex](\sqrt{x+2})^{2} =\sqrt{25}[/tex]
x+2=5
x=3
The length of the original side is 3 inches
Hope it helps!
A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of
cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
300 cupcakes
Step-by-step explanation:
[tex]27 = .09c[/tex]
[tex]c = \frac{27}{.09} = \frac{2700}{9} = 300[/tex]
In total, the bakery sold 300 cupcakes on a certain day.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of cupcakes sold that day.
let, 'x' be the total number of cupcakes sold that day.
Therefore, 9% of 'x' is 27 which is,
(9/100)×x = 27.
0.09x = 27.
x = 27/0.09.
x = 300.
So, The number of cupcakes sold that day is 300.
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Work out the height of this triangle with base, b = 4.7mm and area, A = 137.475mm2.
Step-by-step explanation:
hope you can understand
The height of the triangle will be;
⇒ 58.5 mm
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The base of the triangle = 4.7 mm
The area of triangle = 137.475 mm²
Now,
We know that;
⇒ The area of triangle = 1/2 × Base × Height
Substitute all the values, we get;
⇒ 137.475 = 1/2 × 4.7 × h
⇒ 137.475 = 2.35 × h
⇒ h = 137.475 / 2.35
⇒ h = 58.5 mm
Thus, The height of the triangle = 58.5 mm
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What are the approximate area and circumference, respectively, of a circle with a diameter of 30 inches?
Solution:
[tex]\searrow[/tex]
Detailed explanation:
Here we need to find both the circumference and the area of a circle whose diameter is 30 in.
///\\\///\\\///\\\///\\\///\\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\////\\\\///\\\///\\\///\\\///
⚜ Circumference ⚜
This is the formula that we use for the circumference. [tex]\large\texttt{$C=\pi d$}[/tex].
Here, C is the circumference,
[tex]\pi[/tex] is pi, *
d is the diameter
_____________
* The number pi is an irrational number. This means that no matter how hard we try, we cannot write this number as a fraction. The reason for that is: The number pi has never-ending digits after its decimal point.
To avoid getting never-ending numbers, we will use 3.14 for pi.
_____________
Alright, so now we just stick in the values.
[tex]\boldsymbol{C=3.14\cdot30}[/tex]
[tex]\boldsymbol{C=94.2\:inches}[/tex]
The circumference is successfully calculated.
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\\///\\\///\\\///\\\//\\//\/\/\/\//\///\\//
⚜ Area ⚜
This is the formula we will use to work out the area.
[tex]---\mapsto\boldsymbol{A=\pi r^2}[/tex]
Here,
A denotes the area
[tex]\pi[/tex] denotes pi
r denotes the radius (30/2=15, because the diameter is always two times the radius)
[tex]\large\boldsymbol{\therefore,\;the\;radius\;is\;15}[/tex]
Once again, it's just a matter of sticking in the values.
[tex]---\mapsto\boldsymbol{A=3.14\cdot15^2}[/tex]
NB:Remember the Order of Operations!
P.E.M.D.A.S.
P=Parentheses
This operation tells us to evaluate all expressions in the parentheses first, if any are present.
E=Exponents
This one tells us to evaluate all expressions with exponents, if any are present.
M=Multiplication | D=Division
Unlike the two operations above, these two are completely interchangeable.
A=Addition | S=Subtraction
Like M and D, A and S are interchangeable.
_________________
Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.
[tex]---\mapsto\boldsymbol{A=3.14\cdot225}[/tex]
Now, we need to multiply.
[tex]---\mapsto\boldsymbol{A=706.5\;square\;inches}[/tex]
I will give BRAINLIEST! ANSWER FOR 30 Points !!!!
Pleasee look at picture
What is the frequency of the tangent function represented in the graph below?
Answer CHOICES:
1 , 4 , 3 , 2
Answer:
The answer is 3
Step-by-step explanation:
You can see that it recurs faster than usual for a tan curve so 1 is eliminated and it cant be 2 or 4 because it isnt recurring equally.
Please give brainliestIdentify each of the following as rational or irrational
√23
104.42
√64
49.396
10.97846727460
Answer:
1-irrational 2-rational 3-rational 4-rational 5-irrational
Step-by-step explanation:
A
True
False
P
Given the diagram as marked.
True or False: P is on the angle bisector of A
Answer:
False
Step-by-step explanation:
P is not necessarily on the angle bisector of angle A.
Attached is an example of a carefully constructed shape (so that it's easy to see the measurements):
Angle A measures 45° (again, for convenience)Point P is 4 units to the right of and 3 units above point A.Point P forms a right angle with two congruent line segments, each of which terminate on the rays extending from Point A, forming angle A.The lower point is 8 units to the right of point A; the upper point is 7 units to the right of and 7 units above point A.The length of the two line segments is 5 units, and thus they are congruent.Visually, point P is not on the angle bisector of angle A.
While having two adjacent congruent segments is necessary for P to be on the bisector of angle A, it is not sufficient. The segments on the rays from A to the end of those segments would also need to be a pair of congruent adjacent sides (forming a kite). For a kite, the diagonal from the point between one pair of adjacent congruent sides to the point between the other pair of adjacent congruent sides does form an angle bisector with both angles.
Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two classes, and he took a total of 90 minutes Which value of k would cause the system of linear equations 35 x + 14 y = 119 and 5 x + 2 y = k to have an infinite number of solutions?
3
7
17
21
A system of the equation to be Dependent Consistent System the system must have multiple solutions. The correct option is C.
What is a System of equation?Inconsistent System
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
For the system of equations to have infinite number of solutions, the lines of the equations must coincide, therefore, the line must overlap on each other.
For the lines to overlap the equations must be in a ratio. Therefore, the ratio of the left sides of the equations must be equal to the right side,
[tex]\dfrac{35x+14y}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac{7(5x+2y)}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac71 = \dfrac{119}{k}\\\\k = 17[/tex]
Hence, the value of k must be 17, therefore, the correct option is C.
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A variable is normally distributed with mean 6 and standard 2 deviation .
a. Find the percentage of all possible values of the variable that lie between 5 and 9.
b. Find the percentage of all possible values of the variable that exceed 1.
c. Find the percentage of all possible values of the variable that are less than 4.
The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.
What is a normal distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
A.) The percentage of all possible values of the variable that lie between 5 and 9.
P(5<X<9) = P(X<9) - P(5<X)
= P(z<1.5) - P(-0.5<z)
= 0.9332 - 0.3085
= 0.6247
= 62.47%
B.) The percentage of all possible values of the variable that exceed 1.
P(X>1) = 1 - P(X<-2.5)
= 1-0.0062
= 0.9938
= 99.38%
C.) The percentage of all possible values of the variable that are less than 4.
P(X<4) = P(X <4)
= P(z<-1)
= 0.1587
= 15.87%
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In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.
Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3.
To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and
∠DFE is 4 times greater than ∠GFH.
∠FHG is One-fourth the measure of ∠FED.
∠DFE is congruent to ∠GFH.
∠FHG is congruent to ∠EFD.
To prove that △DFE ~ △GFH by SAS similarity theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.The correct answer is option C.
The image of the triangle is attached with the answer below:-
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:
By comparing ΔDEF and ΔGFH
DF = DG + GF
= 12 + 4
DF = 16
Also,
EF = EH + HF
= 9 + 3
EF = 12
Comparing the sides of ΔDEF and ΔGFH, we have;
[tex]\dfrac{DF}{GF}[/tex] = [tex]\dfrac{EF}{HF}[/tex]
[tex]\dfrac{16}{4}=\dfrac{12}{3}[/tex]
4 = 4
Thus, the two triangles have similar sides.
Comparing the included angle <DFE and <GFH, then;
∠DFE is congruent to ∠GFH
Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;
[tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
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Answer:
C
Step-by-step explanation:
Edg
Solve x: 30 pts if u can figure it out and the first one that sounds right gets brainiest answer
3x+99x=1188
Is this even possible to work out????
Please dont just type random letters Bec then there’s just no point of u being on here.. and ur wasting ur time! So please think about it
Answer:
x = 99
Step-by-step explanation:
3x + 99x = 12x
12x = 1188 divide 1188 ÷ 12
x = 99
The graph of a rational function f is shown below.
Assume that all asymptotes and intercepts are shown and that the graph has no "holes".
Use the graph to complete the following.
We have y+2 = 0 and x - 2 = 0. The provided function has an x and y-intercept of -2 and +2, respectively. There is no vertical asymptote. Two is the horizontal asymptote.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The y-intercept of a function is determined by the intersection of its graph with the y-axis. The value of y on the y-axis at which the considered function crosses it is called the y-intercept.
Assume the following equation: y = f (x)
We have x =0- 2 and y+2 = 0,The x and y intercept of the given function is -2 and +2.
The vertical asymptote is none. The horizontal asymptote is 2.
Hence,we have y+2 = 0 and x - 2 = 0. The provided function has an x and y-intercept of -2 and +2, respectively. There is no vertical asymptote. Two is the horizontal asymptote.
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Select the correct answer from each drop-down menu.
Consider functions hand k.
h(t) = 5r2 – 1
k(x) = √5x + 1
For > 0, the value of h(k(x)) is
0, functions hand k
For
the value of k(h(r
inverse functions.
Answer:
h(t)= 5r2-1
That the answer for the question
Urgent help needed algebra 2
replace F with 95:
95 = 9/5C + 32
Subtract 32 from both sides:
63 = 9/5C
Divide both sides by 9/5:
C = 35
answer: 35 Celsius
A polynomial-function has −5+√3 as a root. Which of the following must also be a root of the function?
O-5-√√3
0 -5+√√√31
05-√√√31
0 5+√√31
Answer:
First option.
Step-by-step explanation:
In ABC, m<2=70 and m
The measure of the third angle in the ΔABC is 70 degrees
Complete questionIn ΔABC, m∠2 = 70 and m∠1 = 40, find the measure of all third angle of ΔABC.
How to determine the third angle?The given parameters are:
m∠2 = 70
m∠1 = 40
The sum of angles in a triangle is:
m∠1 + m∠2 + m∠3 = 180
So, we have:
70 + 40 + m∠3 = 180
Subtract 110 from both sides
m∠3 = 70
Hence, the measure of the third angle in the ΔABC is 70 degrees
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If g(x) = 2^x were shifted 7 units to the right and 3 units down, what would be the new equation?
H(x) = 4(x - 7)^2 - 19
Hope you find it usefull
Rewrite, using the distributive
property (Algebra 1)
Answer:
[tex]24m + 32[/tex]
Step-by-step explanation:
[tex]8(3m + 4) = 24m + 32[/tex]
evaluate -5+(-3)^2+2
Answer:6
Step-by-step explanation:at first calculate (-3)^2=9
then 9+2=11
finally the answer is 11-5=6
Answer:
6
Step-by-step explanation:
Given Problem:
[tex]-5+(-3)^2+2[/tex]
Using the PEMDAS order of operation:
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Thus, Solving in parentheses first.
[tex]-5+(-3)^2+2[/tex]
[tex](-3)^2=9[/tex]
[tex]-5+9+2=[/tex]
[tex]-5+11=[/tex]
[tex]6[/tex]
Hence, the answer to [tex]-5+(-3)^2+2=6[/tex]
RevyBreeze
The ratio of the number of fiction book is 9:4, the different between the number of fiction and non fiction is 245
Answer:
Step-by-step explanation:
The ratio of the number of fiction books is 9:4
the difference between the number of fiction and nonfictionn is 245
so if the number of fiction books = 9x
then the number of nonfiction books = 4x
then difference = 9x-4x = 5x
the difference is given 245
then 5x= 245
x=[tex]\frac{245}{5}[/tex]=49
number of fiction books =49×9=441
number of nonfiction books =49×4=196
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How do you solve 32-34?
Answer:
32. {-4, 1, 2, 12}
33. {2, 6, 9, 31, 65}
34. No
Step-by-step explanation:
32. The domain of a relation is the set that contains all the x-coordinates of all the ordered pairs of the relation.
domain = {-4, 1, 2, 12}
33. The range of a relation is the set that contains all the y-coordinates of all the ordered pairs of the relation.
range = {2, 6, 9, 31, 65}
34. No since the same number, 2, appears twice as an x-coordinate. In a function, no two ordered pairs can have the same x-coordinate.
If the center of a circle is at (5,-7)
and its radius is 6, complete its
equation:
The equation is:
(x-5)^2+(y-(-7))^2=36
I hope it helps!
Answer: [tex]\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}[/tex]
=========================================
Work Shown:
[tex](h,k) = (5,-7) = \text{center}\\\\r = 6 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - 5)^2 + (y - (-7))^2 = 6^2\\\\\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}\\\\[/tex]
The solution to an inequality is given in interval notation as (2,). What is another way to represent this solution
set?
O
-
-5-4-3 -2 -1 0 1 2 3 4 5
-5-4-3-2-1 0 1 2 3 4 5
4
+
-5 -4 -3 -2 -1 0 1 2
44
3 4 5
The correct answer to this question is Option (4).
Answer:
D.
Step-by-step explanation:
EDG 2022
FInd the perimeter
14 3/4
4 1/2
8 1/2
10 2/5
10 2/5
12 4/5
The perimeter of the figure above is [tex]43\frac{22}{40} = 43\frac{11}{20}[/tex]
What is perimeter?The perimeter of a shape is the sum of the whole sides.
Therefore, perimeter of the figure is the addition of the whole length.
Hence,
perimeter = [tex]14\frac{3}{4}+4\frac{1}{2}+8\frac{1}{2}+10\frac{2}{5}+10\frac{2}{5}+12\frac{4}{5}[/tex]
let's convert to improper fraction for easy calculation.
Hence,
perimeter = [tex]\frac{59}{4}+\frac{9}{2}+\frac{17}{2}+\frac{52}{5}+\frac{52}{5}+\frac{64}{5}[/tex]
perimeter = [tex]\frac{590+180+340+60+60+512}{40} =\frac{1742}{40} = 43\frac{22}{40}[/tex]
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Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality 2.50x+3.50y30 represents the food sales in the first hour.
If Ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches Ben could have sold?
The maximum number of turkey sandwiches Ben sold is 6.
What is the maximum number of turkey sandwiches Ben sold?Given this equation : 2.50x + 3.50y ≤ $30
If y is 4, take the following steps in order to determine the value of x:
Substitute for y in the above equation:
2.50x + (3.50 x 4) ≤ $30
2.50x + 14 ≤ $30
2.50x ≤ $30 - 14
2.50x ≤ $16
x ≤ 6.4
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Answer:
6
Step-by-step explanation:
Suppose that you borrow $30,000 for four vears at 8% for
the purchase of a car. Find the monthly payments and the
total interest for the loan.
Answer:
$41269.983
rounded:
$41,269.98
Step-by-step explanation:
well you begin with the equation a=p(1+r/n)[tex]^{nt}[/tex]
so 30,000(1+0.08/12)to the power of 4 times 12
when you plug all of that in a calculator your receive $41269.983
The points (2,3) and (5,9) are on the line. What is the equation of the line
The equation of the line is y = 3x +3 .
What is a Straight Line Equation ?A straight line equation is that can be represented by y = mx +c , where m is the slope and c is the intercept on y axis.
The points given are (2,3) and (5,9)
m = (9-3)/(5-2) = 3
m = 3
Therefore the equation becomes
y = 3x +c
Te equation is given by
(y-y₁) = m(x-x₁)
y-3 = 3(x - 2)
y-3 = 3x -6
y = 3x +3
Therefore the equation of the line is y = 3x +3 .
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or
What is (fg)(x)?
f(x)=
–
3x+1
g(x)=x2
Write your answer as a polynomial or a rational function in simplest form.
The value of (fg)(x)= 3x³+ x²
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x) = -3x+1
g(x) = [tex]x^{2}[/tex]
Now, (fg)(x)
=f(x) * g(x)
= (-3x+1) * ([tex]x^{2}[/tex])
=-3x³+ x²
Hence, (fg)(x)= 3x³+ x²
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