There are 3 two topping sundaes possible.
How many two toppings are possible?It is not crucial to choose the toppings in any particular sequence. For instance, a caramel and strawberry topping is the same as a chocolate and caramel topping. To answer this question, we thus apply the combinations formula.
Mixtures Formula:
C,n,x is the amount of various ways there are to combine x items from a set of n components, as determined by the formula below.
Cn,x = n! / x!(n-x)!
sundaes with two toppings are possible
2 of a set of 3 toppings (chocolate, caramel and strawberry). So
C3,2 = 3! / 2! (3 - 2)! = 3.
Three two-topping sundae combinations are conceivable.
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HELP ASAP
PLEASE REFER TO PHOTO
According to the pattern Brett receives points as follows 5,10,15,20,25,30,35 and according to the pattern of Yolanda, Yolanda receives points as 25,60,95,130,165,200,235 .
What is recursion ?
It is a process in which it calls itself to solve the given problem is called as recursion.
The recursive formula to find the nth term of a geometric sequence is:
an = an-1 * r for n ≥ 2
In Brett's case,
if n=2
a2 = a1 * r
given a2 = 10 a1 =5
10 = 5 *d
d=2
a4 = a3 * d = 20*2 = 40
a5 = a4*d = 40*2 = 80
a6 = a5*d = 80*2 = 160
a7 = a6 * d = 160*2 = 320
In Yolanda case,
The recursive formula to find the nth term of an arithmetic sequence is:
an = an-1 + d for n ≥ 2
if n=2
a2 = a1 + d
60 = 25 + d
d = 35
a4 = a3+d = 95 + 35 = 130
a5 = a4+d = 130 + 35 = 165
a6 = a5+d = 165 + 35 = 200
a7 = a6 +d = 200 + 35 = 235
Hence the pattern in Brett's case could be 5,10,15,20,25,30,35 and in Yolando's case could be 25,60,95,130,165,200,235 .
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According to the pattern Brett receives points as follows 5,10,15,20,25,30,35 and according to the pattern of Yolanda, Yolanda receives points as 25,60,95,130,165,200,235 .
What is recursion ?It is a process in which it calls itself to solve the given problem is called as recursion.
The recursive formula to find the nth term of a geometric sequence is:
an = an-1 * r for n ≥ 2
In Brett's case,
if n=2
a2 = a1 * r
given a2 = 10 a1 =5
10 = 5 *d
d=2
a4 = a3 * d = 20*2 = 40
a5 = a4*d = 40*2 = 80
a6 = a5*d = 80*2 = 160
a7 = a6 * d = 160*2 = 320
In Yolanda case,
The recursive formula to find the nth term of an arithmetic sequence is:
an = an-1 + d for n ≥ 2
if n=2
a2 = a1 + d
60 = 25 + d
d = 35
a4 = a3+d = 95 + 35 = 130
a5 = a4+d = 130 + 35 = 165
a6 = a5+d = 165 + 35 = 200
a7 = a6 +d = 200 + 35 = 235
Hence the pattern in Brett's case could be 5,10,15,20,25,30,35 and in Yolando's case could be 25,60,95,130,165,200,235 .
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Solve the equation t − 3 = 17 for t.
−20
20
−14
14
I already searched the question and none of the answers I saw were an option.
The equation can be solved by adding 3 to both sides of the equation.
Solve the equation t − 3 = 17 for t?To solve the equation t − 3 = 17, we need to add 3 to both sides of the equation. Doing so, we get t = 17 + 3 = 20. Therefore, the value of t is 20.In this case, the variable is t. The equation t - 3 = 17 has 3 subtracted from t on the left side, so to isolate t, we must add 3 to both sides to make the equation equal. Once we do this, we are left with t = 20.The equation t − 3 = 17 is an equation with a single variable, t.The equation t - 3 = 17 is a simple algebraic equation that can be solved by performing the inverse operation of subtraction. To solve this equation, we must first add 3 to both sides of the equation.Therefore, the solution to the equation t - 3 = 17 is t = 20.The equation can be solved by adding 3 to both sides of the equation. When 3 is added to the left side of the equation, it cancels out the -3, leaving just t. When 3 is added to the right side of the equation, it increases the value of the right side from 17 to 20. Therefore, the equation t − 3 = 17 can be solved by adding 3 to both sides, which results in the equation t = 20.This means that the value of t is 20.To learn more about the value of the unknown variable refer to:
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I NEED HELPPPPPPPPPPPPP
Answer:
y= 12
Step-by-step explanation:
3(-12)-24
-36-24
-12
Write f(x)=1/2x^2+1/2x-10 in intercept form. Then find the x-intercepts, the vertex, and the axis of symmetry of the graph of f.
f(x)=1/2x^2+1/2x-10 in intercept form is (1/2)(x+4)(x-3)
The x-intercepts are x=-5 and x=4.
The vertex of symmetry is (-1/2, -81/8).
The axis of symmetry is: x = -1/2
What is intercepts?A vertical intercept is a point where the graph of a function or relation meets the y-axis of the coordinate system in analytical geometry,
f(x) = 1/2x^2+1/2x-10
= (1/2)(x² + x - 20)
= (1/2) (x² + 5x - 4x - 20)
= (1/2) { x(x+5) -4(x+5)
= (1/2) (x+5)(x-4)
Hence, Intercept form: f(x) =(1/2) (x+5)(x-4)
The x-intercepts will be where the factors = 0
x + 5 = 0 ⇒x = -5
x - 4 = 0 ⇒ x = 4
Therefore, the x-intercepts are x=-5 and x=4
To find the axis of symmetry, take the average of intercepts (to find the center of parabola)
(-5 + 4)/2 = -1/2
Axis of symmetry ⇒ x = -1/2
To find the vertex, put the axis of symmetry into the equation
f(x) = (1/2)(x + 5)(x - 4) = (1/2)(-1/2 + 5)(-1/2 - 4) = (1/2)(9/2)(-9/2) = -81/8
vertex is (-1/2, -81/8)
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The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
f(x) = (1/2)x² + (1/2)x - 10
2f(x) = x² + x - 20
2f(x) = x² + x + 1/4 - 1/4 - 20
2f(x) = (x + 1/2)² - 81/4
f(x) = 1/2 (x + 0.50)² - 10.125
The x-intercepts are given as,
f(x) = 0
1/2 (x + 0.50)² - 10.125 = 0
(x + 0.50)² = 20.25
x + 0.50 = ± 4.50
x = - 0.50 ± 4.50
x = - 0.50 - 4.50, - 0.50 + 4.50
x = - 5, 4
The equation of the axis of symmetry is given as,
x + 1/2 = 0
x = - 1/2
The graph is attached below.
The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.
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√2x – 1- x = −8
How do I solve this equation?
The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].
What is an equation?
An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:
expression_1 = expression_2
The given equation is √2x – 1- x = −8.
[tex]2x=x^2-14x+49[/tex]
[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]
Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].
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PLEASE HELP
Explain what the unit rate means in the context of the problem.
Answer in at least two complete sentences.
Answer:
Step-by-step explanation:
A unit rate means a rate for one of something. You should write it as a ratio with a denominator of one.
For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate
IT's 0.80 per serving i think
Help quickly this is for a final!
The polygons are similar.
The perimeter of pentagon RSTPQ is ___ units.
Answer:
unidentified
Step-by-step explanation:
could you please send the other polygon or send an attachment of the whole question because this information is not enough
3 Write an equation for each function, where x is the
number of months and y is the amount owed.
Mr. Allen's plan:
Mr. Jessup's plan:
rriculum Associates, LLC Copying is not permitted.
In
-L-
ODPPY LINAL
The y-intercept represents the loan amount initially. And the rate of change of the function will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the y-intercept of the line represents the value of the loan initially.
From the graph, the slope of both lines is negative, then the rate of change of the function will be negative.
Let 'x' be the number of months and 'y' be the amount owed.
The two points are (0, 560) and (1, 480). Then the equation of the line is given as,
(y - 560) = [(560 - 480) / (0 - 1)](x - 0)
y - 560 = - 80x
y = - 80x + 560
And the equation of the line for Mr. Jessup's plan will be given as,
y = - 40x + 400
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HELP PLEASE 10 POINTS!
a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
Answer for the given problem,
a. Percentage of 160 in number 40 is, 400%
b. The number for which 40 is 160% of that number is, 25
c. The number which is 40% of 160 is, 64
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
a. present quantity = 160
whole quantity = 40
Percentage = 400 %
b. present quantity = 40
Percentage = 160
Whole quantity = 25
c. whole quantity = 160
Percentage = 40%
Present quantity = 64
Hence, Answers are respectively, 400%, 25, 64
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What are the 14 types of angles?
Fourteen types of angles are Acute Angles, Obtuse Angles, Right Angles, Straight Angles, Reflex Angles, Positive Angles, Negative Angles, Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles, Alternate interior angles and Alternate exterior angles.
There are mainly 5 types of angles based on their magnitude. They are Acute Angles, Obtuse Angles, Right Angles, Straight Angles and Reflex Angles.
Positive Angles and Negative Angles are the angles based on the direction of measurement or the direction of rotation.
When two angles are paired, then there exist different angles, such as Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles, Alternate interior angles and Alternate exterior angles.
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Eva gets £42 a month for her allowance. Out of this, for every £5 she spends, she saves £1 how much money does she spend in a month
Answer:
Eva spends £35 in a month.
Step-by-step explanation:
We know that Eva gets £42 a month for her allowance and for every £5 she spends, she saves £1.
We are looking to find out how much money does she spend in a month.
To calculate this, we can use the following formula:
Spent money = Allowance - (Allowance / (5 + 1))
Plugging in the known values:
Spent money = 42 - (42 / (5 + 1))
Spent money = 42 - (42 / 6)
Spent money = 42 - 7
Spent money = 35
So, Eva spends £35 in a month.
Of the 50 members of a staff, 40 percent worked the day shift and the remaining 60 percent worked the night shift in a given week. Of the staff members, 80 percent prefer working the day shift and the remaining 20 percent prefer working the night shift. What is the minimum number of staff members who failed to receive his or her preference of shift that week
The minimal number of employees who did not get their preferred shift that week was 20.
Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.
But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.
We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.
But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.
Thus, 20 is the minimum number of staff members who failed to receive her preference of shift that week.
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At what point the graph of linear equation 2x 3y 6 cuts the Y-axis A 0 2 B 4 0 C 2 6 D 2 0?
The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).
For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.
From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.
To satisfy the second condition the points of a should satisfy the equation given
LHS= 2x+3y
RHS=6
A(0,2)
Substituting the values of x and y in 2x+3y,
2(0)+3(2)=6
Therefore LHS=RHS
Hence, at point A(0,2) the graph of the given equation cuts the Y axis.
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can someone tell me what the answer is to this math problem
(-5 3) and (-1 0)
i thinj the answer is 2-1
What is the formula of third side?
The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:
side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))
The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:
side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))
This formula is derived from the Law of Cosines, which states that the sum of the squares of any two sides of a triangle is equal to the square of the third side, minus twice the product of those two sides multiplied by the cosine of the angle between them.
In other words, the formula states that:
side_3^2 = side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle)
which is then solved for side_3 by taking the square root of both sides. Thus, the formula for the third side can be written as:
side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))
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The force,
F
(Newtons), between two objects is inversely proportional to the square of the distance,
d
(metres), between them.
The force is 0.045 Newtons when the distance between the objects is 2.4 metres.
Work out
d
(rounded to 2 DP) when
F
=
0.7
Newtons.
The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P
How to find inverse variation?Let
F = force in Newton'sd = distance in metersF = k/ d²
Where k = constant of proportionality
If F = 0.045 Newtons and d = 2.4 metres
F = k/ d²
0.045 = k / 2.4²
cross product
k = 0.045 × 2.4²
k = 0.2592
Find d when F = 0.7 Newton's
F = k/ d²
0.7 = 0.2592 / d²
cross product
0.7 × d² = 0.2592
0.7d² = 0.2592
divide both sides by 0.7
d² = 0.2592 / 0.7
d² = 0.370285714285714
find the square root of both sides
d = √0.370285714285714
d = 0.6085110634045
d = 0.61 to 2 decimal place.
Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.
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The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.
what is volume?The area occupied within an object's three-dimensional bounds is referred to as its volume. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.
given
Calculate the box's volume and provide your answer in units.
Due to the fact that x = 4.28, the remaining sides are 2x + 5 = 2(4.28) + 5 = 13.56
and x - 2 = 4.28 -2 = 2.28.
We are aware that volume is calculated as follows: 13.56 (4.28) ( 2.28 )
=[tex]135.25cm^{3}[/tex]
A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.
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i need the ratio i got the numbers
If Point B represents an alternate combination of flutternutters & blank books, then how much of each product could be produced?
From the given graph, at Point B a total of 8000 fluffernutters & 500 blank books could be produced.
The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this context, a graph is made up of vertices connected by edges.
In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.
Straight line graphs called linear graphs are used to show the relationship between two quantities. This graph makes it easier to show a result as a collection of straight lines. The term "linear" simply means a straight line; curves, dots, bars, etc. are not used.
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12. Sarah uses long division to convert
a rational number 2 to a decimal.
P
Which of the following statements
cannot be true?
A. The decimal form of P
q
terminates with a zero in the
tenths place.
B. The decimal form of P
eventually repeats.
C. The decimal form of never
terminates or repeats.
D. The decimal form ofis 0.
Answer:
the answer is
The answer is
The answer is
The answer is 73
Step-by-step explanation:
which operation should be completed first to find the value of the expreesion below 12 + 30 / (6 -3) + 1
In 2010, the population of a city was 191,000. From 2010 to 2015, the population grew by 3.9%. From 2015 to 2020, it fell by 3.3%. To the nearest 100 people, what was the population in 2020?
Answer:
The population by 2020 is 191,900
Step-by-step explanation:
Given that;
population 2010 (population in 2010): 191000
the population grew from 2010 to 2015: by 3.9%
so, population by 2015 = [tex]191000(1 + \frac{3.9}{100})[/tex]
= [tex]191000(1 + 0.039)[/tex]
= [tex]191000(1.039)[/tex]
= [tex]198449[/tex]
the population drop from 2015 to 2020: 3.3%
so, population by 2015 = [tex]198449(1 - \frac{3.3}{100})[/tex]
= [tex]198449(1 - 0.033)[/tex]
= [tex]198449(0.967)[/tex]
= [tex]191,900.183[/tex]
Please I need help my teacher told me to do 3.14 x 81 but it’s wrong
well, let's take a looksie, hmm the sector is really a sector with a central angle of 90°, wait a second!! a circle has a total of 360°, so 90°+90°+90°+90° = 360°, so 90°is really just one quarter that of a circle.
Now, if we just get the whole area of the circle, then grab only one quarter of that, we'll be set, yeahhhh!!
[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies A=\pi (9)^2 \\\\\\ \stackrel{\textit{one quarter of that}}{\cfrac{1}{4}\cdot \pi (9)^2}\implies \cfrac{81\pi }{4}\implies \cfrac{81(3.14)}{4} ~~ \approx ~~ \text{\LARGE 63.6}[/tex]
Compute $17^{-1}\pmod{83}$. Express your answer as a residue from $0$ to $82$, inclusive.(You may find it helpful to consider the fact that $17\cdot 5
The residue from $0 to $82 is 44 ≡ x(mod83)
17−1≡x(mod83)
17∗17−1≡17x(mod83)
5∗1≡5∗17=85(mod83)
5≡2x(mod83)
42∗5=210≡2∗42x=84x≡x(mod83)
44 ≡ x(mod83).
A mathematical operations that performs a calculation on two numbers is known as an arithmetic provider. They are used in everyday arithmetic, and most computer languages include a set of such operators that can be used within equations to perform a variety of sequential calculations. The following are examples of basic arithmetic operations are:
(+) Addition
Subtraction (-) (-)
() Multiplication
() division
In programming, computers use different symbols to represent multiplication (*) and division (/). More complex operators, such as
Let's look at an ice cream multiplication example.
There are two groups, each has its own ice cream.
The total number of ice creams is 2x3=6
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PLEASE HELPP
mia has 3 bags the number of toys in each bag is 6, 8 and x what is the number of toys in the third bag if the average number of toys in the three bags is 6?
a. 3
b.6
c.4
d.8
Answer:
b
Step-by-step explanation:
i think b because it makes more sense than a or c
Why do we use 1st and 3rd quadrant?
The usage of first and third quadrant is explained below.
The term quadrant in math is known as a region defined by the two axes (x-axis and y-axis) of the coordinate system.
Here we need to list down the usage of first and third quadrant is as follows:
As we all know that the Third Angle Projection schema imagines the object in the third quadrant.
And in one can place an object on the bottom of the horizontal plane and behind the vertical planes.
Where as the first angle projection is utilized mostly in the United States and it places the object between the observer and the object.
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Willl mark you brainlieestttt
Answer:
7/12
Step-by-step explanation:
y = 12
x = 7
y = Kx
K = y/x
K = 7/12
what is the difference in the volumes, in cubic inches, of two spheres, one with a radius of 3 inches and the other with a radius of 5 inches.
The difference in the volumes of the sphere is 410.29 inches³.
What is the difference in the volumes?A sphere is a three dimensional circle in which each point on the circumference is equidistant from its center. The volume of a three-dimensional object is the amount of space in the object.
The formula for the volume of the sphere = 4/3πr³
Where:
π = 3.14r = radiusDifference in the volumes = volume of the larger sphere - volume of the smaller sphere
(4/3 x 5³ x 3.14) - (4/3 x 3³ x 3.14)
523.33 - 113.04 = 410.29 inches³
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Find the length of the third side. If necessary, round to the nearest tenth
Answer: 26
Step-by-step explanation:
In the picture, we are given a right triangle. Based on that, we can use the Pythagorean Theorem, which helps us find the missing side length with the formula [tex]a^2+b^2=c^2[/tex].
a and b represent the legs, and c is the hypotenuse. The hypotenuse is the longest side of the right triangle. It is also the side that is diagonal from the right angle.
In the picture, we are presented with the legs. So, we can plug in the legs into a and b to solve for c.
[tex]a^2+b^2=c^2[/tex] [plug in a and b]
[tex]10^2+24^2=c^2[/tex] [exponent]
[tex]100+576=c^2[/tex] [add]
[tex]676=c^2[/tex] [square root both sides]
[tex]c=26[/tex]
This tells us that the length of the third side is 26.
The two congruent angles of an isosceles triangle are called _____ angles.
Answer:
isosceles triangles have two congruent acute angles