Answer:
Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Also
The order in which the food and drinks are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Beverages:
3 from a set of 15. So
[tex]B = C_{15,3} = \frac{15!}{3!12!} = 455[/tex]
Appetizers:
3 from a set of 10. So
[tex]A = C_{10,3} = \frac{10!}{3!7!} = 120[/tex]
Desserts:
3 from a set of 13. So
[tex]D = C_{13,3} = \frac{13!}{3!10!} = 286[/tex]
How many different ways can Luisa pick the food and drinks to serve at the bridal shower?
By the fundamental counting principle, as beverages, appetizers and desserts are independent:
[tex]T = B*A*D = 455*120*286 = 15,615,600[/tex]
Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.
Given the function f(x) = 4x - 2, explain and show how to find the average rate of change between x = 2 and x = 4.
Answer:
The average rate of change between x = 2 and x = 4 is of 4.
Step-by-step explanation:
Average rate of change:
The average rate of change of a function f(x) in an interval [a,b] is given by:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
In this question:
[tex]f(x) = 4x - 2, b = 4, a = 2[/tex]
Thus:
[tex]f(b) = f(4) = 4(4) - 2 = 16 - 2 = 14[/tex]
[tex]f(a) = f(2) = 4(2) - 2 = 8 - 2 = 6[/tex]
Average rate of change:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
[tex]A = \frac{14-6}{4-2}[/tex]
[tex]A = \frac{8}{2}[/tex]
[tex]A = 4[/tex]
The average rate of change between x = 2 and x = 4 is of 4.
Ryan rides his bicycle 5 miles in 34 hour. How many miles can he ride at the same rate in 1 hour?
Determine if the two triangles are congruent. If they are State how you know. NO LINKS!!!
Problem 25
These triangles are congruent.
The reasoning is the AAS congruence theorem. We have two pairs of congruent angles, as shown by the arc markings, and a pair of congruent sides. The sides are not between the angles. That means AAS is slightly different from ASA. The order matters.
=====================================================
Problem 26
The triangles are not congruent
Why not? Well it all comes down to the angle placement. For the triangle on the right side, the arc is between the shared segment and the segment with the double tickmarks. The other arc is not in the proper corresponding location to be able to use SAS. It would need to be adjacent to the arc on the right for us to use SAS.
If it's hard to visualize what I mean, refer to the diagram below.
=====================================================
Problem 27
The triangles are congruent by SAS
The angles aren't marked, but recall that vertical angles are always congruent. So you could add in angle markers if you wanted, to help complete the diagram. The tickmarks of course tell us which segments are the same length. The angles are between the segments.
====================================================
Problem 28
The triangles are congruent by SSS
Like before, the tickmarks tell us which sides are the same length. So the tickmarks say that we have two pairs of congruent sides. The overlapping sides or shared sides are the third pair of congruent segments. So in reality, we have three pairs of congruent sides. It might help to break up the figure into two separate triangles.
Find the value of x.
1680
x = [? ]°
The value of x is 84 degrees.
What is tangent to a circle?
The tangent line to a circle at a given point is the straight line that just touches the circle at the point.
A tangent to a circle is perpendicular to the radius at the point of tangency.
According to the question
we have to find the value of x.
Let us assume that a circle have a center at O. And Mark the end of the given chord P and Q.
Connect OP and OQ.
here,
OP = OQ
⇒∠OQP = ∠QPO
Now in triangle POQ, we have
⇒∠QOP + 2∠ OPQ = 180
⇒168 +2∠OPQ =180
⇒2∠OPQ = 12
⇒∠OPQ =6 degrees.
As we know that, tangent to a circle is perpendicular to the radius at the point of tangency.
⇒ x + ∠QOP = 90
⇒ x + 6 = 90
⇒ x = 90-6 = 84 degrees.
Hence, value of x is 84 degrees.
Learn more about the tangent to the angle here:
https://brainly.com/question/23265136
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A vase is shaped like a rectangular prism with a square base of length 11 cm. It has 2 litres of water poured into it. To what height (to 1 decimal place) does the water reach in the vase?
Answer:
x=16.53cm
Step-by-step explanation:
1 liter = 1000 cm^3
The volume of water in the rectangular prism will be 11*11*x = 2000
121x=2000
x=2000/121
x=16.53cm
Can y’all help on question 29?!
Answer:
Option C: 20 cm^2
Step-by-step explanation:
Essentially, surface area is just area added up. In this question, there are 4 same rectangles and 2 squares with the areas given. So you have to figure out the total.
Since there are 4 rectangles and each of them has an area of 4cm just multiply 4 by 4 to get 16.
Then, since there are 2 squares with an area of 2 cm each just multiply 2 by 2 to get 4.
Add both numbers, 16 + 4 = 20 and you get your answer.
The total surface area would be 20cm^2.
solve the system of equations by graphing
3x+y=7
x+2y=4
9514 1404 393
Answer:
(x, y) = (2, 1)
Step-by-step explanation:
The graph of these equations is attached. The solution is ...
(x, y) = (2, 1)
This is the last one thank u !
Answer and Step-by-step explanation:
The answer is that A'C' will be 1.5 times longer than AC.
This is because you are dilating the figure by a scale of 1.5.
#teamtrese #PAW (Plant and Water)
5х – 4 y = -10
3х + 2y = 16
Answer:
x= 2, y= 5
Step-by-step explanation:
5x -4y= -10 -----(1)
3x +2y= 16 -----(2)
(2) ×2:
6x +4y= 32 -----(3)
(1) +(3):
5x -4y +6x +4y= -10 +32
11x= 22
x= 22 ÷11 (÷11 on both sides)
x= 2
Substitute x= 2 into (2):
3(2) +2y= 16
6 +2y= 16
2y= 16 -6
2y= 10
y= 10 ÷2
y= 5
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $3000 loan for 30 months at 8.5% APR. What is the monthly payment? (Round your answer to the nearest cent.)
Answer:
111.35
Step-by-step explanation:
effective rate: .085/12= .00708333333333
[tex]3000=x\frac{1-(1+.00708333333333)^{-30}}{.00708333333333}\\x=111.35[/tex]
3(7x)-2(4-x) simplify the expression
Answer:
23x - 8 is the answer in simplify that expression
Answer:
[tex]3(7x)-2(4-x)[/tex]
[tex]21x-2(-x+4)[/tex][tex](21x+2x)-8[/tex][tex]23x-8[/tex]-------------------------
hope it helps...
have a great day!!
210
What is the arc length when
=
and the radius is 6 cm?
Answer:
ans : option 2nd
Step-by-step explanation:
total angle substand perimeter of circle so,
so solve by using unitary methods
Determine the value of x
Answer:
the answer is "C" because I did it on Khan academyThe value of x in the triangle is 17.51
Option C is the correct answer.
We have,
From the figure,
We can use the tangent function.
This means,
Tan = perpendicular / Base
i.e
tan 35 = x / 25
0.700 = x / 25
x = 0.700 x 25
x = 17.5
Thus,
The value of x in the triangle is 17.51.
Learn more about trigonometric identities here:
https://brainly.com/question/14746686
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What is the sum of the polynomials?
(6x+7+x2)+(2x2-3)
-x^2 +6x+4, 3x^2 +6x+4, 9x+4, 9x^2 +4
9514 1404 393
Answer:
(b) 3x^2 +6x+4
Step-by-step explanation:
(6x+7+x^2)+(2x^2-3)
= (1 +2)x^2 +(6)x +(7 -3) . . . . combine like terms
= 3x^2 +6x +4
Answer:
3x ² + 6x + 4
Step-by-step explanation:
( 6x + 7 + x² ) + ( 2x² -3 )
Remove unnecessary parantheses6x + 7 + x² + ( 2 x² - 3 )
6 x + 7 + x² + 2x ² - 3
subtract the numbers6 x + 7 - 4 + x² + 2x²
collect like terms6x + 4 + 3x²
use the commutative property to reorder the terms3x ² + 6x + 4
PLS HELP ASAP! FIND THE AREA OF THIS FIGURE, THANK YOU!
Answer:
A = [12 + 9(pi)] yd^2 = 40.3 yd^2
Step-by-step explanation:
A = area of triangle + area of semicircle
A = bh/2 + (pi)r^2
A = (6 yd)(4 yd)/2 + (pi)(3 yd)^2
A = 12 yd^2 + 9(pi) yd^2
A = [12 + 9(pi)] yd^2 = 40.3 yd^2
Which one of these equations match the graph?
Answer:
C y = 2sin(1/3) x
Step-by-step explanation:
It's a sin function since y = 0 at x = 0
The amplitude is 2
There are 2 cycles in 12π
so the period is 6π
The x coefficent is then 2π/6π = 1/3
Answer
C y = 2sin(1/3) x
A card deck for a board game has 20 cards, of which 4 are red, 6 are blue, and 10 are purple.
What is the probability of randomly selecting a blue card, then a purple card, without replacement?
Answer:
6/20 or in simplification, 3/10 would be the correct answer.
30% would also be correct :)
And 0.3
How is 10+10 the same as 11+11?
Answer:
I only remember the funny thing my dad told me
PLEASE HELP ASAP PLSSSSS!!!
Answer:
143 degrees
Step-by-step explanation:
First find angle ACB which is 180-83=97
Then angle ABC which is 180-134=46
Then angle CAB (97+46)-180=37
Finally angle HAB 180-37=143
I need more help with 21 questions
Answer:
45
Step-by-step explanation:
9 ÷ 1/5
9 × 5/1
9 × 5
45
Write the number 0.000 378 21 in standard form.
help please
Answer:
3.7821 (SDF)
Step-by-step explanation:
Take the number by 378 21 and place it in the right forms/place marks. Such as ones and tens place ect. Then there is your answer.
2,6,10,14 cuales son los siguientes tres términos
Answer:
Step-by-step explanation:
2, 6, 10, 14
Entonces, como puede ver, el patrón en la secuencia se suma por 4 como (+4)
(So, as you see that the pattern in the sequence is added by 4 )
2
2+4=6
6+4=10
10+4=14
Entonces, los próximos tres términos serán (Then, the next three terms will be)
14+4=18
18+4=22
22+4=26
A man bought a car for $8200 and sold it for 80% of the price two years later. How much did he lose?
Answer:
I don't know for sure, but I'm pretty sure its 1,640.
Step-by-step explanation:
80% of 8,200 is 6560, and then do 8,200- 6,560, you get 1,640.
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
According to question, The price at which it was sold is equal to :
[tex]80 \% \: \: of \: \: 8200[/tex][tex] \dfrac{80}{100} \times 8200[/tex][tex]80 \times 82[/tex][tex]6560[/tex]The car was sold at $ 6560
Now, loss is equal to :
[tex]8200 - 6560[/tex][tex] \$ \: 1640[/tex]lab scale known to have a standard deviation of 0.001gram, speimen weghtted 8 times. average weiht is 4.1602 gram. what is 99% confidence interval
Answer:
[tex]99\% CI=4.1602 \pm 0.0009[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=8[/tex]
Mean [tex]\=x=4.1602[/tex]
Standard deviation [tex]\sigma=0.001gram[/tex]
Generally 99\% confidence from table is mathematically given by
[tex]99\% CI=4.1602 \pm *2.576*\frac{0.001}{\sqrt{{8}}}[/tex]
[tex]P(-z<x<z)=0.99[/tex]
[tex]Z_{\alpha/2}=2.576[/tex]
Generally the equation for 99\% confidence level (CI) is mathematically given by
[tex]99\% CI=\=x \pm Z_{\alpha/2*\frac{\sigma}{\sqrt{{n}}}[/tex]
[tex]99\% CI=4.1602 \pm 0.0009[/tex]
School is almost over pls help
Answer:
3. pollution
4. the land becomes fertile
Find lim PLEASE I NEED HELP ASAP !!!!
Computing the limit directly:
[tex]\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}[/tex]
Alternatively, you can recognize the limit as being equivalent the derivative of f(x) at x = 2, in which case differentiating and plugging in 2 gives
f'(x) = 2x + 1 => f' (2) = 5
Only answer if you're very good at Math.
Given f(x) = x + 1 and g(x) = x^2, what is
( g o f) (x)?
A: ( g o f) (x) = x^2 + 1
B: ( g o f) (x) = ( x + 1)^2
C: ( g o f) (x) = x^2 + x + 1
D: ( g o f) (x) = x^2 ( x + 1)
Answer:
The answer is B: ( g o f) (x) = ( x + 1)^2
Explanation:
⟹ (g ∘ f) (x) = g [f (x)]
Replace x in g(x) = x^2 with x+1
= ( x + 1 ) ^2
Consider the dataset below and respond to the questions that follow: Advertisement ($'000) Sales ($'000) 1068 4489 1026 5611 767 3290 885 4113 1156 4883 1146 5425 892 4414 938 5506 769 3346 677 3673 1184 6542 1009 5088 Construct a scatter plot with this data. Do you observe a relationship between both variables
Answer:
The scatter plot is attached in the image
There exists a positive linear relationship between the two variables i.e sales and advertisements.
Step-by-step explanation:
The scatter plot is attached in the image
There exists a positive linear relationship between the two variables i.e sales and advertisements.
Nathan is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1978 cans.
What is the mass, in kilograms, of these cans?
Answer:
33.5 kg
Step-by-step explanation:
Each 59 cans are about 1 kg.
He collected 1978 cans.
How many times 59 cans did he collect?
1978/59 = 33.5
He collected 1978 cans which is 33.52 times 59 cans, so he collected 33.5 kg
URGENT PLEASE ANSWER
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
Answer:
A)$60
B)$9
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
Cleopatra has $15.
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
A)
Total ratio=(5 +7 +8)= 20
Cleopatra has $15.
Let X = total money
Ratio of Cleopatra= 5/20 ×X=15
5X /20 = 15
5X= (15×20)
X= $60
They have $60 in total
B) ratio of Dalila= 7/20 × 60 = $21
But 12$ was spent by Dalila on a hat
Then Dalila will have ($21 - 12$) Left
= $9