Use algebraic rules of equations to predict the solution type to the system of equations

Answer:

1716 soda mixtures

A person can choose in 1716 different ways.

A combination is a way of selecting items from a collection where the order of selection does not matter.

Given that there 13 flavors at a soda station, a person has to choose 6 out of this,

We need to find how many possible soda mixtures can you make,

So, using here the concept of combination,

ⁿCₓ = n! / x!(n-x)!

Here, n = 13 and x = 6,

So,

¹³C₆ = 13! / 6!(13-6)!

= 13! / 6! × 7!

= 13 × 12 × 11 × 10 × 9 × 8 × 7! / 6! × 7!

= 13 × 12 × 11 × 10 × 9 × 8 / 6!

= 13 × 12 × 11 × 10 × 9 × 8 / 720

= 1716

Hence a person can choose in 1716 different ways.

Learn more about combination click;

https://brainly.com/question/31596715

#SPJ2

Answer:

9 burritos and 18 tacos

Step-by-step explanation:

We can start this problem by assigning a variable to our unknowns.

Let's name x the number of burritos he buys.

The question states he buys half as many burritos as tacos.

Therefore, the number of tacos he bought is 2x.

Let's set up an equation.

(Cost of burrito)(number of burritos)+(Cost of taco)(number of tacos)=Total Cost

2.19x+1.29(2x)=42.93

Simplify

2.19x+2.58x=42.93

4.77x=42.93

x=9

Michael bought 9 burritos.

2*9=18

Michael bought 18 tacos.

Answer:

[tex] \displaystyle 18[/tex]

Step-by-step explanation:

we are given that,

let the number of tacos and burritos be t and b respectively

according to the 3rd condition we get:

[tex] \displaystyle 1.29t + 2.19b = 42.93[/tex]

according to the 4th condition we obtain:

[tex] \displaystyle t = 2b[/tex]

therefore our system of linear equation is

[tex]\begin{cases}\displaystyle t=2b \\ \displaystyle 1.29t + 2.19b = 42.93\end{cases}[/tex]

so now we end up with a system of linear equation in order to solve the equation we can consider substitution method

so substitute the value of t which yields:

[tex] \displaystyle 1.29 \cdot 2b+ 2.19b = 42.93[/tex]

simplify multiplication:

[tex] \displaystyle 2.58b+ 2.19b = 42.93[/tex]

since we have same variable we can consider the like terms:

[tex] \displaystyle 4.77b = 42.93[/tex]

divide both sides by 4.77:

[tex] \displaystyle \frac{4.77b }{4.77}= \frac{ 42.93}{4.77}[/tex]

reduce fraction:

[tex] \displaystyle \bcancel{ \frac{4.77b }{4.77}}= \cancel \frac{ \stackrel{ \large9}{ 42.93}}{4.77}[/tex]

[tex] \displaystyle b = 9[/tex]

now substitute the value of b:

[tex] \displaystyle t = 2.9[/tex]

simplify multiplication:

[tex] \displaystyle t =18[/tex]

hence,

he bought 18 tacos

Answer:

They should guarantee the lifetime of their batteries for 32 months.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 36 months and a standard deviation of 2 months.

This means that [tex]\mu = 36, \sigma = 2[/tex]

If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries?

The guarantee should be the 2th percentile of lengths, which is X when Z has a pvalue of 0.02. So X when Z = -2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.054 = \frac{X - 36}{2}[/tex]

[tex]X - 36 = -2.054*2[/tex]

[tex]X = 31.89[/tex]

Rounding to the closest month, 32.

They should guarantee the lifetime of their batteries for 32 months.

ANSWER:

By determining the number of possible outcomes, we have to examine many reasons behind the events. When examining the reasons behind these events we will eventually find a pattern. This pattern is what tells us how often something may or may not happen. By knowing how often something may or may not happen we can determine when it will reoccur in the future.

Step-by-step explanation:

Answer:

Quarterly interest rate= 0.8974%

Step-by-step explanation:

Giving the following formula:

Initial investment (PV)= $3,500

Future Value (FV)= $6,200

Number of periods (n)= 16*4= 64 quarters

It is almost impossible to calculate the interest rate using a formula. To determine the interest rate, we need to use a financial calculator:

Function: CMPD

n= 64

I%= SOLVE= 0.8974

PV= 3,500

FV= -6,200

Quarterly interest rate= 0.8974%

Answer:

3.6%

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

12 didved by 4 is 3

Answer:

3 cakes

Step-by-step explanation:

3 cakes can be bake with dozen if eggs

Answer:

I kind of need the models to help with this one

Answer:

492 yd^2

Step-by-step explanation:

Way 1: 250 + 242 = 492

Way 2: 800 - 132 - 176 = 492

Answer:

Step-by-step explanation:

V = L * W * D

V = 9 * 7 * 3

V = 189 cm^3

Answer: 189

Step-by-step explanation: 3*9*7

Answer:

if there are 300 m&m's there will be 120 red

Answer:

Step-by-step explanation:

I first added 13 and 8 to get 21

After that I do 7.5*21 to get 157.5

Then I multiplied 2.5 by 8 to get 20.  But it is a triangle so I have to divide by 2 to get 10

I add 10+10+157.5=20+157.5=177.5

177.5 units²

Answer:

I need 1 Brainliest before I can become Virtuoso

Step-by-step explanation:

Answer:

a = -2

Step-by-step explanation:

15-a =17

a=15 - 17

a=-2

Answer:

hi

Step-by-step explanation:

-a=17-15

-a=2

have a nice day

Answer:

Its 81

Step-by-step explanation:

Answer:

B the error can be reproduced

9514 1404 393

Answer:

 55 hours

Step-by-step explanation:

The number of hours will be ...

  ($1567.50) ÷ ($19/driveway) ÷ (6 driveways)/(4 h)

  = (1567.50×4)/(19×6) h = 55 h

Minnie needs to shovel driveways for 55 hours to hear enough for the new phone.

Answer:

about 55.275 hours. You may have to round it to the nearest tenth or whole number, whatever the question tells you to do, but this is the approximate answer. PLEASE VOTE BRAINLIEST!

Step-by-step explanation:

What we know:

6 driveways in 4 hours

$19 per driveway

needs $1,567.50

first, find amount of hours for one drive way by setting up a proportion.

6/4 =1/x

x= about 0.67 hours, or about 40.2 minutes.

now think: how many driveways does it take to make 1,567.50?

1,567.50/19= 82.5

This means it will take her 83 driveways to earn all of her money.

The final step is to multiply this by the amount of minutes, and then you will have your answer! 82.5*40.2= 3316.5

Divide by 60 to convert to hours.

Answer: 55.275

Answer:

500

Step-by-step explanation:

Answer:

Absolute maximum at (3,0)

Absolute minimum at (1,1)

Step-by-step explanation:

Given - f(x, y) = x⁴ + y⁴ − 4xy + 2, D = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}

To find - Find the absolute maximum and minimum values of f on the set D.

Proof -

Given that, f(x, y) = x⁴ + y⁴ − 4xy + 2

Now,

Differentiate f(x,y) with respect to x and y , we get

[tex]f_{x}(x,y)[/tex] = 4x³ - 4y

[tex]f_{y}(x,y)[/tex] = 4y³ - 4x

Now,

For the critical point, put [tex]f_{x}(x,y)[/tex] , [tex]f_{y}(x,y)[/tex]  = 0

we get

4x³ - 4x = 0

⇒x = 0, -1, 1

but given the range of x is 0 ≤x ≤ 3

⇒x = 0, 1

⇒y = 0, 1

∴ we get

2 critical points (x,y) = (0,0) , (1,1)

Now,

Put the values of x and y in f(x,y), we get

f(0,0) = 0 + 0 - 0 + 2 = 2

f(1,1) = 1 + 1 - 4 + 2 = 0

Now,

for the max and min values, finding the critical value is not enought, we have to find the values in the domain also.

Given domain is 0 ≤ x ≤ 3, 0 ≤ y ≤ 2

So, we have to check the values at the rectangle that have the coordinates

(0,0), (0,2), (3,2), (3,0)

Now,

f(0,0) = 0 + 0 - 0 + 2 = 2

f(0,2) = 0 + 16 - 0 + 2 = 18

f(3,2) = 81 + 16 - 24 + 2 = 75

f(3,0) = 81 + 0 - 0 + 2 = 83

∴ we get

Absolute maximum at (3,0)

Absolute minimum at (1,1)

Answer:

ok cool, bro'

Step-by-step explanation:

amazing

Answer:

paint

clean your room

call some friends

find a new hobby

bake/cook

re-do your room

make a wishlist

do some skincare

start learning a new language

start a new netflix series

bike ride/skate/drive

9514 1404 393

Answer:

  88.9

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(77°) = 20/x

  x = 20/cos(77°)

  x ≈ 88.9

Answer:

A

Step-by-step explanation:

We want to solve the equation:

[tex]5\sin(2x)=3\cos(x)[/tex]

To do so, we can rewrite the equation.

Recall the double-angle identity for sine:

[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]

By substitution:

[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]

Distribute:

[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]

We can subtract 3cos(x) from both sides:

[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]

And factor:

[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.

Answer:

A. cosx(10sinx-3)=0

Step-by-step explanation:

5(2sinxcosx)=3cosx

10sinxcosx-3cosx=0

cosx(10sinx-3)=0

Answer:

the surface area S of the red solid is 90m^2

Step-by-step explanation:

The computation of the surface area of the red solid is shown below:

First find the scale factor i.e.

= 6 ÷ 4

= 1.5

Now the surface area of the red solid is

= 40 × 1.5 × 1.5

= 90m^2

Hence, the surface area S of the red solid is 90m^2

The same would be considered

Answer and step-by-step explanation:

On the graph, it shows no kind of function, all it shows is the coordinate plane. That means that it has no x-intercept, no y-intercept, and has no minimum/maximum. Otherwise, there is not enough information to graph it.

Answer: The most important aspect in doing algebra is having a pen/pencil and paper in hand. It'll give you a better understanding of the question being posed.

Answer:

121

Step-by-step explanation:

3% of 100 = 3

18% of 100 = 18

100+3+18=121

Answer:

subtracting 14 from sides of the number sentence

Step-by-step explanation:

14 + n = 84

Since 14 is being added to n, you need to subtract 14 from both sides to solve for n.

Answer: subtracting 14 from sides of the number sentence

Answer:

3x−y=5;x+2y=4

x=2 and y=1

Step-by-step explanation:

Answer:

125 more students arrive buy school bus than by car

Step-by-step explanation:

20% + 25% + 15% = 60%

Bus

100 - 60 = 40% ( bus = 40%)

40% = 0.4

0.4 × 500 = 200 (200 students get to school by the school bus)

Car

15% = 0.15

0.15 × 500 =

car = 75 (75 students get to school by car)

difference

200 - 75 = 125 students (125 more students get to school on the school bus then by a car)