Oki and Stephen are making bags of trail mix to sell. Oki’s trail-mix recipe requires 3 cups of nuts and 3 cups of dried fruit per bag. Stephen’s trail-mix recipe requires 4 cup of nuts and 2 cups of dried fruit per bag. Together, they want to make as many bags of trail mix as possible. They have exactly 120 cups of nuts and 90 cups of dried fruit. Find the maximum number of bags of trail mix Oki and Stephen can make together.
A. write a system of inequalities
B. Graph and find coordinates of the vertices of the feasible region.
C. Find the maximum number of bags of trail mix oki and stehpen can make. How many of each type of recipe should they make to maximize the total number of bags

Answer:

E is \(\frac{1}{2\\}\) F is 6\(\frac{1}{4}\) and G is \(1\frac{1}{2}\)

Step-by-step explanation:

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids, a cylinder and a cone combined (a frustum)

We are required to solve for the total curve surface areas both solids

hence the curve surface area (henceforth CSA) of a cylinder is given as

\(CSA-cylinder=2\pi rh\)

\(CSA-cone= \pi rl\)

\(Total CSA= 2\pi rh+\pi rl\)

Given data

diameter d= 20

radius = d/2= 20/2= 10

height of cylinder h= 9

slant height of cone l= 16

substituting our data into the expression we have

\(Total -CSA= 2*\pi *10*9+\pi *10*16\\\\Total -CSA= 565.56+502.72\\\Total -CSA= 1068.28\)

\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)

Answer:

3x+2y=15 : y=-3/2x+15/2

y-4x=2 : y=4x+2

they are not parallel lines

Step-by-step explanation:

formula:

y=mx+b

Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

Read more about Domain and Range at: https://brainly.com/question/10197594

#SPJ1

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

Learn more on dot plots here: https://brainly.com/question/14217166

#SPJ1

Answer:

1/2 divided by 6

6/12 divided by 6

Step-by-step explanation:

Answer:

a - d

Step-by-step explanation:

we want to find the number of hours (or rather days) until only 4.25% of the drives fail.

that means for an exponential distribution we have

P(X < x) = 1 - e^(-Lx)

L = 1/mean = 1/12500

and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).

so, we get

0.0425 = 1 - e^(-x/12500)

0.0425 - 1 = -e^(-x/12500)

-0.9575 = -e^(-x/12500)

0.9575 = e^(‐x/12500)

ln(0.9575) = -x/12500

-x = ln(0.9575)×12500

x = -ln(0.9575)×12500 = - -0.043429558...×12500 =

= 0.043429558...×12500 = 542.8694741... hours

after 542.8694741... hours = 22.61956142... days

it is expected that 4.25% of the hard drives fail.

you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).

please round yourself as you need.

Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

To solve the exercise, we can use a rule of three:

Therefore, the falcon can fly 322,000m/hour or 322,000 meters per hour.

Answer:

C

-16(0.5x-0.75y+2)

Step-by-step explanation:

I got it right on edge 2022 Hope it helps <3

The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

Read more about similar triangles at; https://brainly.com/question/14285697

#SPJ1

Answer: -21

Step-by-step explanation:

Let the number be x.

Then, this means 2(x+8)+5=x.

Answer:

Explanation:

√8², 3² and √17² satisfy a²+b²=c²

√8²+3² = √17²

8+9=17

Answer:30

Step-by-step explanation:47-17 = 30

Answer:

half of 20 is 1010

Step-by-step explanation:

half of 20 is 1010 is your new radius so10^2 = 100100 x 3.14 = 314Now we multiply by the height:314 x 11 = 3,454 cm^3

Answer:

23

Step-by-step explanation:

FH=FG+GH

FH=11+12

FH=23

Given statement solution is :-  For the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.

Regular Pay:

Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:

Regular Pay = Regular Hours x Hourly Rate

Regular Pay = 40 hours x $11.90/hour

Regular Pay = $476

Overtime Pay:

Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.

Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)

Overtime Pay = 13 hours x ($11.90/hour x 1.5)

Overtime Pay = 13 hours x $17.85/hour

Overtime Pay = $231.45

Gross Pay:

Gross Pay is the sum of Regular Pay and Overtime Pay.

Gross Pay = Regular Pay + Overtime Pay

Gross Pay = $476 + $231.45

Gross Pay = $707.45

Therefore, for the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

For such more questions on Pay Calculation for Patricia

https://brainly.com/question/32055117

#SPJ8

The most appropriate values are:

z = - 2.23

The corresponding probability is : 0.01297

Mean, μ = 45

Standard deviation, σ = 5

Sample size, n = 31

The standard score, Z ; Since distribution is normal is obtained thus;

Z= (x - μ) ÷ (σ/√n)

For, x = 43

Z = (43 - 45) ÷ (5/√31)

Z = - 2.227

The probability :

Using the standard normal distribution table:

P(Z < - 2.227)

P = 0.01297

Hence, Z = - 2.23

P(x ≤ 43) = 0.0129



Learn more on Z probability :

https://brainly.com/question/4555552

Answer: Yes, it is.

Step-by-step explanation:

given: x is 0 and y is 3. Plug in the equation and solve

y=x+3

3=0+3

3=3

Yes, it is a solution

The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: \((\frac{d}{dx} ) (x^n ) = nx^{n-1}\). Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=\(18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432\)

\(t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}\)

\(t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}\)

\(t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}\)

Like t is a positive number, you should use \(t_2\). Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is \(2\sqrt{3}\).

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=\(2\sqrt{3}\)

a(t)= -6*\(2\sqrt{3}\)t+18

a(t)= \(-12\sqrt{3}\)t+18

a(t)=-2.76

Read more about the derivative here:

https://brainly.com/question/29257155

#SPJ1

Answer:

Step-by-step explanation:

take angle C as reference angle

using tan rule

tan C=oppposite/adjacent

tan C=6/12

tan C=0.5

C=\(tan^{-1}\)0.5

C=26.6 degree

Answer:

\(P(40<X<55)\)

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

\(P(40<X<55)=0.819\)

Step-by-step explanation:

Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:

\(X \sim N(50,5)\)  

Where \(\mu=50\) and \(\sigma=5\)

We are interested on this probability

\(P(40<X<55)\)

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

\(P(40<X<55)=0.819\)

Answer:

1st from the left

Step-by-step explanation:

Answer:First one from the left

Step-by-step explanation:

Therefore, the dresser will now be sold for $295

Answer:

3/11 x 3 1/4

= 3/11 * 7/4

= 12/77

Thank you and please rate me as brainliest as it will help me to level up