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Chef should prepare 4 cakes and 5 batches of pastry in order to achieve maximum profits and his maximum profit or revenue by solving through inequality is $260.

Given Chef uses 5 cups of cake batter for 1 cake and 4 cups of batter for 1 batch of cupcakes. Chef wants to make at least 4 cakes. Profit on 1 cake is $35 and $30 for 1 batch of cupcake.

let the number of cakes be x and the number of batches of cupcakes be y such that

5x+4y<=40--------1

x>=4---------------2

Maximize Profit=35x+30y

Inequalities contains different signs so we have to change one inequality.

5x+4y<=40

-x<=-4

Now assume them equalities

5x+4y=40-------3

-x=-4

multiply second equations by 5

-5x=-20-----------4

now  add 3 and 4

5x+4y-5x=40-20

4y=20

y=5

now put the value of y in 5x+4y=40

5x+4*5=40

5x+20=40

5x=20

x=4.

Maximum Profit=35x+30y

=35*4+30*5

=$260

Hence chef should make 4 cakes and 5 batches of pastry and maximum profit of $260.

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Answer:

33in

Step-by-step explanation:

Answer:

[tex]x \leqslant - 21[/tex]

Step-by-step explanation:

[tex]5(x + 27) \geqslant 6(x + 26)[/tex][tex]5x + 135 \geqslant 6x + 156[/tex]

[tex] - 21 \geqslant x[/tex]

[tex]x \leqslant - 21[/tex]

The PMF of [tex]X[/tex] is almost geometric in nature. Let [tex]p=\frac{11}{29}[/tex]. Then

[tex]P(X = x) = \begin{cases} p & \text{if }x = 0 \\ (1-p)p & \text{if }x = 1 \\ (1-p)^2 p & \text{if }x = 2 \\ (1-p)^3p & \text{if }x = 3 \\ (1-p)^4 & \text{if }x = 4 \\ 0 & \text{otherwise}\end{cases}[/tex]

Compute the first moment/expected value.

[tex]E(X) = \displaystyle \sum_x x\, P(X=x) \\\\ ~~~~~~~~ = 0\cdot p+1\cdot(1-p)p + 2\cdot(1-p)^2p + 3\cdot(1-p)^3p + 4\cdot(1-p)^4 \approx 1.39349[/tex]

Compute the second moment.

[tex]E(X^2) = \displaystyle \sum_x x^2\, P(X=x) \\\\ ~~~~~~~~ = 0\cdot p+1\cdot(1-p)p + 4\cdot(1-p)^2p + 9\cdot(1-p)^3p + 16\cdot(1-p)^4 \approx 4.01103[/tex]

Compute the variance.

[tex]V(X) = E(X^2) - E(X)^2 \approx 2.06921[/tex]

The standard deviation is the square root of the variance.

[tex]\sqrt{V(X)} \approx \boxed{1.43848}[/tex]

Answer:

this is a cube so it has 6 faces

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Answer:

Other answer is wrong. The answer is this choice

The table C correctly shows the marginal frequencies.

A two-way table is a way to display frequencies or relative frequencies for two variables.

One of the variables is represented using rows and the other one using columns.

They are used to see if there is any relationship between the two variables.

Given that, the ages and grades of some of the 19 girls on a club soccer team are shown in the given table.

We need to select the table showing the correct marginal frequencies.

So, we see that,  

Table A and Table D add up to a total of 21 girls.

The question says there are 19 girls, so those two are eliminated.

Table B's data doesn't even add properly so that is eliminated too.

This leaves Table C.

Hence, the table C correctly shows the marginal frequencies.

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The complete question is attached.

The equation which represents the measure of the unknown angles is x + x + 10 =130. Hence, option C is correct.

Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the data given in the question,

As per the rules, the sum of the three sides of a triangle is 180°.

The angles are x, x+10, and 50.

Now,

x + x + 10 + 50 = 180

x + x + 10 = 180 - 50

x + x + 10 = 130°.

Therefore, the equation option above is the correct answer.

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Answer: C

Step-by-step explanation:

When doing an indirect proof, you begin by assuming the inverse of the statement you want to prove.

The area of a parallelogram is simply its base (6.1 miles) multiplied by its height (2.6 miles).

Substitute the values into the formula for area.

[tex]A=6.1\cdot2.6[/tex]

Multiply.

[tex]A=\boxed{15.86}[/tex]

Note that the answer is given in square miles ([tex]\text{mi}^2[/tex]) since both of the measurements used are in miles.

The sum of the first six terms of the geometric series is -364.

A geometric series is a sequence of terms in a fixed common ratio.

Apparently, the expression "geometric progression" comes from the "geometric mean" (Euclidean term) of segments of lengths a and b: it is the length of the side c of a square whose area is equal to the area of ​​the rectangle. a and b. May

The series given is

2 – 6 + 18 – 54 + ...

The sum of n terms of a geometric series is given by

Sn=a1 * 1 - rn/1 - r

here the first term is 2

r = -6 /2 = -3

S = 2 (1-(-3)⁶)/(1-(-3))

S = -364

Therefore the sum of the First six terms of the geometric series is -364 .

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Answer:

B

Step-by-step explanation:

Edge

Answer:

Step-by-step explanation:

1x + 4 ≤ 8

x + 4 ≤ 8

x ≤ 8 - 4

=x ≤ 4



Answer:

How long is each piece of wood?

Expression = 32/x

Solve: How long is each piece of wood if

Hunter cuts the original piece into 8

pieces?

32/8 = 4 foot

Answer:

If you didn't graduate from High school ,Then you are not in college

Step-by-step explanation:

statement :

if you are in college, then you graduated from high school

In the given statement we have :

The Hypothesis is : you are in college

The conclusion is : you graduated from high school

in order to get the contrapositive ,

• first we switch the hypothesis and the conclusion

( H ⇒ C becomes C ⇒ H )

• Second, we negate the hypothesis and the conclusion.

Then

• first ,if you graduated from high school , then you are in college

• second , If you didn't graduate from High school ,Then you are not in college

Answer:

they are no instructions so no answers either.

Step-by-step explanation:

am sorry I can't help you, the question might not have been complete. please do contact me when it's.

If combination requires 3 numbers ranging from 0 to 4 then number of combinations is 10.

Given A combination lock contains three numbers from 0 to 4.

Combinations refers to a technique that determines the number of possible arrangements in  a collection of items where the order of the selection does not matter.

Total numbers available to be selected are 5 from 0 to 4.

In this 0 is also included because it is also a number.

Numbers to be filled in the combination lock =3

So to calculate the combinations we need to use nCr formula in which n=5 and r=3.

Combinations=5C3

=5!/3!*(5-3)!

=5!/3!*2!

=5*4*3!/3!*2!

3! will be cancelled from numerator and denominator

=5*4/2

=10

Hence the number of possible combinations are 10.

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Answer: B. 150°

Step-by-step explanation:

The angle is obviously obtuse and is therefore greater than 90°.

This rules out A. and C.

Also, this angle is not 180° because then it would be flat.

This rules out D.

Leaving the correct answer to be B. 150°

[tex]\huge\boxed{45^\circ}[/tex]

See the attached diagram.

Together, angles BDC and ADB form a right angle, which is 90 degrees.

The angles are split straight down the middle, meaning they're equal to each other. This means each one is equal to half of 90 degrees, which is 45 degrees.

The required scale factor for the dialed triangle is given by SF= 6.28

A triangle with vertices at A(0,0), B(0,4), and C(6,0) is dilated to yield a triangle with vertices at A(0,0), (B(0,10), and C (C(15,0).

The scale factor is defined as the ratio of modified change in length to the original length.

Since, the height and base of the triangle is y coordinate of B and x coordinate of c is given by 4, 6
Area of triangle =1/2(base x height)
                         = 1/2 (4 x 6)
                         =   4.8
Similarly, for dilated triangle
Area of dilated triangle =  30

Now, scale factor(SF) = area of dilated triangle \ area of triangle
SF = 30/4.8
SF = 6.25

Thus, the required scale factor is SF = 6.25

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Answer:

12

Step-by-step explanation:

16/4=4

4+8=12

Answer:

f(5)

-2(5)-3

-10-3=-13

g(-2)

-2(-2)^3-5

-2(-8)-5

16-5=11

Step-by-step explanation:

Answer:

a = 2

Step-by-step explanation:

Given:

To find:

Steps:

a = V^1/3 = 8^1/3 = 2

Answer:

Area of triangle = (base x height)/2

There are all together 4 triangles and 1 square.

Therefore, surface area = area of square + 4 x area of triangle

height = 5.8 in, base = 6 in. area of square = 6x6 = 36 in^2.

area of 1 triangle = (5.8x6)/2

area of 4 triangles = 2x5.8x6 = 69.6 in^2

surface area = 69.6 + 36 = 105.6 in^2

Step-by-step explanation:

Answer:

7y + 15 - 2y = 5(y + 3)

Step-by-step explanation:

So two equations have infinitely many solutions, when they are exactly the same equation, in their most simplified form, for example: 2x = 3x-x which simplifies to 2x=2x. So in the options, three of the options have the same equation on the right side, so I'll distribute the 5. [tex]5(y+3) = 5y+15[/tex]. Now let's look at the options:

7y + 3-2y

5y+3 (this is not the same as 5y + 15)

7y + 15 (this is not the same as 5y + 15)

7y + 15 - 2y

5y + 15 = 5y + 15 (this is the same)

Answer:

7.5 cm

Step-by-step explanation:

The perimeter of a rectangle is the sum of the length of all its sides.

Perimeter of rectangle= 2(length +breadth)

Given: perimeter= 24 cm, breadth= 4.5 cm

Substitute the given information into the formula:

24= 2(length +4.5)

Divide both sides by 2:

length +4.5= 12

Subtract 4.5 from both sides:

length

= 12 -4.5

= 7.5

Thus, the rectangle is 7.5 cm long.

Considering the given information in the question, the value of x is [tex]12^{o}[/tex], and that of y is [tex]7.5^{o}[/tex].

A transversal is a line that cuts through two given parallel lines. Thus it intersects each parallel line at a point, forming four angles each.

From the given information in the question, it can be inferred that:

the given bottom right angle of the first intersection and the bottom right angle with the second intersection are congruent (corresponding angle property).

So that,

[tex](5x+4y)^{o}[/tex] = [tex](12y)^{o}[/tex]

[tex]5x^{o}[/tex] = [tex]12y^{o}[/tex] - [tex]4y^{o}[/tex]

[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]............ 1

Also given that the top right angle at the second intersection is a right angle, then;

    [tex]12y^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)

This implies that;

    [tex]12y^{o}[/tex] = [tex]180^{o}[/tex] -    [tex]90^{o}[/tex]

       [tex]12y^{o}[/tex]  =     [tex]90^{o}[/tex]

So that,

y = [tex]\frac{90}{12}[/tex]

y = [tex]7.5^{o}[/tex]

Thus substituting the value of y in equation 1, we have;

[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]........ 1

     = 8(7.5)

5x = 60

x = [tex]\frac{60}{5}[/tex]

x = [tex]12^{o}[/tex]

Therefore, x = [tex]12^{o}[/tex] and y = [tex]7.5^{o}[/tex]

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The new amount of neon gas when the temperature drops is 2.30L.

Charles's law

Charles's law states, "The volume occupied by a particular amount of gas is directly proportional to its absolute temperature.

Initial temperature of gas T₁ = 50 ° C = 323.15K

Initial volume of gas V₁ = 2.5L

Final temperature T₂ = 25 ° C = 298.15K

Final capacity V₂ =? Neon gas, substitute the given value into the above equation:

V₁ / T₁ = V₂ / T₂

V₂ = V₁T₂ / T₁

V₂ = (2.5L × 298.15K) ) / 323.15K

V₂ = 2.30 l

Therefore, the new volume when the temperature of the neon gas drops is 2.30l.

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Answer:

A. 2.3

Step-by-step explanation:

The proportion of people who preferred foreign cars than domestic cars is 0.24 and the confidence interval  for the population proportion of new cars over domestic cars of 98% confidence interval is (641.955,642.045).

Given sample size of 2676 and number of people preferred foreign cars than domestic cars is 642.

We have to calculate the proportion of people who preferred foreign cars than domestic cars and the confidence interval which shows the confidence interval of 98%.

Number of people prefer foreign cars than domestic cars=642

Sample size=2676

Proportion=642/2676

=0.2399

=0.24   (After rounding off)

Now we will find confidence interval.

X=642

n=2676

z value for the confidence interval 98% is 2.33

Confidence interval =X± z*s/[tex]\sqrt{n}[/tex]

Upper =642+2.33*1/[tex]\sqrt{2676}[/tex]   (we have taken s=1)

=642+0.045

=642.045

Lower=642-2.33*1/[tex]\sqrt{2676}[/tex]

642-0.045      (putting values in formula given above)

=641.955

Hence the proportion of people preferred foreign cars than domestic cars is 0.24 and the confidence interval is (641.955,642.045).

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