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stepladder [879]
3 years ago
11

Of the cakes at Naomi's Bakery, 1/6 have chocolate frosting. Of the cakes with chocolate frosting, 1/5 have raspberry filling. W

hat fraction of the cakes at Naomi's Bakery have both chocolate frosting and raspberry filling?
Mathematics
1 answer:
Sever21 [200]3 years ago
5 0

Answer:

\frac{1}{6}  \times  \frac{1}{5 }  \\  \frac{1}{30}

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What is –36° converted to radians?
Stells [14]

let's recall that there are 180° in π radians, thus


\bf \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ -36&x \end{array}\implies \cfrac{180}{-36}=\cfrac{\pi }{x}\implies -5=\cfrac{\pi }{x}\implies x=\cfrac{\pi }{-5}\implies x=-\cfrac{\pi }{5}

4 0
3 years ago
Help please calculus
VLD [36.1K]

Let x, y, and z denote the side lengths of the box, with the bottom face having dimensions x-by-y and z is the height. Naturally this means each of x, y, and z must be greater than 0.

The box has a fixed volume of 252 cm³, so

xyz = 252

The surface area of the box is

2xy + 2xz + 2yz

and we're told that the material cost for each face is different. The total cost of the material needed to make the box is given by

C (x, y, z) = ($5/cm²) xy + ($2/cm²) xy + 2 ($3/cm²) (xz + yz)

or, omitting units and simplifying,

C (x, y, z) = 7xy + 6 (x + y) z

In the volume constraint, solve for any one variable; I'll do z.

z = 252/(xy)

Substitute this into the cost function:

C (x, y, 252/(xy)) = 7xy + 1512 (x + y)/(xy)

Since this is now a function of 2 variables, I'll rewrite this as

C* (x, y) = 7xy + 1512 (1/y + 1/x)

Compute the partial derivatives of C and find the critical points:

∂C/∂x = 7y - 1512/x² = 0   ⇒   x² y = 216

∂C/∂y = 7x - 1512/y² = 0   ⇒   x y² = 216

It follows that

x² y = x y²   ⇒   x = y

Just like before, we can think about C* as yet another function but only of 1 variable,

C** (x) = 7x² + 3024/x

Now find the critical points of C** :

dC**/dx = 14x - 3024/x² = 0   ⇒   x = 6

All of this tells us that C (x, y, z) has a critical point when x = y = 6 and z = 252/6² = 7. So the box that costs the least has dimensions 6 × 6 × 7 cm, which gives the box a surface area of 240 cm² and a total cost of $756.

6 0
2 years ago
a circle is centered at the point -3,2) and passes through the point (1,5). The radius of the circle is blank units. The point (
lianna [129]
It's important that you share the complete question.  What is your goal here?  Double check to ensure that you have copied the entire problem correctly.

The general equation of a circle is x^2 + y^2 = r^2.  Here we know that the circle passes thru two points:  (-3,2) and (1,5).  Given that a third point on the circle is (-7, ? ), find the y-coordinate of this third point.


Subst. the known values (of the first point) into this equation:  (-3)^2 + (2)^2 = r^2.  Then 9 + 4 = 13 = r^2.

Let's check this.  Assuming that the equation of this specific circle is 
x^2 + y^2 = r^2 = 13, the point (1,5) must satisfy it.

(1)^2 + (5)^2 = 13 is not true, unfortunately.

(1)^2 + (5)^2 = 1 + 25 = 26 (very different from 13).

Check the original problem.  If it's different from that which you have shared, share the correct version and come back here for further help.



3 0
3 years ago
Help me please i shall give the correct answer brainliest
Olenka [21]

Answer:

9514 1404 393Answer: c = 6√2 d = 12Step-by-step explanation:The sides of any isosceles triangle (opposite the congruent angles) are congruent. Hence ...

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Mrs. Julien’s and Mrs. Castillejo’s classes are selling cookie dough for a school fundraiser. Customers can buy packages of maca
Oksi-84 [34.3K]

Answer: the cost of one package of macadamia nut chip cookie dough is $1.5

the cost of one package of triple chocolate cookie dough is $2.5

Step-by-step explanation:

Let x represent the cost of one package of macadamia nut chip cookie dough.

Let y represent the cost of one package of triple chocolate cookie dough.

Mrs. Julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $112.50. This means that

25x + 30y = 112.5 - - - - - - - - - - - - -1

Mrs. Castillejo’s class sold 8 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $124.50. This means that

8x + 45y = 124.5 - - - - - - - - - - -2

Multiplying equation 1 by 8 and equation 2 by 25, it becomes

200x + 240y = 900

200x + 1125 = 3112.5

Subtracting, it becomes

- 885y = - 2212.5

y = - 2212.5/- 885

y = 2.5

Substituting y = 2.5 into equation 1, it becomes

25x + 30 × 2.5 = 112.5

25x + 75 = 112.5

25x = 112.5 - 75 = 37.5

x = 37.5/25 = 1.5

The method used is the elimination method. It is more convenient to use.

8 0
3 years ago
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