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3 years ago

A restaurant cook makes 4 gallons of soup to divide equally into 44 bowls.

Mathematics

1 answer:

Ann [662]3 years ago

3 0

Answer:

0.344

Step-by-step explanation:

3.785×4= 15.14

15.14÷44=0.344

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Geometric Series assistance

Levart [38]

we have been asked to find the sum of the series

$\sum _{n=1}^5\left(\frac{1}{3}\right)^{n-1}$

As we know that a geometric series has a constant ratio "r" and it is defined as

$r=\frac{a_{n+1}}{a_n}=\frac{\left(\frac{1}{3}\right)^{\left(n+1\right)-1}}{\left(\frac{1}{3}\right)^{n-1}}=\frac{1}{3}$

The first term of the series is $a_1=\left(\frac{1}{3}\right)^{1-1}=1$

Geometric series sum formula is

$S_n=a_1\frac{1-r^n}{1-r}$

Plugin the values we get

$S_5=1\cdot \frac{1-\left(\frac{1}{3}\right)^5}{1-\frac{1}{3}}$

On simplification we get

$S_5=\frac{121}{81}$

Hence the sum of the given series is $\frac{121}{81}$

5 0

3 years ago

What is the product of 2x + y and 5x – y + 3? x2 + xy + x + y2 + y

miskamm [114]

Answer: $10x^2+3xy+6x-y^2+3y$

Step-by-step explanation:

You need to remember the Product of powers property:

$(a^m)(a^n)=a^{(m+n)}$

Then, knowing this property, now you have to apply the Distributive property. So:

$(2x+y)(5x-y+3)=\\\\=(2x)(5x)-(2x)(y)+(2x)(3)+(y)(5x)-(y)(y)+(y)(3)\\\\=10x^2-2xy+6x+5xy-y^2+3y$

Finally, to simplify this expression, you need to add the like terms.

Therefore, you get that the product is:

$=10x^2+3xy+6x-y^2+3y$

3 0

3 years ago

Read 2 more answers

The disk enclosed by the circle x+y = 4 is revoived about the y-axis to generate solid sphere. A hele of diameter 2 units is the

Vesnalui [34]

Step-by-step explanation:

Suppose we have a curve, y = f(x).

y = f(x)

x = a x = b

Imagine that the part of the curve between the ordinates x = a and x = b is rotated about the

x-axis through 360◦

. The curve would then map out the surface of a solid as it rotated. Such

solids are called solids of revolution. Thus if the curve was a circle, we would obtain the surface

of a sphere. If the curve was a straight line through the origin, we would obtain the surface of

a cone. Now we already know what the formulae for the volumes of a sphere and a cone are,

but where did they come from? How can they calculated? If we could find a general method

for calculating the volumes of the solids of revolution then we would be able to calculate, for

example, the volume of a sphere and the volume of a cone, as well as the volumes of more

complex solids.

To see how to carry out these calculations we look first at the curve, together with the solid it

maps out when rotated through 360◦

y = f(x)

Now if we take a cross-section of the solid, parallel to the y-axis, this cross-section will be a

circle. But rather than take a cross-section, let us take a thin disc of thickness δx, with the face

of the disc nearest the y-axis at a distance x from the origin.

www.mathcentre.ac.uk 2

6 0

3 years ago

What is the equation of the line in slope -intercept form?

V125BC [204]

Slope intercept form is y=mx+b

6 0

3 years ago

What is the recursive rule for the sequence?

love history [14]

Answer : option d

4.4, 5.8, 7.2, 8.6, 10, …

First we find the common difference between two terms

5.8 - 4.4 = 1.4

7.2 - 5.8 = 1.4

8.6 - 7.2 = 1.4

10 - 8.6 = 1.4

So common difference is 1.4

To find recursive rule, we add the difference with previous term

Recursive rule is $a_n = a_{n-1} + d$

a1 is the first term so a1= 4.4

d is the difference = 1.4

So recursive rule is

$a_n = a_{n-1} + 1.4$ , where a1 = 4.4

4 0

3 years ago