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2 years ago

Use area model to explain the product 4.6 and 3. Write the product in standard form, word form and expanded form.

2 answers:

4 0

Use area model to explain the product and 4.6 3. Write the product in standard form, word form and expanded form.
Standard form: 4.6 3
Word form: 4.0 + 0.6 3
<span>expanded form: four point six three</span>

enyata [817]2 years ago

3 0

Answer: Product = 13.8

Step-by-step explanation:

<u>As we have to use area model :</u>

So, we

Let length of rectangle be 4.6

Let breadth of rectangle be 3

As we know that

Area of rectangle is given by

$Length \times breadth\\\\=4.6\times 3\\\\=13.8\text{ squared units }$

Now, we must write in standard form, word form and expanded form:

So,

Standard form = 13.8

Word form = thirteen and 8 tenths

Expanded form is given by

$13.8=1\times 10+3\times 1+8\times \frac{1}{10}$

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A pet store owner set the price of a bag of cat food at 50% above the cost. When it did not sell, the price was reduced by 20%,

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Answer:

Step-by-step explanation:

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2 years ago

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five people, each working 8 hours a day, can assemble 400 toys in a five day work week. what is the average number of toys assem

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The question asks for the rate of toys per hour.

So we shall divide the total toys assembled by the total hours.

Its a five day week.

The number of hours allotted per day are 8.

So total allotted during the week are 8 × 5 = 40 hours.

Number of toys made during the week are 400.

Hence the number of toys assembled per hour per person

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2 years ago

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You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as y

pochemuha

Answer:

I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

Step-by-step explanation:

The number of total objects collected by me = 20

The number of objects collected by my friend = 20

Let us assume:

The number of rocks collected by me = m

The number of fossils collected by me = 2 k

⇒ m + 2 k = 20 .... (1)

So, according to the question:

The number of rocks collected by my friend = 3 x (rocks collected by me)

= 3 x (m) = 3 m

The number of fossils collected by my friend = 1/2 x (fossils collected by me) = 1/2 x (2k ) = k

⇒ 3 m + k = 20 .... (2)

Solving (1)and (2) for the value of m and k, we get:

m + 2 k = 20 ⇒ m = 20 - 2 k ... Put this in (2)

3 m + k = 20 ⇒ 3 (20 - 2 k) + k = 20

⇒ 60 - 6 k + k = 20

or, - 5k = -40

or, k = 40/5 = 8

⇒ k= 8

m + 2(8) = 20

or, m = 4

Hence, the number of rocks collected by me = m = 4

The number of fossils collected by me = 2 k = 2 (4) = 16

Hence, the number of rocks collected by my friend = 3 m = 3 x 4 = 12

The number of fossils collected by my friend = k = 8

Hence, I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

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2 years ago

Imagine that 30% of all U.S. Households own a dog, P(A)=.3 and that 10% of U.S. households own a Honda vehicle, P(B)=.1. In addi

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P(A|B)= P(B and A) / P(A)

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2 years ago

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to $(xyz)^2$ then it means that it is positive i.e $f(x,y,z)\geq 0$ .

Consider the function $F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)$

We want that the gradient of this function is equal to zero. That is (the calculations in between are omitted)

$\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0$

$\frac{\partial F}{\partial \lambda} = (x^2+y^2+z^2-1)=0$

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

$-2y\lambda = -2z\lambda$ . If lambda is not zero, then y =z. But, since $-2y\lambda=0$ and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set $y^2+z^2=1$ .

If both x,y are zero, then we have the solution set $z^2=1$ . We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

$\lambda = y^2z^2 = x^2z^2$ which implies $x^2=y^2$

Also, from the first and third equation we have that

$\lambda = y^2z^2 = x^2y^2$ which implies $x^2=z^2$

So, in this case, replacing this in the restriction we have $3z^2=1$ , which gives as another solution set. On this set, we have $x^2=y^2=z^2=\frac{1}{3}$ . Over this solution set, we have that the value of our function is $\frac{1}{3^3}= \frac{1}{27}$

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2 years ago