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2 years ago

Is the product of two mixed number less than, between,or greater than the two factors?explain

1 answer:

7 0

The product of two mixed numbers is greater than the two factors (assuming that the two numbers are positive and greater than or equal to 1).
To better understand this, let's take as an example the multiplication of 1.5 and 2.25.
Both are mixed numbers, their multiplication is as follows:
1.5 * 2.25 = 3.375
The two factors here are 1.5 and 2.25 and the product is 3.375 which is greater than the factors

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Marcie bought a total of 20 used books and cds during a yard sale for a total of 54.50$. of books cost 1.50$ each and cds 5$ eac

melomori [17]

Let numbers of books be 'b' and numbers of CDs be 'c'

We can set up two equations:
Equation [1] ⇒ $b+c=20$
Equation [2] ⇒ $1.50b+5c=54.50$

We are solving for the number of books and the number of CDs bought

When we have two equations in terms of two different variables; $b$ and $c$ , that we need to solve, then this becomes a simultaneous equation problem.

First, rearrange Equation [1] to make either $b$ or $c$ the subject:
$b+c=20$
$b=20-c$

Then we substitute $b=20-c$ into Equation [2]
$1.50b+5c=54.50$
$1.50(20-c)+5c=54.50$
$30-1.50c+5c=54.50$
$5c-1.5c=54.50-30$
$3.5c=24.50$
$c=7$

Now we know the value of $c$ which is $c=7$ , substitute this value into $b=20-c$ we have $b=20-7=13$

Answer:
Numbers of books = 13
Numbers of CDs = 7

5 0

2 years ago

The width of a triangle is six more than twice the height. The area of the triangle is 88in2. Find the height and base of the tr

malfutka [58]

For this case we have that by definition, the area of a triangle is given by:

$A = \frac {b * h} {2}$

Where:

b: It is the base of the triangle

h: It is the height of the triangle

According to the statement data we have:

$b = 6 + 2h$

Substituting we have:

$88 = \frac {(6 + 2h) * h} {2}\\176 = 6h + 2h ^ 2\\2h ^ 2 + 6h-176 = 0$

We divide between 2 on both sides:

$h ^ 2 + 3h-88 = 0$

We factor by looking for two numbers that, when multiplied, are obtained -88 and when added together, +3 is obtained.

These numbers are +11 and -8.

$(h + 11) (h-8) = 0$

We have two roots:

$h = -11\\h = 8$

We choose the positive value.

Thus, the base of the triangle is: $b = 6 + 2 (8) = 22$

Answer:

The base of the triangle is 22 units.

5 0

2 years ago

Read 2 more answers

Can you answer this plzz and the pic that goes with it???????? Thx soo much!!!!!

kkurt [141]

Answer: c. t > 82

Step-by-step explanation:

Let t represent the number of tickets that the committee would sell.

The dance committee of Pine Bluff Middle School earns $72 from a bake sale and will earn $4 for each ticket they sell to the Spring Fling dance. This means that the revenue that they would generate from selling x tickets is

72 + 4x

The dance will cost $400.

To make profit, revenue must be greater than cost. Therefore, the inequality to determine the number of tickets the committee could sell to have money left over after they pay for this year's dance is

72 + 4x > 400

4x > 400 - 72

4x > 428

x > 328/4

x > 82

5 0

2 years ago

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Brad is hoping to package exactly 48 baseballs together. He sees the side of a box in his storeroom that is 2 x 3. What is he ho

lakkis [162]

The given dimensions of the base of the box are 2 x 3 units.

Let h be the height of the box.

So, the volume of the box = 2 x 3 x h ...(i)

The shape of baseball is spherical and one baseball fits in a cubical box having the minimum dimensions equal to the diameter of the spherical ball.

Assuming the diameter of the baseball is d units.

So, the volume occupied by one baseball= volume of the cubical box having the side $d$ units.

$=d^3$ cubic units

So, the volume required to pack 48 baseballs

$= 48 d^3 \cdots(ii)$

Assuming that all the baseballs fit in the box, i.e peripheral balls in every horizontal and vertical layer touched the box as shown in the figure.

So, the length, 3 units and the width, 2 units, must be the integral multiple of the diameter, $d$ units, of the baseball. i.e

The length, $3 = ad\cdots(iii)$

The width, $2=bd\cdots(iv)$

The height, $h=cd\cdots(iv)$

where $a,b$ and $c$ belong to the natural number.

This required volume must be equals to the volume of the box.

From equations (i) and (ii),

$2\times 3\times h=48d^3$

[from (iii) and (iv)]

$\Rightarrow abhd^2=48d^3$

$\Rightarrow h=\frac{48d^3}{6abd^2}$

$\Rightarrow h=\frac{48}{ab}d$

On comparing with the equation (iv)

$c=\frac{48}{ab}\cdots(v)$

Now, if the diameter of the baseball is unity,i.e, d=1 unit

( integer) and (integer) [from (iii) and (iv)]

(also an integer) [from (v)]

Now, the height of the box,

$h=8 \times 1= 8$ unit.

Hence, the other dimension of the box, is 8 units corrosponding to the unity diameter of the baseball.

Note the height of the box depends on the diameter of the baseball, so it will have infinite possible value for different value of the diameter.

For example, the value of height for d=1 unit has been shown.

and another example may be if units, then (integer) and (integer)

(also an integer) [from (v)]

Now, the height of the box,

$h=2 \times 0.5= 1$ unit. [from (iv)]

Here, the height of the box is 2 units corrosponding to 0.5 unit diameter of the baseball.

The possivle values of d can be taken for which $a,b$ and $c$ must be integers.

6 0

2 years ago

Which of the following statements is true? a. sin 30° = cos 30° b. sin 35° = cos 55° c. sin 60° = cos 60° d. sin 55° = cos 25°

Makovka662 [10]

<span>b. sin 35° = cos 55° is the correct answer i believe :)</span>

6 0

2 years ago

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