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1 year ago

Natalia solved the problem 74.4/12=6.2. complete the model with partial products check Natalia's work using multiplication

Mathematics

1 answer:

tia_tia [17]1 year ago

5 0

Answer:

Natalia's work is wrong.

Step-by-step explanation:

Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:

1) $x = 6.2\times 12$ Given.

2) $x = \left(6+0.2\right)\times 12$ Definition of addition.

3) $x = 6\times 12 + 0.2\times 12$ Distributive property.

4) $x = 72 + \frac{2}{10}\times 12$ Definitions of multiplication and decimal number.

5) $x = 72 +[2\cdot (10)^{-1}]\cdot 12$ Definition of division/Associative property.

6) $x = 72 + [2\cdot 12]\cdot (10)^{-1}$ Associative property.

7) $x = 72 + 24\cdot 10^{-1}$ Definition of multiplication.

8) $x = 72 + \frac{24}{10}$ Definition of divsion.

9) $x = 72 + 2.4$ Defintion of decimal number.

10) $x = 74.4$ Definition of addition/Result

Natalia's work is wrong.

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A bar graph titled Album Type Sold per Year has year on the x-axis and number of albums sold on the y-axis. For C D s, in 2008 t

stira [4]

Answer:

True, True, False, True, False, True

Step-by-step explanation:

CDs have a higher mean than digital

Let's check. CD mean is (1000 + 800 + 800 + 600 + 400 + 200)/6 = 633.33

Digital mean: (100 + 300 + 300 + 500 + 700 + 900)/6 = 466.67

CD's mean is higher. Since you are dividing byt he same number you also could have just added the amount and found which was a larger number. But yes, this is true.

The range of digital is 800

The range is the highest number inus the lowest number. For digital the highest is 900 and lowest is 100 so the ange is 900-100 = 800. So this is true.

The median of CDs is 400.

The median is the middle value for odd numbers of values, or the average of the two middle values. 6 total values means you have to take the third and fourth and average them. in CDs the middle values are 800 and 600, the average is 700, so that is what the median is. this is false.

Both have the same interquartile range.

Interquartile range is to find the middle number or numbers like in median, then take the two parts it is split into and find the "median" of those. Then subtract the larger one fromt he smaller one.

IQR of CD the first half is 200, 400, 600 so the middle here is 400, second half has a middle number of 800 so IQR here is 800-400=400

IQR of digital is 700-300 = 400 so yes both are the same.

Both have the same median

We know the medan of CDs is 700 then findign the median of digital is (300+500)/2 = 400. So no, the medians are not the same.

Digital’s mean is around 467.

We founf the mean for digital to be 466.67 which rounds up to 467, So I would say it is true.

8 0

2 years ago

Read 2 more answers

Trapezoid A B C D is shown. Sides A B and D C are parallel. Sides A D and B C are congruent. Angle B is (3 x) degrees and angle

photoshop1234 [79]

Answer: The value of x in trapezoid ABCD is 15

Step-by-step explanation: The trapezoid as described in the question has two bases which are AB and DC and these are parallel. Also it has sides AD and BC described as congruent (that is, equal in length or measurement). These descriptions makes trapezoid ABCD an isosceles trapezoid.

One of the properties of an isosceles trapezoid is that the angles on either side of the two bases are equal. Since line AD is equal to line BC, then angle D is equal to angle C. It also implies that angle A is equal to angle B.

With that bit of information we can conclude that the angles in the trapezoid are identified as 3x, 3x, 9x and 9x.

Also the sum of angles in a quadrilateral equals 360. We can now express this as follows;

3x + 3x + 9x + 9x = 360

24x = 360

Divide both sides of the equation by 24

x = 15

Therefore, in trapezoid ABCD

x = 15

4 0

2 years ago

Read 2 more answers

An experiment on memory was performed, in which 16 subjects were randomly assigned to one of two groups, called "Sentences" or "

FromTheMoon [43]

Answer:

There is no significant difference between the averages.

Step-by-step explanation:

Let's call

$\large X_{sentences}$ the mean of the “sentences” group

$\large S_{sentences}$ the standard deviation of the “sentences” group

$\large X_{intentional}$ the mean of the “intentional” group

$\large S_{intentional}$ the standard deviation of the “intentional” group

Then, we can calculate by using the computer

$\large X_{sentences}=28.75$

$\large S_{sentences}=3.53553$

$\large X_{intentional}=31.625$

$\large S_{intentional}=1.40788$

$\large X_{sentences}-X_{intentional}=28.75-31.625=-2.875$

The standard error of the difference (of the means) for a sample of size 8 is calculated with the formula

$\large \sqrt{(S_{sentences})^2/8+(S_{intentional})^2/8}$

So, the standard error of the difference is

$\large \sqrt{(3.53553)^2/8+(1.40788)^2/8}=1.34546$

In order to see if there is a significant difference in the averages of the two groups, we compute the interval of confidence of 95% for the difference of the means corresponding to a level of significance of 0.05 (5%).

If this interval contains the zero, we can say there is no significant difference.

Since the sample size is small, we had better use the Student's t-distribution with 7 degrees of freedom (sample size-1), which is an approximation to the normal distribution N(0;1) for small samples.

We get the $\large t_{0.05}$ which is a value of t such that the area under the Student's t distribution outside the interval $\large [-t_{0.05}, +t_{0.05}]$ is less than 0.05.

That value can be obtained either by using a table or the computer and is found to be

$\large t_{0.05}=2.365$

Now we can compute our confidence interval

$\large (X_{sentences}-X_{intentional}) \pm t_{0.05}*(standard \;error)=-2.875\pm 2.365*1.34546$

and the confidence interval is

[-6.057, 0.307]

Since the interval does contain the zero, we can say there is no significant difference in these samples.

6 0

2 years ago

Point b has coordinates (3,-4) and lies on the circle whose equation is x^2 + y^2= 25. If angle is drawn in a standard position

lakkis [162]

Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:

 $BO^2=AO^2+AB^2 \\ BO^2=3^2+4^2 \\ BO^2=9+16 \\ BO^2=25 \\ BO=5$ .

{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
The sine of the angle BOA is
$\sin \angle BOA= \dfrac{AB}{BO} = \dfrac{4}{5} =0.8$

Since point B is placed in the IV quadrant, the sine of the angle that is drawn in a standard position with its terminal ray will be 


 $\sin \theta=-0.8$ .

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2 years ago

What is the scale if: 3.2 cm on the map correspond to 4 km in the actual distance?

aliya0001 [1]

Scaling on map is defined as the ratio of a distance on the map to the corresponding distance on the ground.

Here, 3.2 centimeters on the map is equivalent to 4 kilometers.

We can use unitary method to find, how many kilometer/kilometers each centimeter corresponds to.

Using the unitary method:

$3.2 cm=4 km$