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2 years ago

THE DECIMAL 104.3 BECOMES 1,043 WHEN MULTIPLIED BY 10. THE SAME NUMBER BECOMES 10.43 WHEN MULTIPLIED BY 0.10 EXPLAIN WHY

Mathematics

2 answers:

tekilochka [14]2 years ago

8 0

Answer:

When we multiply the number 104.3 by 10, the decimal is shifted to one right place. Because whenever a decimal value is multiplied by 10, the decimal is shifted to one place on the right side.

When we multiply 104.3 by 0.10, we can say that we are multiplying it by $\frac{1}{10}$ or simply we are dividing 104.3 by 10.

When we divide any number by 10, we move the decimal to one left place.

cricket20 [7]2 years ago

5 0

Since 0.10 is a decimal, multiplying 104.3 by 0.10 is actually dividing 104.3 by 10. Thus 104.3 multiplied by 0.10 is 10.43.

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The equations below represent the numbers y of tickets sold after x weeks for two different local music festivals

Anton [14]

Assuming you mean y=10x+150 and y=20x+115, you need to use a simultaneous equation, because you have two equations with two unknowns (x and y)

rearrange so
10x-y=-150
20x-y=-115

multiply the top by -1, so that if we add the two lines together, the y will cancel out
-10x+y=150
20x-y=-115

add the two lines together
10x=35
x=3.5

so the time is 3 and a half weeks

then we can sub in x to find y
20x-y=-115
20(3.5)-y=-115
70-y=-115
-y=-185
y=185

so 185 tickets were sold !
you can sub these values into your original equations to check your answer :)

5 0

2 years ago

Read 2 more answers

If line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c?

slega [8]

we know that

If line b is perpendicular to line a, and line c is perpendicular to line a,

then

line b and line c are parallel

and two lines parallel have the same slope

Find the slope of the line b

Let

$A(-3,-2)\\B(2,3)$

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

$(x1,y1)=(-3,-2)\\(x2,y2)=(2,3)$

substitute

$m=\frac{(3+2)}{(2+3)}$

$m=\frac{(5)}{(5)}$

$m=1$

therefore

the answer is

the slope of the line c is

$mc=1$

8 0

2 years ago

Read 2 more answers

When Cara drives to work, it takes her 30 minutes to drive 15 miles. On her days off, she likes to drive to her favorite donut s

brilliants [131]

Answer:

3 miles

Step-by-step explanation:

First, we find the rate at which she drives, that is her speed.

Speed is given as:

speed = distance / time

When Cara drives to work, it takes her 30 minutes to drive 15 miles. Her speed is:

s = 15 / 30 = 0.5 miles per minute.

She drives at the same rate to The Dreamy Donut Shop and it takes her 6 minutes.

From the formula of speed, distance is given as:

distance = speed * time

Therefore, the distance of The Dreamy Donut Shop is:

distance = 0.5 * 6 = 3 miles

The Dreamy Donut Shop is 3 miles away.

3 0

2 years ago

Find all x in set of real numbers R Superscript 4 that are mapped into the zero vector by the transformation Bold x maps to Uppe

sukhopar [10]

Answer:

$x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]$

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the $\bar x$ so that $A \bar x = 0$

$\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right]$

Now the augmented matrix is

$\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right]$

After this, we decrease this to reduce the formation of the row echelon

$R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right]$

$R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]$

$R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]$

$R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right]$

$R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]$

$R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]$

$= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0$

$x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]$

By applying the above matrix, we can easily reach an answer

5 0

2 years ago

Let x be the number of successes throughout n independent repetitions of a random experiment having probability of success p=1/4

Llana [10]

To answer problems like this you have to use binomial:

P (x > 1) = 1 – p (0 < x < 1) > .7

So:

1 – p (0) – p (1) > .7

1 – (3/ 4) ^n – (3/ 4) ^n (n – 1 ) (1/ 4) > .7

Therefore n > 5.185, and the smallest value of n so that we can satisfy the given condition is 6 (rounded up)

6 0

2 years ago