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3 years ago

Billy worked for 38 hours last week. His boss gave him $361 for his work

1 answer:

4 0

Billy makes $9.50 per hour at work. The equation for Billy’s wage is y=9.5x, where y is Billy’s money and x is how many hours Billy works.

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The mean daily rainfall for a week was 5.5mm.for the first six days the mean rainfall was 1mm.How much rainfall on the seventh d

spayn [35]

Answer:

There was 32.5mm of rainfall on the seventh day.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values of a data-set divided by the number of values in the data-set.

The mean daily rainfall for a week was 5.5mm.for the first six days the mean rainfall was 1mm.

This means that during the week(7 days), the total amount of rain was of:

$6*1 + x = 6 + x$

How much rainfall on the seventh day ?

This is x. We have that:

$\frac{6 + x}{7} = 5.5$

$6 + x = 7*5.5$

$6 + x = 38.5$

$x = 38.5 - 6 = 32.5$

There was 32.5mm of rainfall on the seventh day.

7 0

3 years ago

Dilate the the triangle, scale factor = 3 (positive 3, ignore the

HACTEHA [7]

Answer:

The rule of dilation is $P'(x,y) = 3\cdot P(x,y)$ .

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

$P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$k$ - Scale factor, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0,0)$ , $k = 3$ , $A(x,y) = (-7,-6)$ , $B(x,y) = (-5,-2)$ and $C(x,y) =(-1,-5)$ , then dilated points of triangle ABC are, respectively:

$A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]$ (2)

$A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)]$

$A'(x,y) = (-21, -18)$

$B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]$ (3)

$B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)]$

$B'(x,y) = (-15,-10)$

$C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]$ (4)

$C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)]$

$C'(x,y) = (-3,-15)$

The rule of dilation is:

$P'(x,y) = 3\cdot P(x,y)$ (5)

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

7 0

2 years ago

A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at

ozzi

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Jamal hiked on two trails the 1st trail was 5 1/3 miles long and the 2nd trail was 1 3/4 time as long as the 1st trail how many

lisov135 [29]

5 1/3 + 1 3/4(5 1/3) = 16/3 + 7/4(16/3) = 16/3 + 28/3 = 44/3 or 14 2/3 <==

5 0

3 years ago

A box contains $7.45 in nickels, dimes, and quarters. There are 43 coins in all, and the sum of the numbers of nickels and dimes

kari74 [83]

Answer:

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Step-by-step explanation:

Total number of coins = 43

Let number of nickels = n

Let number of dimes = d

Let number of quarters = q

$n+d+q=43 ...... (1)$

Money in n nickels = $n \times 0.05$

Money in d dimes = $d \times 0.10$

Money in q quarters = $q \times 0.25$

Total money = $7.45

$0.05n +0.10d+0.25q = 7.45\\\Rightarrow 5n +10d+25q = 745 .... (2)$

The sum of the numbers of nickels and dimes is 3 less than the number of quarters.

i.e.

$n+d=q-3$

Let us put the value in (1):

$q-3+q=43\\\Rightarrow 2q= 43+3\\\Rightarrow q =23$

Putting the value of q in (1) and (2):

n+d = 20 .... (3)

$5n+10d+575 =745\\\Rightarrow 5n+10d =170\\\Rightarrow n+2d =34 .... (4)$

(4) - (3):

d = 14

Now, from (3):

n = 6

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

5 0

3 years ago