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3 years ago

Mrs marks wants to buy 89 pens. If the pens come in packs of 10, how many packs does she need to buy

Mathematics

2 answers:

vesna_86 [32]3 years ago

6 0

Answer:

9 packs

Step-by-step explanation:

$\frac{89}{10} = 8\frac{9}{10}$

Since you can't buy $\frac{9}{10}$ of a pack, you must round up to 9.

Andrei [34K]3 years ago

4 0

Answer: 9 packs

Step-by-step explanation:

Mrs. Marks wants 89 pens.
Pens come in packs of 10

89 is about 90. The pens come in packs of 10, so divide 90 by 10 and the quotient is 9.

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You triple your account balance by making a deposit. Then you withdraw $28.50 from your bank account. Now your account is overdr

Crazy boy [7]

Answer:

Your original account balance before you made the deposit is $6

Step-by-step explanation:

Let x = your original account balance.

You triple your account balance by making a deposit. This means

New account balance = 3 × x = 3x

Then you withdraw $28.50 from your bank account. This means that you have $(3x - 28.5) left.

Now your account is overdrawn by $10.50. This means you have withdrawn beyond what you have in your account. Your new account balance is -$10.5. Therefore,

3x - 28.5 = - 10.5

3x = -10.5 + 28.5 = 18

x = 18/3 = 6

Your original account balance before you made the deposit is $6

8 0

3 years ago

Solve the inequality.

sattari [20]

X >- 5

-2x -4 < 3x +21
+4 +4
-2x < 3x +25
-3x -3x
-5x < +25
-5x/-5 25/-5
X > -5

6 0

3 years ago

Considering the number of questions incorrect from classmates on a quiz {10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19,

IrinaK [193]

Answer:

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

Step-by-step explanation:

We are given the following data in the question:

10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{225}{15} = 15$

Sum of squares of differences = 25 + 16 + 9 + 4 + 4+ 4 + 1 + 0+ 1+ 1 + 4 + 9 + 9+ 16 + 25 = 128

$S.D = \sqrt{\dfrac{128}{14}} = 3.02$

Empirical rule:

According to this rule almost all the data lies within three standard deviation of the mean for a normal distribution.
About 68% of data lies within one standard deviation of the mean.
About 95% of data lies within two standard deviations of mean.
Arround 99.7% of data lies within three standard deviation of mean.

Thus, by empirical rule,

$\mu \pm 1\sigma = 15\pm (3.02) = (11.98,18.02)$

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

5 0

3 years ago

A car rental agency has 150 cars. The owner finds that at a price of $48 per day, he can rent all the cars. For each $2 increase

hram777 [196]

Given that for each $2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
$(48 + 2x) \times (150 - 4x)=7,200+108x-8x^2$ .

Also, given that for each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
$5(150-4x)=750-20x$

Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
 $(7,200+108x-8x^2)-(750-20x)=6,450+128x-8x^2$

For maximum profit, the differentiation of the profit function equals zero.
i.e.
 $\frac{d}{dx} (6,450+128x-8x^2)=0 \\ \\ 128-16x=0 \\ \\ x= \frac{128}{16} =8$

The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.

Therefore, the rental charge will maximize profit is $64.

3 0

3 years ago

A train travels from Washington DC to new york(225 miles). The train departs at 4:55 PM and arrives in New York at 7:55 PM. What

mylen [45]

Answer:

The average speed is:

$\var{v}=75\: miles/h$