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natima [27]
2 years ago
11

Sonja's house is 4 blocks west and 1 block south of the center of town. Her school is 3 blocks east and 2 blocks north of the ce

nter of town.
What is the direct distance from Sonja's house to her school?

(Hint: The center of town should be the origin, and north is up.)
Mathematics
1 answer:
lorasvet [3.4K]2 years ago
6 0
The answer is √58 = 7.62

So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).
Use the Pythagorean theorem:
c² = a² + b²
a = 3
b = 7

c² = 3² + 7²
c² = 9 + 49
c² = 58
c = √58
c = 7.62
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irina [24]

Answer:

The initial amount in the account is $333.33

Step-by-step explanation:

Here, we want to calculate the initial amount in the account.

Let the initial amount be $x

Mathematically;

Simple interest = PRT/100

where P is the amount deposited = $x

R is the rate = 10%

T is the time = 5 years

Simple interest = Present amount - Principal = $(500-x)

By substituting;

500-x = (x * 10 * 5)/100

100(500-x) = 50x

50,000 - 100x = 50x

50,000 = 100x + 50x

150x = 50,000

x = 50,000/150

x = 333.33333333

Which to the nearest penny ; x = $333.33

6 0
3 years ago
Santa Claus can buy 3 reindeer and a sleigh for $800. If the sleigh cost $230, how much did each reindeer cost? Define the varia
nydimaria [60]

Answer:

$190

Step-by-step explanation:

800-230=570

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8 0
3 years ago
A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distribut
klemol [59]

Answer:

Step-by-step explanation:

Since the amount of soft drink dispensed into a cup is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = amount in ounce of soft drink dispensed into cup.

µ = mean amount

σ = standard deviation

From the information given,

µ = 7.6oz

σ = 0.4 oz

a) The probability that the machine will overflow an 8-ounce cup is expressed as

P(x > 8) = 1 - P(x ≤ 8)

For x = 8,

z = (8 - 7.6)/0.4 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

P(x ≤ 8) = 1 - 0.84 = 0.16

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c) when the machine has just been loaded with 848 cups, the number of cups expected to overflow when served is

0.16 × 848 = 136 cups

4 0
3 years ago
Your parents purchase a computer for $1,257.00 plus 6% sales tax. They decide to finance it through the store’s 0% program for 6
Katena32 [7]

Answer:

$111.59

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The total amount of the purchase was the cost of the computer plus the sales tax:

$1,257*1,06= $1,332.42

Now, to determine the interest that they will have to pay, you have to consider that the interest rate is 16,75% APR that is the annual percentage rate but as only 6 month have passed, the interest rate at this point that they have to pay is 8.375%:

$1,332.42*8.375%= $111.59

The interest that they will be charged is  $111.59

5 0
3 years ago
Find the perimeter of a square with a side length of 10 meters
Vlad [161]

side length of square=10

Now,

perimeter of square =4l

=4×10

=40m

6 0
2 years ago
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