Which diagram represents the postulate that states exactly one line exists between any two points?

Together, Katya and Mimi have 480 pennies in their piggy banks. After Katya lost ½ of her pennies and Mimi lost 2/3 of her penni

vesna_86 [32]

Answer:

288 pennies

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year,

IrinaVladis [17]

Use compound interest formula F=P(1+i)^n twice, one for each deposit and sum the two results.

For the P=$40,000 deposit,
i=10%/2=5% (semi-annual)
number of periods (6 months), n = 6*2 = 12
Future value (at end of year 6),
F = P(1+i)^n = 40,000(1+0.05)^12 = $71834.253

For the P=20000, deposited at the START of the fourth year, which is the same as the end of the third year.
i=5% (semi-annual
n=2*(6-3), n = 6
Future value (at end of year 6)
F=P(1+i)^n = 20000(1+0.05)^6 = 26801.913

Total amount after 6 years
= 71834.253 + 26801.913
=98636.17 (to the nearest cent.)

8 0

1 year ago

A dairy sells $3 and $5 ice creams. In one day they sell 50 ice creams earning a total of $180. How many of each type of ice cre

murzikaleks [220]

We are going to make simultaneous equations.
x will be our $3 ice cream and y will be our $5 ice cream

Equation1 ---- x + y = 50 (the sum of all the ice creams they sell)
Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180
Since we can't solve for both variables we will put one of the variables in terms of the other.
Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50)
Now I am going to take equation 2 and replace the x with -y +50

3 (-y +50) + 5y = 180
Now I will use the distributive law on the 3 and what's in the parentheses:
-3y + 150 + 5y = 180
Now I will combine like terms (the -3y and the 5y)
2y + 150 = 180
Now subtract 150 from both sides of the equation
2y = 30
Divide both sides by 2
and get y= 15 They sold 15 ice creams that cost $5 each
Since equation 1 is x+y=50 we can replace y with 15
x + 15 = 50 Now subtract 15 from both sides x = 35
Since x represents the $3 ice creams, they sold 35 of those.
Check:
35 X 3 = $105
15 x 5 = + <u>75
</u> $180

8 0

1 year ago

HELP MEEEEEEEEEE Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards

hodyreva [135]

Answer:

Each birthday card costs $2.2 ⇒ answer c

Step-by-step explanation:

* Lets explain how to solve the problem

- Package A contains 3 birthday cards and 2 thank-you notes

- It costs $9.60

- Package B contains 8 birthday cards and 6 thank-you notes

- It costs $26.60

- x represents the cost of birthday card and y represents the cost of

thank-you note

* Lets change these information to two equations

∵ x represents the cost of each birthday cards

∵ y represents the cost of each thank-you notes

∵ Bag A contains 3 birthday cards and 2 thank-you notes

∵ Bag A costs $9.60

∴ 3x + 2y = 9.60 ⇒ (1)

∵ Bag B contains 8 birthday cards and 6 thank-you notes

∵ Bag B costs $26.60

∴ 8x + 6y = 26.60 ⇒ (2)

* Lets solve this system of equations to find x and y

- Multiply equation (1) by -3 to eliminate y

∵ -3(3x) + -3(2y) = -3(9.60)

∴ -9x - 6y = -28.8 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -2.2

- Multiply both sides by -1

∴ x = 2.2

∵ x represents the cost of each birthday cards

∴ The cost of each birthday card is $2.2

* Each birthday card costs $2.2

6 0

2 years ago

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A student repeatedly measures the mass of an object using a mechanical balance and gets the following values: 560 g, 562 g, 556

MrRissso [65]

Answer: 2.76 g

Step-by-step explanation:

The formula to find the standard deviation:-

$\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{n}}$

The given data values : 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g.

Then, $\overline{x}=\dfrac{\sum_{i=1}^{10} x_i}{n}\\\\\Rightarrow\ \overline{x}=\dfrac{560+562+556+558+560+556+559+561+565+563}{10}\\\\\Rightarrow\ \overline{x}=\dfrac{5600}{10}=560$

Now, $\sum_{i=1}^{10}(x_i-\overline{x})^2=0^2+2^2+(-4)^2+(-2)^2+0^2+(-4)^2+(-1)^2+1^2+5^2+3^2\\\\\Rightarrow\ \sum_{i=1}^{10}(x_i-\overline{x})^2=76$

Then, $\sigma=\sqrt{\dfrac{76}{10}}=\sqrt{7.6}=2.76$

Hence, the standard deviation of his measurements = 2.76 g

6 0

2 years ago