In a sport competition Alyssa was penalized -16 points in each of the 4 events how many points was she penalized in each event?

How many pieces of wire 3.6cm long can be cut from a coil of 1m long?What is the length of the piece left over?

sp2606 [1]

Answer:

We can get 27 pieces of wire 3.6 cm long and have a piece 7/9 cm left over

Step-by-step explanation:

Find the "unit length" by dividing 1 m by 3.6 cm:

1 m

-----------

3.6 cm

Recall that 1 m = 100 cm. Multiply the following by the conversion factor 100 cm / 1 m:

1 m 100 cm

----------- * ----------------- = 27,7777777...

3.6 cm 1 m

We can get 27 pieces of wire 3.6 cm long and have a piece 7/9 cm left over (verify this by dividing 7 by 9 on a calculator).

8 0

3 years ago

Read 2 more answers

Given the function () = $

elena-s [515]

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

<h3>The inverse of the function?</h3>

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4

Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

<h3>Sum of arithmetic series</h3>

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

<h3>The common ratio of the sequence</h3>

Here, we have:

T11 = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2

Read more about sequence at:

brainly.com/question/7882626

#SPJ1

6 0

2 years ago

Please help me ASAP

vovikov84 [41]

1018262910101101 explanation:

8 0

3 years ago

A number next to a variable always showd

Juliette [100K]

The number next to a variable, for example: 5x, is called a coefficient. And all you do is multiply the number with the variable

8 0

3 years ago

12

Sergeu [11.5K]

Answer:

5 pints per hour.

Step-by-step explanation:

Morning:

Given:

Number of strawberries packed in every 4 minutes = 3

∴ Number of strawberries packed in every one minute = $\frac{3}{4}$

So, number of strawberries packed in every 60 minutes = $\frac{3}{4}\times 60=45$

1 hour = 60 minutes.

So, strawberries are packed at a rate of 45 pints per hour in the morning.

Afternoon:

Number of strawberries packed in every 3 minutes = 2

∴ Number of strawberries packed in every one minute = $\frac{2}{3}$

So, number of strawberries packed in every 60 minutes = $\frac{2}{3}\times 60=40$

1 hour = 60 minutes.

So, strawberries are packed at a rate of 40 pints per hour in the afternoon.

Difference between the packing rates is given as:

Morning rate - Afternoon rate = 45 - 40 = 5 pints per hour.

So, she packed 5 more pints in one hour in the morning than in the afternoon.

3 0

3 years ago