MATHEMATICS HIGH SCHOOL

In a refrigerator, there are 6 bottles of soft drinks (each a different brand) and 8 cans of juice (each a different type). How many combinations can be made with one soft drink and one fruit drink?a. 1
c. 36
b. 14
d. 48

Answers

Answer 1
Answer: The number of ways of choosing 1 soft drink from 6 soft drinks is 6C1 = 6!/((6-1)! * 1!) = 6!/(5!) = (6*5*4*3*2*1)/(5*4*3*2*1) = 6.

Similarly, the number of ways of choosing 1 fruit juice from 8 cans of juice is 8C1 = 8!/((8-1)! * 1!) = 8!/7! = 8

number of combinations of 1 soft drink AND 1 fruit drink = 6 x 8 = 48

Answer: D [48]

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The designer also programs a bird with a path that can be modeled by a quadratic function. The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8). What is the slope of the line that represents the turtle's path?

Answers

Answer:

-1.2

Step-by-step explanation:

Given that the designer also programs a bird with a path that can be modeled by a quadratic function.

The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8).

If we treat this curve as line joining these two points then we can find the slope by the formula

Slope = change in y coordinate/change in x coordinate

Here the points given are

(0,20) and (10,8)

Change in y coordinate = 8-20 = -12\nChange in x coordinate = 10-0 = 10\nSlope = -1.2

Slope of the line that represents the turtle's path

=-1.2

Answer: 0.8

Step-by-step explanation: i got it right on edg

second part to the question is

h= 0

k= 20

a= -0.12

third part is letter B

What is the term of a 7-term geometric series if the first term is -11 the last term is -45,056 and the common ratio is -4

Answers

I assume you mean to ask how to find the sum of the seven terms?

You have

a_2=ra_1
a_3=ra_2=r^2a_1
a_4=ra_3=r^3a_1
...
a_7=ra_6=r^6a_1

So the sum is

a_1+ra_1+r^2a_1+\cdots+r^6a_1=a_1(1+r+r^2+\cdots+r^6)=a_1*(1-r^7)/(1-r)

You know that a_1=-11 and r=-4, so the sum is equal to

-4*(1-(-4)^7)/(1-(-4))=-13108

My question is, what is:  log6(4x-8)=3

Answers

log_6(4x-8)=3\ (*)\n\nD:4x-8 > 0\to4x > 8\to x > 2\to x\in(2;\ \infty)\n\n(*)\ 4x-8=6^3\n\n4x=216+8\n\n4x=224\ \ \ \ /:4\n\nx=56\in D
4x-8=6^3
4x-8=216
4x=224
x=56

Write 2 eggs is to 3 cups of flour as 12 eggs is to 18 cups of flour as a proportion.A. 2 eggs / 3 cups of flour = 12 eggs / 18 cups of flour.
B. 3 eggs / 2 cups of flour = 12 eggs / 18 cups of flour.
C. 2 eggs / 3 cups of flour = 18 cups of flour / 12 eggs.
D. 3 eggs / 12 cups of flour = 32 eggs / 18 cups of flour.

Answers

The answer is A. 2 eggs / 3 cups of flour = 12 eggs / 18 cups of flour because 2 x 18 = 3 x 12 = 36.

On a recent trip to the convenience store, you picked up 4 gallons of milk, 6 bottles of water and 5 snack size bags of chips. You total bill before tax was $ 27.2. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.80 more than a bottle of water, how much does each item costHow much does a snack size bag of chips cost?


How much does a bottle of water cost?


How much does a gallon of milk cost?

Answers

Answer:

Cost of a snack size bag of chips = $0.8

Cost of a water bottle = $1.6

Cost of a gallon of milk = $3.4

Step-by-step explanation:

Let the cost of water bottle = $a

Cost of 1 gallon milk = $b

and cost of 1 bag of chips = $c

So, cost of 4 gallons of milk, 6 bottles of water and 5 bags of chips = $(4b + 6a + 5c)

4b + 6a + 5c = 27.2 -----(1)

Cost of one water bottle = 2 × cost of one bag of chips

a = 2c -----(2)

A gallon of milk = cost of water bottle + $1.80

b = a + 1.8

From equation (2)

b = 2c + 1.8 -----(3)

Now we substitute these values from equations (2) and (3) in equation (1)

4(2c + 1.8) + 6(2c) + 5c = 27.2

8c + 7.2 + 12c + 5c = 27.2

25c = 27.2 - 7.2

c = (20)/(25)

c = $0.8

From equation (2)

a = 2×0.8

a = $1.6

From equation (3)

b = 2(0.8) + 1.8

b = 1.6 + 1.8

b = $3.4

Therefore, cost of a snack size bag of chips = $0.8

Cost of a water bottle = $1.6

Cost of a gallon of milk = $3.4

1. El tamaño de un glóbulo blanco de aproximadamente es de aproximidamente 0,000012 metros, mientras que el tamaño de un glóbulo rojo es de 0.0000065m. ¡Cuál es la diferencia entre el tamaño de un glóbulo blanco y el tamaño de un glóbulo rojo?.Expresar el resultado en Notación Científica.

Answers

Answer:

The difference between the size of white blood cells and the size of red blood cells in scientific notation is 5.5 * 10^(-6) m.

Step-by-step explanation:

we are given that the size of white blood cells is 0.000012 metres and the size of red blood cells is 0.0000065 metres.

And we have to find the difference between the size of both cells in scientific notation.

SO, Size of White blood cells = 0.000012 m

      Size of Red blood cells = 0.0000065 m

Now, Difference between both cell sizes = Size of white blood cells - Size of Red blood cells

                           =  0.000012 m - 0.0000065 m

                           =  0.0000055 m

Now, in scientific notation it is represented as =  5.5 * 10^(-6) m

Hence, the difference between the size of white blood cells and the size of red blood cells in scientific notation is 5.5 * 10^(-6) m.
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