What is the probability that a randomly selected camper likes swimming or having a cookout, but not both?

Multiply (x + 1)³

nlexa [21]

Answer:

x³+3x²+3x+1

Step-by-step explanation:

=(x+1)(x+1)(x+1)

=(x+1)(x²+x+x+1)

=(x+1)(x²+2x+1)

=(x³+2x²+x+x²+2x+1)

=x³+3x²+3x+1

4 0

1 year ago

Read 2 more answers

The Walnut Cove Ruritan Club sells hot dogs and drinks from a concession stand at the annual July 4 parade. Carl bought 6 hot do

pickupchik [31]

Based on the two different purchases, you can write equations for the price of a hotdog (h) and that of a drink (d). These equations can be solved by your favorite method to find the individual prices.

... 6h +4d = 17.00 . . . . . . Carl's purchase

... 3h +4d = 12.50 . . . . . . Susan's purchase

We can see that the difference in purchase cost (of $4.50) is due entirely to the difference in the number of hotdogs (3). Thus, the price of a hotdog must be

... $4.50/3 = $1.50

The 4 drinks are then ($12.50 -4.50) = $8, so must be $2 each. You don't need to figure the cost of a drink to determine that the appropriate answer choice is ...

... D. $1.50 for a hot dog; $2.00 for a drink.

5 0

3 years ago

Of 560 marbles in a bag, 65% are red and the rest are blue. After 28 red marbles are replaced with blue ones, how many blue marb

jonny [76]

Answer: The answer is 400 blue marbles.

Step-by-step explanation: Given that there are 560 marbles in a bag, out of which 65% are red and rest are blue.

So, number of red marbles is

$n_r=65\%\times 560=\dfrac{65}{100}\times 560=364,$

and number of blue marbles is

$n_b=560-364=196.$

Now, if 28 red marbles are replaced by blue marbles, the the new number of red and blue marbles will be

$n_r^\prime=364-28=336~~~\textup{and}~~~n_b^\prime=196+28=224.$

Now, to get 65% of the marbles blue, we need to add some more blue marbles to the bag. Let 'x' number of blue marbles are added to the bag, then

$65\%\times (560+x)=224+x\\\\\Rightarrow \dfrac{65}{100}\times (560+x)=224+x\\\\\Rightarrow 13(560+x)=20(224+x)\\\\\Rightarrow 7280+13x=4480+20x\\\\\Rightarrow 7x=2800\\\\\Rightarrow x=400.$

Thus, 400 blue marbles need to be added to the bag.

5 0

3 years ago

Read 2 more answers

A rectangle is placed around a semicircle as shown below. The length of the rectangle is 14mm. Find the area of the shaded regio

Damm [24]

Image is missing, so i have attached it

Answer:

21.07 mm²

Step-by-step explanation:

We will use the Formulas:

Area of semicircle = πr²/2

Area_rectangle = Length x width = Lw

We are given:

Length of rectangle = 14 mm

From the attached image, the diameter of the semicircle is equal to the length of the rectangle.

Thus;

diameter of semicircle = length of rectangle

Therefore,

diameter of semicircle = 14 mm

Also, from the attached image, the radius of the semicircle is equal to the width of the rectangle.

Thus;

diameter of semicircle/2 = radius of semicircle

Hence;

radius of semicircle = 14/2 = 7mm = width of rectangle

Thus;

Area of rectangle = L*w = 14 × 7 = 98 mm²

Area of semicircle = πr²/2 = π×7²/2 = 76.93 mm²

To get the area of the shaded region, we will subtract area of the semi-circle from the area of the rectangle.

Area of shaded region = Area_rectangle - Area_semicircle = 98 - 76.93 = 21.07 mm²

7 0

3 years ago

A right triangle has sides of integer lengths a, 40, and 41. Find a.

balandron [24]

Answer:

b) 9

Step-by-step explanation:

9 squared + 40 squared = 41 squared, which follows Pythagorean theorem.

7 0

3 years ago