Which expression is NOT equivalent to 8 (x-2)+13-2x
?
Responses
A
6 x minus 3
B
3 times open paren 2 x minus 1 close paren
C
8 x minus 16 plus 13 minus 2 x
D
6 times x minus 3
A number cube that has sides numbered 1 through 6 is rolled 210 times.
How many times would you expect the result to be a number greater than 4?
Responses
A 35 times35 times
B 2 times2 times
C 70 times70 times
D 140 times
C. 70 times
Explanation: Since there are 6 sides on the number cube, and numbers greater than 4 are 5 and 6, they each have a probability of 2/6 or 1/3. So, if the cube is rolled 210 times, you would expect to get a number greater than 4 approximately 1/3 of the time, which is 70 times.
A circular play mat has a diameter of 6 feet.
Part A What is the circumference, in feet, of the play mat rounded to the nearest hundredth? Use 3.14 for
.
feet
The circumference of a circle is given by the formula C = π * d, where d is the diameter of the circle.
Given that the diameter of the play mat is 6 feet, we can substitute this value into the formula:
C = π * 6
C = 3.14 * 6
C ≈ 18.84 feet
Rounded to the nearest hundredth, the circumference of the play mat is approximately 18.84 feet.
A circular play mat has a diameter of 6 feet.
Part B What is the area in square feet, of the play mat rounded to the nearest hundredth? Use 3.14 for
.
square feet
The area of a circle is given by the formula A = π * r^2, where r is the radius of the circle. Since the diameter is given, we first need to find the radius.
The radius (r) is half the diameter, so r = 6 / 2 = 3 feet.
Now, we can substitute the radius into the area formula:
A = 3.14 * 3^2
A = 3.14 * 9
A ≈ 28.26 square feet
Rounded to the nearest hundredth, the area of the play mat is approximately 28.26 square feet.
Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
Responses
A $4.73$4.73
B $14.70$14.70
C $8.40$8.40
D $8.30
To find the constant of proportionality (k) in the equation y = kx, we need to use one of the data points where both x (pounds) and y (cost) are given. We can use any of the data points, and for simplicity, let's pick the data point (2.5, $21.00).
Using this data point, we can substitute the values into the equation:
$21.00 = k * 2.5
Solving for k:
k = $21.00 / 2.5
k = $8.40
Therefore, the constant of proportionality is $8.40.
So, the correct option is:
C) $8.40
Bella's Boutique is having their annual three-day Bella's Blowout Sale.
On the first day of the sale, all merchandise with a red tag is reduced by 25% from its regular price.
On the second day of the sale, the price of each sale item is reduced to 80% of its price from the previous day.
On the third day of the sale, the price of each sale item is reduced to 50% of its price from the previous day.
One sale item has a regular price of $40.
Plot 3 points on the number line to show the price of this item on each of the three days of the sale.
Do NOT plot a point for the regular price of the item.