Answer: y = -1,2x + 3.4
Step-by-step explanation:
y = ax + b
(2,1) => 1 = 2a + b (1)
(17,-17) => -17 =17a + b (2)
Using caculator Mode => 5 =>1
We get : a=- 1.2 , b = 3.4
=> y = -1.2x + 3.4
We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ =

π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.
R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14
a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³
b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂
</span>Vₐ = 3 × <span>

π r³
</span>Vₐ = 3 ×

3.14<span> (6.5 cm)³</span>
Vₐ = 3,449.3 cm³
c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V =

×100
V =

×100
V = 0.6666 ×100
V = 66.66%
Hello! The formula for simple interest is prt. That means you multiply the principal (initial amount) by the rate (simple interest percentage), by the amount of time (could be in months or years). So, the loan is $3,750 and the rate is 8.25% for 9 months. 9 months is 3/4 of the year, because there are 12 months in 1 year and 9/12 is 0.75. Let's multiply. 3,750 * 8.25% (0.0825) is 309.375 Now, multiply that number by 0.75 to get 232.03125 or 232.03 when rounded to the nearest hundredth (cent). The amount of simple interest is $232.03.
Answer:
59 to 66
Step-by-step explanation:
Mean test scores = u = 74.2
Standard Deviation =
= 9.6
According to the given data, following is the range of grades:
Grade A: 85% to 100%
Grade B: 55% to 85%
Grade C: 19% to 55%
Grade D: 6% to 19%
Grade F: 0% to 6%
So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.
6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)
The formula for z score is:

For z = -1.56, we get:

For z = -0.88, we get:

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)
6 quarts equals 12 pints
8 quarts equals 2 gallons
48 fl oz equals 6 cups