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Aleksandr [31]
3 years ago
8

The perimeter P of a square (measured in inches) is expanding in size at a constant rate of change of 4 inches per inch with res

pect to the square's side length s (measured in inches). If the length of the side of the square changes from:
a. 0 to 2.5 inches, how does the square's perimeter P change?
b. 1 to 3 inches, how does the square's perimeter P change?
c. Express the change in the square's perimeter P in terms of the change in the square's side length s.
Mathematics
1 answer:
vivado [14]3 years ago
6 0

Answer:

a. 10 inches

b. 8 inches

c. \frac{dP}{ds} = 4

Step-by-step explanation:

a. At side 0, perimeter is 0*4 = 0 in. At side 2.5 inches, perimeter = 2.5*4 = 10 inches, a change of 10 - 0 = 10 inches

b. At side 1, perimeter is 1*4 = 4 inches. At side 3 inches, perimeter = 3*4 = 12 inches, a change of 12 - 4 = 8 inches.

c. We can express the change in the square's perimeter P in terms of the change in the square's side length s as

\frac{dP}{ds} = 4

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If x varies inversely as y, which statement is true?
grin007 [14]

Answer: The Inverse variation

Step-by-step explanation:

The phrase “ y varies inversely as x” or “ y is inversely proportional to x” means that as x gets bigger, y gets smaller, or vice versa. This concept is translated in two ways. yx = k for some constant k, called the constant of proportionality.

3 0
2 years ago
In 1990, 1000 adults were randomly selected and each was asked if they smoked, 300
Oduvanchick [21]

Answer:

 The proportion of smokers was higher in 1990 than in 2000

Step-by-step explanation:

Solution

Recall that,

The total number of sample 1 (n1) = 1000

Total  sample 2 number  (n2) = 2000

The number of favourable events (X1) = 300

The number of favourable events (X2) = 500

so,

p₁ = X₁/n₁ = 300/1000 = 0.3

p₂ = X₂/n₂ =500/2000 =0.25

α = 0.05

We are interested in testing the hypothesis.

The  hypothesis (Null) ....>  H₀ : p₁ = p₂

Alternate hypothesis------ > H₁ : p₁ > p₂

Thus,

P = X₁ + X₂/ n₁ + n₂

P =300 + 500/1000 +2000

P =800/3000

=0.2667

Now,

Z₀ = P₁ - P₂/√ P (1 -P) (1/n₁ + 1/n₂)

Z₀ =  0.3 - 0.25/√0.2667  (1 - 0.2667) (1/1000 + 1/2000)

Z₀ = 0.4999999999999999/√ 0.2667 (0.7333000000000001) (0.001 +0.0005)

Then,

Z₀ = 0.4999999999999999/√0.00029335666500000004

Z₀ = 2.9193

so,

zα/2 = z0.05/2 =z0.025

zα/2 = 1.6448536269514722

Now, we apply the decision rule:

Decision Rule: Reject the null hypothesis if the statistic value test is higher than the critical value 1.6448536269514722

The statistic value, 2.9193 is greater than the critical value 1.6448536269514722,  then we will reject the null hypothesis.

Therefore, the proportion of smokers was higher in 1990 than in 2000

3 0
3 years ago
Help me pls thank you
Marianna [84]

Answer:

More than half the students scored 81 or better on the test

There were 12 students who scored 80 on the test

The same number of students scored between 81 and 90 on the test as scored between 61 and 80.

Step-by-step explanation: Please think this through, I don't know if I'm correct. It is either all or one of these

7 0
2 years ago
Mrs. Ramiriz is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30
belka [17]
5p + 30 = 12p <== ur equation
5p - 12p = -30
-7p = -30
p = -30/-7
p = 4 2/7 pies to break even
4 0
3 years ago
Use the diagram to determine which statement is true
hichkok12 [17]
A. Area of ABCD - Area of DGA = Area of DEFG
s^2 - 1/2bh = s^2
(5)^2 - 1/2(4)(3) = (3)^2
25 - 1/2(12) = 9
25 - 24 = 9
1 not equal to 9

B. Area of ABCD - Area of GHIA = Area of DGA
s^2 - s^2 = 1/2bh
(5)^2 - (4)^2 = 1/2(4)(3)
25 - 16 = 1/2(12)
9 not equal to 6

C. Area of ABCD + Area of DGA = Area of GHIA
s^2 + 1/2bh = s^2
(5)^2 + 1/2(4)(3) = (4)^2
25 + 1/2(12) = 16
25 + 6 = 16
31 not equal to 16

D. Area of DEFG + Area of GHIA = Area of ABCD
s^2 + s^2 = s^2
(3)^2 + (4)^2 = (5)^2
9 + 16 = 25
25 = 25

The answer is D.
5 0
3 years ago
Read 2 more answers
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