Allie bought 15.6 gallons of milk. There are approximately 11.4 liters in 3 gallons. How many liters of milk did Allie buy?

Based on the graph, what is the initial value of the linear relationship?

alex41 [277]

Answer: two over three

Step-by-step explanation:

$y=ax+b$

line intercepts y at (0,-2)

Therefore, $y=ax-2$

Substitute x = 3 in y =ax-2

$y=3a-2$

To find the x-intercept, y = 0

$3a-2=0\\3a=2\\a=\frac{2}{3}$

The slope is 2/3

y-intercept is -2

So two over three

4 0

3 years ago

Helppppppppppppppppppppppppppppp

Inessa [10]

Divide the volume value by 1000, which is 0.194 .

8 0

2 years ago

The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find th

Zielflug [23.3K]

Answer:

(a) $\frac{7}{25}$

(b) $\frac{19}{116}$

(c) $\frac{28}{125}$

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

Total of those who attended prom=125

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

Total of those who attended prom=75
Total Number of students=200

(a) P (a junior who did not attend prom)

$P(J')=\frac{56}{200}= \frac{7}{25}$

(b)

$P(Senior)=\frac{116}{200}$

$P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}$

(c)P (junior | attended prom)

$P(Senior)=\frac{84}{200}$

$P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}$

3 0

2 years ago

Read 2 more answers

A photo originally measuring 11 inches by 9 inches needs to be enlarged to a size of 55 by 45 inches. Find the scale factor of t

mariarad [96]

Answer:

scale factor = 5

Step-by-step explanation:

To determine the scale factor calculate the ratio of corresponding sides of the enlargement to the original, that is

scale factor = $\frac{55}{11}$ = $\frac{45}{9}$ = 5

8 0

2 years ago

A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin

Natalija [7]

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

$x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2} or \frac{30-21.21 }{2}\\ = \frac{51.21 }{2} or \frac{8.79}{2}\\ = 25.605 or 4.395$

x ≅ 25.61 or 4.4

V = (30 - 2x)(16 - 2x)x

Substituting the values of x into L and B, we have )x

L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22

B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22

Since L and B cannot be negative, we use the other value for x = 4.4, So

L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2

B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2

So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³

3 0

2 years ago