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2 years ago

The line with the equation 4/5x +1/3y=1 is graphed one the xy-plane. What is the x-coordinate of the x-intercept of the line?

Mathematics

1 answer:

leva [86]2 years ago

4 0

Answer:

x = 4/5

Step-by-step explanation:

The x-intercept looks like (x, 0); the coordinate 0 indicates that the point lies on the x-axis. If we start with 4/5x + 1/3 y= 1 and let y = 0, we will get an equation for the x-intercept:

(4/5)x + (1/3)(0) =1

Then 4/5x = 1, and (5/4)(4/5)x = (1)(4/5).

Thus, x = 4/5, and the x-intercept is (4/5, 0).

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The rectangular playground in tim's school is three times as long as it is wide. the area of the playground is 75 square meters.

qwelly [4]

Let x be the width of the playground, then 3x is the length of the
<span>playground

х * 3х = 75
3x</span>² = 75
x² = 25
x = 5 m (width)
5*3=15 m (length)

Perimeter = 2(5+15) = 2*20 = 40 meters.

8 0

2 years ago

32% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find t

Lorico [155]

Answer:

A. 21.06%

B. 66.88%

C. 81.56%

Step-by-step explanation:

There are two possible answer for the question asked, yes(more likely to make purchases) or no. The probability for a random adults answer yes to the question is 32% so the probability that the adults answer no is 68%.

(a) exactly two

There is only one case for this question, 2 people say yes and 8 people say no. The calculation for this problem will be:

2P10 * P(yes)^2 * P(no)^8= 10!/2!8!* 32%^2 * 68%^8 = 0.21066= 21.06%

(b) more than two

There are a lot of case for more than two, its easier to find out the negation of the probability which is "two or less". Case that fulfill "two or less" will be: 2 yes and 8 no

1 yes and 9 no

0 yes and 10 no

The calculation for the negation will be:

~P(X)= 0P10 * P(yes)^0 * P(no)^10 + 1P10 * P(yes)^1 * P(no)^9 + 2P10 * P(yes)^2 * P(no)^8 =

10!/0!10!* 32%^0 * 68%^10 + 10!/1!9!* 32%^1 * 68%^9 + 10!/2!8!* 32%^2 * 68%^8

0.02113 + 0.09947 + 0.21066 = 0.33126= 33.12%

Since its the negation, you need to subtract 1 with the negation

P(X)= 1 - ~P(X)

P(X)= 1 - 33.12%= 66.88%

Same formula as above, but the case is:

2 yes and 8 no

3 yes and 7 no

4 yes and 6 no

5 yes and 5 no

The calculation will be:

2P10 * P(yes)^2 * P(no)^8 + 3P10 * P(yes)^3 * P(no)^7 + 4P10 * P(yes)^4 * P(no)^6 + 5P10 * P(yes)^5 * P(no)^5 =

10!/2!8!* 32%^2 * 68%^8 + 10!/3!7!* 32%^3 * 68%^7 + 10!/4!6!* 32%^4 * 68%^6 + 10!/5!5!* 32%^5 * 68%^5

0.21066 + 0.26435 + 0.21770 + 0.1229= 0.81561= 81.56%

8 0

2 years ago

Which of the following predictions can be calculated using a geometric distribution?

snow_lady [41]

Answer: C

both a and b

Step-by-step explanation:

Both options A and B deals with the number of trials required for a single success. Thus, they are negative binomial distribution where the number of successes (r) is equal to 1.

The geometric distribution is a special case of the negative binomial distribution that deals with the number of trials required for a single success.

3 0

2 years ago

Read 2 more answers

Olivia had math and reading homework tonight. Olivia can solve each math problem in 1 minute and she can read each page in 1.5 m

ziro4ka [17]

Answer: the system of equations are

x + y = 22

x + 1.5y = 30

Step-by-step explanation:

Let x represent the number of math problems that Olivia solved.

Let y represent the number of pages that Olivia read.

Olivia completed a total of 22 math problems and pages of reading. This means that

x + y = 22- - - - - - - - - - - - - - -1

Olivia can solve each math problem in 1 minute and she can read each page in 1.5 minutes. Olivia completed a total of 22 math problems and pages of reading in 30 minutes. This means that

x + 1.5y = 30 - -- - - - - - - - - -2

8 0

2 years ago

Evaluate the line integral by the two following methods. xy dx + x2y3 dy C is counterclockwise around the triangle with vertices

nadezda [96]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

a) The first part requires that we use line integral to evaluate directly.

The line integral is

$\int_C xydx + {x}^{2} {y}^{3} dy$

where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)

The boundary of integration is shown in the attachment.

Our first line integral is

$L_1 = \int_ {(0,0)}^{(1,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

$\therefore \: L_1 =0$

Our second line integral is

$L_2 = \int_ {(1,0)}^{(1,2)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is:

$x = 0 \implies \: dx = 0$

y varies from 1 to 2.

We substitute the boundary and the values to get:

$L_2 = \int_ {1}^{2}1 \cdot y(0) + {1}^{2} \cdot \: {y}^{3} dy$

$L_2 = \int_ {1}^2 {y}^{3} dy = \frac{8}{3}$

The 3rd line integral is:

$L_3 = \int_ {(1,2)}^{(0,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is

$y = 2x \implies \: dy = 2dx$

x varies from 0 to 1.

We substitute to get:

$L_3 = \int_ {1}^{0} x \cdot \: 2xdx + {x}^{2} {(2x)}^{3}(2 dx)$

$L_3 = \int_ {1}^{0} 8 {x}^{5} + 2 {x}^{2} dx = - 2$

The value of the line integral is

$L = L_1 + L_2 + L_3$

$L = 0 + \frac{8}{3} + - 2 = \frac{2}{3}$

b) The second part requires the use of Green's Theorem to evaluate:

$\int_C xydx + {x}^{2} {y}^{3} dy$

Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.

This is given by:

$\int_C \: Pdx +Q \: dy = \int \int_ R \: Q_y - P_x \: dA$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int \int_ R \: 3 {x}^{2} {y}^{2} - y \: dA$

We choose our region of integration parallel to the y-axis.

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \int_ 0^{2x} \: 3 {x}^{2} {y}^{2} - y \: dydx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: {x}^{2} {y}^{3} - \frac{1}{2} {y}^{2} |_ 0^{2x} dx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: 8{x}^{5} - 2 {x}^{2} dx = \frac{2}{3}$

8 0

2 years ago