The graph below shows a line segment AB:

What are 3 ways to get a substance to dissolve more quickly?

Nastasia [14]

Answer:

Step-by-step explanation:

mixed with spoon

use blinder

shanke

7 0

3 years ago

The number of gnats G(x), in millions, in a certain area depends on the May rainfall x, in inches. That relationship can be expr

puteri [66]

Answer:

9 inches of rainfall produces the maximum number of gnats.

Step-by-step explanation:

Given : $G(x) = - x^2 + 18x$

To Find :How many inches of rainfall produces the maximum number of gnats?

Solution:

$G(x) = - x^2 + 18x$

G(x) =The number of gnats in millions.

x denotes the length of rainfall

To Find the maximum length find the mid point of zeroes .Since parabolas are symmetrical, the x value of the max falls 1/2 way between the zeros.

$0= - x^2 + 18x$

$0= x^2-18x$

$0= x(x-18)$

So, x = 0 , x= 18

Now Formula of midpoint : $x=\frac{x_1+x_2}{2}$

$x=\frac{0+18}{2}$

$x=9$

Hence 9 inches of rainfall produces the maximum number of gnats.

8 0

3 years ago

A regular hexagon has sides of 2 feet. What is the area of the hexagon?

yuradex [85]

I'm getting the last answer

5 0

3 years ago

Read 2 more answers

Each polio vaccination consist of four doses, and each measles vaccination consist of two doses. Last year, Dr. Potter gave a to

Mrac [35]

To solve this equation we need to set up a system of equations because we need to find out the value of 2 variables given 2 equations

Equation 1: Polio vaccination has 4 doses, measles vaccination has 2 doses, and he gave out 184 doses total

Equation 2: He gave 2 types of vaccinations: polio and measles, and he gave a total of 60 vaccinations.

To convert the word form of these equations, we first have assign polio and measles a variable to make them easier to keep track of

Lets just say that the number of polio shots = x and number of measles shots = y

Equation 1: 4 doses of x added with 2 doses of y equaled 184 doses total

4x+2y = 184

Equation 2: x vaccines added with y vaccines equaled 60 total vaccines

x + y = 60

We know have our system of equations

Equation 1: 4x+2y = 184

Equation 2: x + y = 60

To solve a system of equations, we can either do elimination or substitution, depending on which is easier.

In this case, substitution is pretty easy because for equation 2 we just need to have only 1 variable on a side then we can substitute it into equation 1

Equation 2: x + y = 60

Lets subtract x from both sides of the equation to "move" the x to the other side

y = -x + 60

And using y in terms of x, we can plug it into equation 1

Equation 1: 4x+2y = 184

4x+2(-x + 60) = 184

Now distribute the 2 to (-x+60)

4x-2x+120 = 184

Simplify by combining like terms

2x+120 = 184

Subtract 120 from both sides of the equation so all variables are on one side and the constants on the other

2x = 64

Divide 2 from both sides of the equation to isolate x, when we want to find

x = 32

Now we know the number of polio vaccines he gave, plug this into an equation to find y- the number of measles vaccine

Equation 2: x + y = 60

32 + y = 60

Subtract 32 from both sides to isolate y

y = 28

We know now that x, the number of polio vaccinations = 32 and y, the number of measles vaccinations = 28

Dr. Potter gave 32 polio vaccinations and 28 measles vaccinations last year.

6 0

4 years ago

The USDA conducted tests for salmonella in produce grown in California. In an independent sample of 252 cultures obtained from w

Marat540 [252]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 252$

The number that tested positive is $k_1 = 18$

The second sample size is $n_2 = 476$

The number that tested positive is $k_2 = 20$

The level of significance is $\alpha = 0.01$

Generally the first sample proportion is mathematically represented as

$\^ p _1 = \frac{k_1 }{ n_1 }$

=> $\^ p _1 = \frac{18 }{ 252 }$

=> $\^ p _1 = 0.071$

Generally the second sample proportion is mathematically represented as

$\^ p _2 = \frac{k_2 }{ n_2 }$

=> $\^ p _2 = \frac{20 }{ 476}$

=> $\^ p _2 = 0.042$

The null hypothesis is $H_o : p_1 - p_2 = 0$

The alternative hypothesis is $H_a : p_1 - p_2 \ne 0$

Generally the test statistics is mathematically represented

$z = \frac{ \^ p_1 - \^ p_2 - ( p_ 1 - p_2 )}{ \sqrt{\frac{\^ p_1 (1-\^ p_1)}{ n_1 } + \frac{\^ p_2 (1-\^ p_2)}{ n_2 } } }$

=> $z = \frac{ 0.071 - 0.042 - 0 }{ \sqrt{\frac{0.071 (1-0.071)}{ 252 } + \frac{0.042 (1-\^ 0.042)}{ 476 } } }$

=> $z = 1.56$

From the z table the area under the normal curve to the right corresponding to 1.56 is

$P(Z > 1.56 ) =0.05938$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.56 )$

=> $p-value = 2 * 0.05938$

=> $p-value = 0.1188$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

5 0

3 years ago