The graph of f(x)=4x^3-13x+9x+2 is shown below.

What is the percentage of sugar in the syrup made of 10 kg of water and 5 kg of sugar?

OlgaM077 [116]

33.3% sugar
you do 5÷15 (part÷whole)

7 0

3 years ago

(-1,-2) and (3, -162) a. Is there a line th(at goes through these two points? How do you know? If there is one, what is the equa

lana [24]

Answer:

The equation of line for given points is y = - 40 x - 42

Step-by-step explanation:

Given two points as :

( -1 , - 2 ) and ( 3 , - 162 )

Now, Equation of line in points form

y - $y_1$ = m × ( x - $x_1$ )

Where m is the slope of line

And, m = $\frac{y_2 - y_1}{x_2 - x_1}$

or, m = $\frac{ - 162 + 2}{ 3 + 1}$

or, m = $\frac{ - 160}{ 4}$

∴ m = - 40

So, Slope of line for given points is - 40

Now equation of line can be written as

y - ( - 2 ) = ( - 40 ) × ( x - ( - 1 ) )

or, y + 2 = ( - 40 ) × ( x + 1 )

or, y + 2 = - 40 x - 40

or, y = - 40 x - 40 - 2

∴ y = - 40 x - 42

Hence the equation of line for given points is y = - 40 x - 42 Answer

4 0

3 years ago

In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S

lys-0071 [83]

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court