Which table shows a proportional relationship between x and y?

The mayor of renee's town chose 160 students from her school to attend a city debate. This amount is no more than 1/4 of the stu

azamat

The answer is d.
First you have to divide 160/ 1/4. So you would do 160/1 divided by 1/4. Because of keep, change and flip. (k.c.f) you would keep 160/1, change the division sign, then flip 1/4 to 4/1. Then you multiply 160/1*4/1. Then you would get 640. Hope this helped.

7 0

3 years ago

If a= 2^x and b =2^x+1; show that: 8a^3 / b^3 = 2^x+1

kkurt [141]

Step-by-step explanation:

Given that:

a = 2ˣ

b = 2ˣ⁺¹ = 2ˣ * 2¹ = 2.2ˣ

Now,

{(8a³)/b²}

Substitute the value of x and y in expression then

= [{8(2ˣ)³}/(2.2ˣ)²]

= [(8*2³ˣ)/{2² * (2ˣ)²}]

= {(8*2³ˣ)/(4 * 2²ˣ)}

[since, (aᵐ)ⁿ = aᵐⁿ]

= {(2 * 2³ˣ)/2²ˣ}

= {(2 * 2²ˣ * 2ˣ)/2²ˣ}

[since (2a = a+a, that means 3x = 2x + x)]

= 2 * 2ˣ

= 2ˣ⁺¹

[since (aᵐ * aⁿ = aᵐ+ⁿ)]

Answer: Therefore, {(8a³)/b²} = 2ˣ⁺¹ .

Please let me know if you have any other.

7 0

2 years ago

Is this a quadratic function 2x+13=13

lys-0071 [83]

Answer:

Step-by-step explanation:

Simplifying

2x + 13 = 0

Reorder the terms:

13 + 2x = 0

Solving

13 + 2x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0

0 + 2x = 0 + -13

2x = 0 + -13

Combine like terms: 0 + -13 = -13

2x = -13

Divide each side by '2'.

x = -6.5

Simplifying

x = -6.5

7 0

2 years ago

An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in less than 10 minutes. For a test of the

nalin [4]

Answer:

$z=\frac{9.25-10}{\frac{2}{\sqrt{35}}}=-2.219$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.

Step-by-step explanation:

Data given and notation

$\bar X=9.25$ represent the sample mean

$\sigma=2$ represent the population standard deviation

$n=35$ sample size

$\mu_o =10$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 10 minutes, the system of hypothesis would be:

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{9.25-10}{\frac{2}{\sqrt{35}}}=-2.219$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.

6 0

4 years ago

What is the approximate length of arc s on the circle below? Use 3.14 for

ryzh [129]

The length of arc is 69.1 feet

Solution:

The length of arc when angle given in degrees is given as:

$Arc\ length = \frac{ \theta }{360} \times 2 \pi r$

Where,

r is the radius

$\theta$ is the central angle in degrees

From given,

$r = 12\ feet\\\\\theta = 330^{\circ}$

Substituting the values we get,

$Arc\ length = \frac{ 330 }{360} \times 2 \times 3.14 \times 12\\\\Arc\ length = \frac{ 330 }{360} \times 6.28 \times 12\\\\Arc\ length = 69.08 \approx 69.1$

Thus the length of arc is 69.1 feet

5 0

3 years ago