3/4 write the fraction or mixed number as a percent

There are 8 red marbles and 32 blue marbles in a jar. What is the ratio of red marbles to blue marbles?

andrey2020 [161]

8:32 simplyfies to 1:4 .....there is your answer 1:4

3 0

3 years ago

In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alc

Fynjy0 [20]

Answer:

We conclude that the proportion of adults who totally abstain from alcohol has changed.

Step-by-step explanation:

We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"

Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in

Let p = proportion of adults who totally abstain from alcohol.

where, p = $\frac{429}{1100}$ = 0.39

So, Null Hypothesis, $H_0$ : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}

Alternate Hypothesis, $H_A$ : p $\neq$ 39% {means that the proportion of adults who totally abstain from alcohol has changed}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who totally abstain from alcohol = $\frac{352}{1100}$ = 0.32

n = sample of adults surveyed = 1100

So, test statistics = $\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }$

= -4.976

The value of z test statistics is -4.976.

Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.

4 0

3 years ago

Simplify ; √12 - 7√75

BigorU [14]

$\sqrt{12} = 2 \sqrt{3}$ and $7 \sqrt{75} = 35 \sqrt{3}$ . Thus, $2 \sqrt{3} - 35\sqrt{3} = -33\sqrt{3}$ .

5 0

3 years ago

Solve for x in the triangle. Round your answer to the nearest tenth.

Ulleksa [173]

Check the picture below.

4 0

2 years ago

A person standing close to the edge on top of a 24-foot building throws a ball vertically upward. The quadratic function h(t)=−1

Nutka1998 [239]

Answer:

a) maximum height is 156.25 ft

b) 6 seconds

Step-by-step explanation:

a) The maximum height can be found by finding the y-coordinate of the vertex. The vertex is the highest point in a parabola opened downward.

I start with by finding the t-coordinate of the vertex.

The t-coordinate of the vertex is $\frac{-b}{2a}$ where the expression $-16t^2+92t+24$ will need to be compared to $at^2+bt+c$ .

We see that $a=-16,b=92,c=24$ .

So the t-coordinate of the vertex is $\frac{-b}{2a}=\frac{-92}{2(-16)}=\frac{-92}{-32}=\frac{23}{8}$ .

We can find the h, the height, that corresponds to this t by using the equation $h=-16t^2+92t+24$ where $t=\frac{23}{8}$ .

So inserting 23/8 for $t$ .

$-16(23/8)^2+92(23/8)+24$

Plugging into calculator gives you 625/4.

So the maximum height is 625/4 or 156.25.

b) Let's find how long it takes the ball to hit the ground. If the ball is on the ground, then the distance between the ball and the ground is 0. So we are looking to solve h(t)=0 for t.

So this is equation we are solving for t:

$-16t^2+92t+24=0$