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3 years ago

1

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

3 0

Answer: 9 × 6 = 54

Step-by-step explanation:

In the Product Game, we need to multiply the both number of factor markers.

Chris and Katie were playing The Product Game. Their factor markers were on 9 and 2.

Number = 9 × 2 = 18

Chris decided to move the marker from 2 to 6.

Now, one maker is on 9 and other is on 6. So,

Number = 9 × (2 + 4)

Number = 9 × 6 = 54

Therefore, 9 × 6 = 54 is a numerical expression to represent his move.

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A brochure claims that the average maximum height for a certain type of plant is 0.7 m. A gardener suspects that this is not acc

larisa [96]

Answer:

As $Z$ , it is possible to reject null hypotesis. It means that the local mean height is less tha 0.7 m with a 5% level of significance.

Step-by-step explanation:

1. Relevant data:

$\mu=0.70\\N=40\\\alpha=0.05\\X=0.65\\s=0.20$

2. Hypotesis testing

$H_{0}=\mu=0.70$

$H_{1} =\mu< 0.70$

3. Find the rejection area

From the one tail standard normal chart, whe have Z-value for $\alpha=0.05$ is 1.56

Then rejection area is left 1.56 in normal curve.

4. Find the test statistic:

$Z=\frac{X-\mu_{0} }{\sigma/\sqrt{n}}$

$Z=\frac{0.65-0.70}{0.20/\sqrt{40}}\\Z=-1.58$

5. Hypotesis Testing

$Z_{\alpha}=1.56\\Z=-1.58$

$-1.58$

As $Z$ , it is possible to reject null hypotesis. It means that the local mean height is less tha 0.7 m with a 5% level of significance.

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3 years ago

From a height of 50 meters above sea level on a cliff, two ships are sighted due west. The angles of depression are 61° and 28°.

Olenka [21]

Answer:

The ships are 66 meters apart.

Step-by-step explanation:

For the sake of convenience, let us label ships A and B

As shown in the figure, the distances to the ships from right triangles.

The distance to the ship A is $d_1$ and it is given by

$tan (61^o)= \dfrac{50}{d_1}$

$d_1=\dfrac{50}{tan (61^o)}$

$\boxed{d_1= 27.71m}$

And the distance to the ship B is $d_2$ and is given by

$tan (28^o)= \dfrac{50}{d_2}$

$d_2=\dfrac{50}{tan (28^o)}$

$\boxed{ d_2=94.04m}$

Therefore, the distance $d$ between the ships A and B is

$d= d_2-d_1=94.04-27.7\\\\\boxed{d=66m}$

In other words, the ships are 66 meters apart.

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Answer:

155=35= 120

120+20x=155

Step-by-step explanation:

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What is the difference of 35- (-8)

Dennis_Churaev [7]

35-(-8)=35+8=43

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