Please help!

What is the ratio of the longer leg of a 30 60 90 triangle to its hypotenuse?

galben [10]

30: x
60: xsqrt3
90: 2x (hypotenuse)

7 0

3 years ago

I need an accurate answer please

kotykmax [81]

x = –6

Solution:

Given expression is $\sqrt[3]{x-2}+5=3$ .

Step 1: Isolate the radical by subtracting 5 from both sides of the equation.

$\Rightarrow\sqrt[3]{x-2}+5-5=3-5$

$\Rightarrow\sqrt[3]{x-2}=-2$

Step 2: Cube both sides of the equation to remove the cube root.

$\Rightarrow(\sqrt[3]{x-2})^3=(-2)^3$

Cube and cube root get canceled in left side of the equation.

$\Rightarrow\ x-2=-8$

Step 3: To solve for x.

Add 2 on both sides of the equation.

$\Rightarrow\ x-2+2=-8+2$

$\Rightarrow\ x=-6$

Hence the solution is x = –6.

6 0

3 years ago

A recipe that serves 10 uses 5 teaspoons of molasses. How many teaspoons are needed to serve 6?

Lady bird [3.3K]

Answer:

3 teaspoons.

Step-by-step explanation:

I am going to do this by figuring out how many teaspoons of molasses is need to serve 2 and then multiply that number by 3. because 3 x 2 = 6.

10 divided by 5 is 2. 5 divided by 5 equals 1. This means that to feed 2 people you need 1 teaspoon of molasses.

1 tsp + 1 tsp + 1 tsp = 3 tsp.

This means that I need 3 tsp of molasses to feed 6 people.

4 0

3 years ago

Can someone help me with this? Ava uses 8⁄9 gallonsof water every time she waters her lemon tree. If she waters her lemon tree 1

Nataly_w [17]

If Ava waters her lemon tree 12 times, then she has used 10.667 gallons of water.

<u>Solution:</u>

Given that , Ava uses $\frac{8}{9}$ gallons of water every time she waters her lemon tree.

If she waters her lemon tree 12 times, we have to find how much water will she use

Total water used = water used for 1 time $\times$ number of time water used for plants

Here water used for one time = $\frac{8}{9} gallons$

Number of time watered = 12

$\text { Total water used }=\frac{8}{9} \text { gallons } \times 12 \text { times }$

$\text { Total water used }=\frac{8}{9} \times 12=\frac{8}{3} \times 4=\frac{32}{3}=10.667$

Hence, Ava used 10.667 gallons of water.

6 0

3 years ago

Find the P-value for a test of the claim that more than 60% of the people following a particular diet will experience increased

lina2011 [118]

Answer:

The p-value of the test is 0.0207.

Step-by-step explanation:

Test of the claim that more than 60% of the people following a particular diet will experience increased energy (H1: p > 0.6).

The null hypothesis is:

$H_0: p = 0.6$

The alternate hypothesis is:

$H_1: p > 0.6$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.6 is tested at the null hypothesis:

This means that $\mu = 0.6, \sigma = \sqrt{0.6*0.4}$

Of 100 randomly selected subjects who followed the diet, 70 noticed an increase in their energy level.

This means that $n = 100, X = \frac{70}{100} = 0.7$

Test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.7 - 0.6}{\frac{\\sqrt{0.6*0.4}}{\sqrt{100}}}$

$z = 2.04$

P-value of the test:

The p-value of the test is the probability of finding a sample proportion of at least 0.7, which is 1 subtracted by the p-value of z = 2.04.

Looking at the z-table, z = 2.04 has a p-value of 0.9793

1 - 0.9793 = 0.0207

The p-value of the test is 0.0207.

4 0

3 years ago