Tyra’s father is two years more than three times as old as she is. If Tyra is nine years old, how old is her father?

Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people w

Lera25 [3.4K]

Answer:

A. We have extremely strong evidence to reject H0.

Step-by-step explanation:

Let P be the proportion of non-retirees in 2015 who did not think that Social Security would be able to pay a retirement benefit by the time that they retire.

According to the data null and alternative hypotheses should be:

$H_{0}$ : P=0.60

$H_{a}$ : P<0.60

Test statistics is -4.29 and p-value of the statistics is p<0.001

At every significance levels higher than 0.001, we can reject the null hypothesis since p<0.001.

8 0

3 years ago

Explain how convection currents cause tectonic plates to move. Your explanation should be 1-3 sentences long. Use and bold the f

tester [92]

Answer:

Step-by-step explanation:

Convection is the process by which less dense material rises and more dense material sinks. The former are said to be more “buoyant” than the latter, and the vertical forces due to density difference are referred to as buoyancy forces. Rocks, water, and air—indeed, most materials—expand and thus become less dense as temperature increases, so convection is typically driven by temperature differences. In Earth’s mantle hot rock rises and slightly cooler rock sinks.

Convection drives our dynamic planet. The planet’s liquid outer core convects, creating the Earth’s magnetic field; the ocean convects, enabling exchange of CO2 with the atmosphere and transporting nutrients from depth that support important fisheries; and the atmosphere convects, acting in concert with the ocean to transport heat and moisture around the planet to create climate.

Everyday examples of convection in liquids include lava lamps or water heating on a stove. But the mantle is, in general, solid. It turns out that rocks, along with most other solids, flow by a solid-state, creeping motion, especially when they are hot and given enough time. This is what happens in the mantle. Based on observations of the rates at which the surface of Earth moves, geologists estimate the mantle convectively flows at rates of several centimeters a year.

The heat driving mantle convection has three sources. "Primordial" heat (left over from the accretion and differentiation that led to the formation of Earth’s core) contributes 20 to 50% of the heat. Heating due to the decay of radioactive isotopes (mainly potassium, thorium, and uranium) contributes 50 to 80%. Thirdly, tidal friction from the Moon’s pull on the Earth contributes perhaps 10%. Mantle convection is the main mechanism by which this heat escapes from the interior of Earth.

Plate tectonics refers to the movement of the rigid plates around the surface of Earth. The outer portion of the planet, or lithosphere, is relatively rigid because it is relatively cold. The lithosphere varies in thickness but is typically a hundred or so kilometers thick. It includes the upper mantle and both the continental and oceanic crust. The mantle’s convective motions break the lithosphere into plates and move them around the surface of the planet. These plates may move away from, move by, or collide with each other. This process forms ocean basins, shifts continents, and pushes up mountains.

Tectonic plates break apart and diverge where the mantle beneath is upwelling. In such regions mid-ocean ridges develop, and new lithosphere and crust form to replace the material that is moving away. Where plates converge, usually where the mantle is downwelling, one plate is forced beneath another. When this involves plates with embedded continental crust, mountain belts such as the Alps and Himalayas form. If the collision involves plates with oceanic crust, subduction zones form where one plate descends into the mantle beneath the other plate. Above these subduction zone chains of volcanoes and island arcs like the Aleutians, develop.

The churning of the mantle also affects the chemical composition of the ocean and has a long-term influence on climate. Mantle convection is the main way heat from Earth’s interior is transported to its surface, and this heat escapes principally through mid-ocean ridges. In fact, the connected mid-ocean ridge system is in essence a 80,000 km long volcano. Escaping heat along these ridges causes hot water to circulate through the crust in a “hydrothermal system.” As seawater reacts with the hot rocks, its composition changes. Over the course of several million years, all of the water in the world's oceans cycles through the oceanic crust at mid-ocean ridges. This is how the hydrothermal circulation influences ocean composition.

How about atmospheric and oceanic circulation? Atmospheric circulation involves the movement of large air masses, and mountains act as barriers, redirecting circulation in the atmosphere. Also, as tectonic plates move, continents and ocean basins open and close. The position of continents and ocean basins strongly influences global ocean circulation, which exerts a major, albeit, long-term, influence on climate.

8 0

3 years ago

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m

love history [14]

Answer:

a) The expected value of the sample mean weight is 20.4 pounds.

b)The standard deviation of the sample mean weight is 0.123.

c) There is a 14.46% probability the sample mean weight will be less than 20.27.

d) This value is $c = 20.6153$ .

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that $\mu = 20.4, \sigma = 1.23$

Consider the sample mean weight of 100 watermelons of this variety. This means that $n = 100$ .

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123$

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when $X = 20.27$ .

Since we are working with the sample mean, we use $s$ instead of $\sigma$ in the Z score formula

$Z = \frac{X - \mu}{s}$

$Z = \frac{20.27 - 20.4}{0.123}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of $X = c$ that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use $Z = 1.75$

$Z = \frac{X - \mu}{s}$

$1.75 = \frac{c - 20.4}{0.123}$

$c - 20.4 = 0.123*1.75$

$c = 20.6153$

This value is $c = 20.6153$ .

6 0

2 years ago

70% of the 30 sandcastles at Donatello Beach have moats. how many more moats are there

bixtya [17]

Answer:

21 moats

Step-by-step explanation:

.70 x 30 = 21

4 0

3 years ago

Read 2 more answers

Geometry please help

alisha [4.7K]

Answer:

x = 4

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below

P.s: I used the Law of Sines, but there are many other ways to solve it

5 0

2 years ago