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postnew [5]
2 years ago
6

In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment.

A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. What is the null and alternative hypothesis?
Mathematics
1 answer:
max2010maxim [7]2 years ago
4 0

Answer:

H_{0}: p \leq 0.6\\H_A: p > 0.6

Step-by-step explanation:

We are given the following in the question:

Percentage of vote required for constitutional amendment = 60%

p = 60% = 0.6

Hypothesis:

More than sixty percent of the voters would support a new amendment about higher education.

We design the null and the alternate hypothesis  

H_{0}: p \leq 0.6\\H_A: p > 0.6

Interpretation:

The null hypothesis states that less than or equal to 60% of the voter support the new amendment and the alternative hypothesis states that gretaer than 60% supports the amendment about higher education.

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Gavin and Jim win some money and share it in the ratio 5:2. Gavin gets £39 more than Jim. How much did they get altogether?
gregori [183]

Answer:

Altogether Gavin and Jim won £95.

Step-by-step explanation:

We are given the following in the question:

Ratio of money won by Gavin and Jim = 5:2

Gavin gets £39 more than Jim.

Let x be the amount of money Won by Jim.

Then, money won by Gavin =

=(x+39)

Thus, we can write the equation:

\dfrac{\text{Gavin}}{\text{Jim}} = \dfrac{5}{2}=\dfrac{x+39}{x}

Solving, we get,

\dfrac{5}{2}=\dfrac{x+39}{x}\\\\5x = 2x + 78\\\Rightarrow 3x = 78\\\Rightarrow x = 26\\\Rightarrow (x+39) = 65

Thus, Gavin won £65 and Jim won £26.

Money won altogether =

=65 + 26\\=95

Thus, altogether Gavin and Jim won £95.

5 0
2 years ago
In two sample surveys, 125 people were asked about their favorite fruit. In the first survey, 40 people chose apples, 64 chose o
Artemon [7]

Answer: Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likley that oranges are the favorite fruit of the entire population.


Step-by-step explanation:


6 0
2 years ago
Read 2 more answers
What is the area of the composite figure whose vertices have the following coordinates? (2, −2) , (2, 1) , (4, 2) , (6, 2) , (4,
jok3333 [9.3K]

we have that

using a graph tool

the answer is 36 units²

Have a great day :)

5 0
2 years ago
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Mr.Sasi paid $152 for a pair of shoes and a belt. The pair of shoes cost 7 times as much as the belt. He also bought a shirt whi
mario62 [17]
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4 0
2 years ago
Let F(x, y, z) = (5ex sin(y))i + (5ex cos(y))j + 7z2k. Evaluate the integral C F · ds, where c(t) = 8 t , t3, exp( t ) , 0 ≤ t ≤
maria [59]

I'm going to assume this reads

\vec F(x,y,z)=5e^x\sin y\,\vec\imath+5e^x\cos y\,\vec\jmath+7z^2\,\vec k

and the path C is parameterized by

\vec c(t)=8t\,\vec\imath+t^3\,\vec\jmath+e^t\,\vec k

with 0\le t\le1. Under this parameterization,

\vec F(x,y,z)=\vec F(x(t),y(t),z(t))=5e^{8t}\sin(t^3)\,\vec\imath+5e^{8t}\cos(t^3)\,\vec\jmath+7e^{2t}\,\vec k

and

\mathrm d\vec c=\dfrac{\mathrm d\vec c}{\mathrm dt}\,\mathrm dt=(8\,\vec\imath+3t^2\,\vec\jmath+e^t\,\vec k)\,\mathrm dt

Then in the integral,

\displaystyle\int_C\vec F\cdot\mathrm d\vec s=\int_0^1\vec F(x(t),y(t),z(t))\cdot\frac{\mathrm d\vec c}{\mathrm dt}\,\mathrm dt

=\displaystyle\int_0^1(7e^{3t}+15e^{8t}t^2\cos(t^3)+40e^{8t}\sin(t^3))\,\mathrm dt\approx\boxed{12586.5}

(It's unlikely that an exact answer can be found in terms of elementary functions)

4 0
2 years ago
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