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4 years ago

It is known that x=7 is a root of the equation ax^2 + bx + 2= 0, where a<0. Solve the inequality ax²4 +bx^2 + 2>0.

Mathematics

1 answer:

kap26 [50]4 years ago

7 0

Answer:

2/(7a) < x < 7

Step-by-step explanation:

The product of roots of ax² +bx +c is c/a. In this case, that means the second root of the equation is ...

... 2/(7a)

Since a < 0, the parabola opens downward and 2/(7a) < 0. The quadratic function will be positive between the two roots, on the interval ...

... 2/(7a) < x < 7

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What is -3/8, 5/16, -0.65, 2/4 from least to greatest

storchak [24]

-3/8, -0.65, 5/16, 2/4

8 0

3 years ago

We have been asked to investigate two flights, AA flight and U A flight. Both flights are at 33,000 feet, and the flight paths i

Varvara68 [4.7K]

Answer:

Both flights approach each other at a speed of 624.70 Knots. The FAA minimum separation is not violated as both airplanes are 7.26 Nautical miles away from each other at the time when one of the flights( flight AA) passes through Frada Heights.

Step-by-step explanation:

To solve this kind of problem, the knowledge of concept of relative velocity is needed as the first question requested how fast the flights were approaching each other. To find the minimum distance between both flights, the closest point of approach between both flights should be taken into consideration which was Frada heights. Flight AA passes through Frada Heights in a shorter time of 0.079 hours. This is the time at which both flights approach each other the closest and so the minimum distance (separation) between them. This was calculated to be 7.26NM which is greater than the FAA's minimum this requirement for flight was not violated.

Detailed calculation steps can be found in the attachment below.

8 0

4 years ago

Assume that a random sample of 4 Goldfinch birds are going to be used to test the above hypothesis. Compute the largest value of

Misha Larkins [42]

This question is incomplete, the complete question is;

Assume that body masses of Goldfinch birds follow a normal distribution, with a standard deviation equal to 0.04 oz. An ornithologist who would like to make some inference about the average body mass of the Goldfinch birds. In particular, at a significance level of 0.01, she would like to test the null hypothesis H₀: Average body mass of the Goldfinch birds is 0.5 oz, against the alternative claim that average body size is less than 0.5 oz.

Assume that a random sample of 4 Goldfinch birds are going to be used to test the above hypothesis. Compute the largest value of the sample mean, that will allow the experimenter reject the null and prove the alternative at significance level 0.01. For this problem, make sure that your solution includes all steps of your computation. You will not earn points if you just use a formula

Answer: the largest value of the sample mean that will enable the experimenter to reject the null hypothesis is 0.4534 oz.

Step-by-step explanation:

Let us consider testing a hypothesis about a population mean with population standard deviation that is known,

Let the average body mass of the Goldfinch bird be μ^μ

Now our hypotheses are will be;

H₀ : μ = 0.5 and

H₁ : μ < 0.5

For the test, we shall use the z statistic which will be

z = (x"-μ)/(σ/√n)

Now given that;

σ = 0.04 and n = 4

sample mean x" = ?

Now in order to be able to reject the null hypothesis, the p-value should be ≤ α = 0.01.

so to find the largest value of sample mean, we will use the maximum of p-value that is 0.01.

For a p-value = 0.01 at the lower tail (which is the percentile for z),

the corresponding z will be -2.33

so we substitute our values into our formula

z = (x"-μ)/(σ/√n)

z(σ/√n) = (x"-μ)

-2.33(0.04/√n) = (x"-0.5)

-0.0466 = x" - 0.5

x" = 0.5 - 0.0466

x"= 0.4534

therefore the largest value of the sample mean that will enable the experimenter to reject the null hypothesis is 0.4534 oz.

4 0

3 years ago

Bryan and Jadyn had barbeque potato chips and soda at a football party. Bryan ate 3 oz of chips and drank 2 cups of soda for a t

Diano4ka-milaya [45]

Answer:

200 mg sodium is in 1 oz of chips and 50 mg sodium is in 1 cup of soda.

Step-by-step explanation:

Let x mg sodium is in 1 oz of chips and and y mg is in 1 cup of soda.

∵ Bryan ate 3 oz of chips and drank 2 cups of soda for a total of 700 mg of sodium.

i.e. 3x + 2y = 700 --------(1),

Jadyn ate 1 oz of chips and drank 3 cups of soda for a total of 350 mg of sodium.

i.e. x + 3y = 350 ---------(2),

Equation (1) - 3 × equation (2),

We get,

2y - 9y = 700 - 1050

-7y = -350

$\implies y = \frac{-350}{-7}= 50$

From equation (1),

3x + 2(50) = 700

3x + 100 = 700

3x = 700 - 100

3x = 600

$\implies x = \frac{600}{3}=200$

Hence, 200 mg sodium is in 1 oz of chips and 50 mg sodium is in 1 cup of soda.

7 0

4 years ago

According to the fundamental theorem of algebra, how many zeros does the function f(x) = 4x3 − x2 − 2x + 1 have?

jarptica [38.1K]

Answer: 3 zeroes.

Explanation:-

The fundamental theorem of algebra states that any polynomial with degree m>0 and complex coefficients has atleast one complex root.
Corollary of fundamental theorem states that for any polynomial with degree m>0 has exactly m solutions.

The given function is $f(x)=4x^3-x^2-2x+1$

Because it is a polynomial function with degree 3>0 , Therefore by corollary of fundamental theorem of algebra , it has 3 zeroes.

8 0

4 years ago

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