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3 years ago

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A chemist has 500 ml of a 30% acid solution. She adds x milliliters of a 10% acid solution. Which statement is true about the gr

aph of the function that represents the concentration of the final solution? The horizontal asymptote y = 30 means that the final concentration will always be less than 30%. The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%. The vertical asymptote x = 500 means that the volume of solution will always be greater than 500 ml. The vertical asymptote x = 0 means that the volume of the solution will always be greater than 0.

1 answer:

prohojiy [21]3 years ago

3 0

Answer: The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.

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A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

3 years ago

A pump fills a pool at the rate of 20 cubic meters in an hour. If each cubic meter of water costs $10, how many minutes will the

fomenos

The first thing any good mathematician does is convert the measurements to the same unit as what the question is asking. In this problem, it states that the pool fills at a rate of 20 cubic meters per hour. Just keep in mind that an hour is 60 minutes.

The next step is to see how many cubic meters will cost $300. This can be done by dividing 300 by 10. This gets you 30 cubic meters of water.

You already know that 60 minutes is 20 cubic meters of water. That leaves the remaining 10 cubic meters of water. By dividing the rate given, you get that 30 minutes is 10 cubic meters of water. Add the 60 and 30 together to get 90 minutes.

It will take 90 minutes for the pump to use $300.

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3 years ago

A Fulcrum of a Pyramid is 6cm Square at the

Len [333]

Answer:

288 cubic cm

Step-by-step explanation:

Volume of the pyramid = 1/3 * base area * height

Base area = 12 * 12

Base area - 144 sq. cm

Height = 6cm

Volume of the pyramid = 144 * 6/3

Volume of the pyramid = 144 * 2

Volume of the pyramid = 288 cubic cm

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3 years ago

Drag the tiles to the correct boxes to complete the pairs not all tiles will be used match each quadratic graph to its respectiv

ch4aika [34]

Answer:

Part 1) The function of the First graph is $f(x)=(x-3)(x+1)$

Part 2) The function of the Second graph is $f(x)=-2(x-1)(x+3)$

Part 3) The function of the Third graph is $f(x)=0.5(x-6)(x+2)$

See the attached figure

Step-by-step explanation:

we know that

The quadratic equation in factored form is equal to

$f(x)=a(x-c)(x-d)$

where

a is the leading coefficient

c and d are the roots or zeros of the function

Part 1) First graph

we know that

The solutions or zeros of the first graph are

x=-1 and x=3

The parabola open up, so the leading coefficient a is positive

The function is equal to

$f(x)=a(x-3)(x+1)$

Find the value of the coefficient a

The vertex is equal to the point (1,-4)

substitute and solve for a

$-4=a(1-3)(1+1)$

$-4=a(-2)(2)$

$a=1$

therefore

The function is equal to

$f(x)=(x-3)(x+1)$

Part 2) Second graph

we know that

The solutions or zeros of the first graph are

x=-3 and x=1

The parabola open down, so the leading coefficient a is negative

The function is equal to

$f(x)=a(x-1)(x+3)$

Find the value of the coefficient a

The vertex is equal to the point (-1,8)

substitute and solve for a

$8=a(-1-1)(-1+3)$

$8=a(-2)(2)$

$a=-2$

therefore

The function is equal to

$f(x)=-2(x-1)(x+3)$

Part 3) Third graph

we know that

The solutions or zeros of the first graph are

x=-2 and x=6

The parabola open up, so the leading coefficient a is positive

The function is equal to

$f(x)=a(x-6)(x+2)$

Find the value of the coefficient a

The vertex is equal to the point (2,-8)

substitute and solve for a

$-8=a(2-6)(2+2)$

$-8=a(-4)(4)$

$a=0.5$

therefore

The function is equal to

$f(x)=0.5(x-6)(x+2)$

3 0

4 years ago

Can u pls fix the grammer in this Choose the correct punctuation marks in the passage.

MissTica

Answer:

It was a rainy day , but Joan and I had planned a trip. Joan wanted to go to the beach for a swim. I wasn't sure if we should go.

"I think we should wait a little longer , at least until the rain shows some signs of slowing down," I suggested.

"We can't swim without getting wet anyway," replied Joan, questioning my choice of swimsuit , the one my mom had bought at a secondhand store.

Step-by-step explanation:

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3 years ago