MATHEMATICS COLLEGE

A survey by the American Veterinary Medical Association found that out of 120 families surveyed, 18 owned a bird. Fifteen years ago, a similar study found that only 5 families out of 100 surveyed had a bird. Are the validity conditions for a two-sample z-test/interval adequately met

Answers

Answer 1

Answer:

Step-by-step explanation:

The assumptions include:

The samples from each population must be independent of one another: this was adequately met.

The populations from which the samples are taken must be normally distributed: this was not talked about

The population standard deviations must be known: not known

or the sample sizes must be large (i.e. n1≥30 and n2≥30: true

The validity conditions for a two-sample z-test/interval were not all adequately met

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In a right triangle, the length of the hypotenuse is 12m and the measure of one of the acute angles is 36°.Find the measure of the other acute angle and the lengths of the legs.
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PLEASE ANSWER!!!!!!!! Which system of equations does this graph represent? Linear graph and parabola. They intersect at 2, negative 1 and negative 3, 4 (1 point) A. y = x2 − 5 y = −x + 1
B. y = x2 − 5 y = −x − 1
C. y = x2 + 5 y = −x + 1
D. y = x2 + 5 y = −x − 1

Answers

Answer:

Option (A)

Step-by-step explanation:

For equation of the line,

Let the equation is, y = mx + b

Slope 'm' of the line passing through two points (-3, 4) and (2, -1),

m = $(y_2-y_1)/(x_2-x_1)$

= $(4+1)/(-3-2)$

= -1

y-intercept of this line, b = 1

Now we substitute these values in the equation,

y = -x + 1

Let the equation of the parabola is,

y = a(x - h)² + k

Here, (h, k) is the vertex of the parabola,

Since vertex of the given parabola is (0, -5),

then the equation will be,

y = a(x - 0)²- 5

y = ax² - 5

Since a point (2, -1) lies on this parabola,

-1 = a(2)² - 5

5 - 1 = 4a

a = 1

Equation of the parabola will be,

y = x² - 5

Therefore, Option (A) will be the answer.

How to display the work for this problem.
-2x-3=8
-2x+4y=22
Answer (-7,2)

Answers

Assuming that this particular type of question is a system of equations one. More specifically linear equations, you would simply substitute one of the equations into the other one. Then upon doing so, plug in the x and y coordinates for the point into the x and y variables of the equation and then see if it is a solution, by checking if the left hand side of the equation equals that of the right hand side of the equation.

Find the scale factor of the line segment dilation. AB: endpoints (-6, -3) and (-3,-9) to A'B': endpoints at (-2, -1) and (-1, -3). A) -1/3 B) 1/3 C) 3D) -3

Answers

we know that the endpoints of AB are

$\begin{gathered} (x_1,y_1)=\mleft(-6,-3\mright) \n (x_2,y_2)=(-3,-9) \end{gathered}$

and the distance formula is given by

$d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

By substituying these points, we have that

$d=\sqrt[]{(-3-(-6))^2+(-9-(-3))^2}$

which is equal to

$\begin{gathered} d=\sqrt[]{(-3+6)^2+(-9+3)^2} \n d=\sqrt[]{3^2+(-6)^2} \end{gathered}$

then

$\begin{gathered} d=\sqrt[]{9+36} \n d=\sqrt[]{45} \n d=\sqrt[]{9\cdot5} \n d=\sqrt[]{9}\cdot\sqrt[]{5} \n d=3\sqrt[]{5}\ldots..(A) \end{gathered}$

On the other hand, if

$\begin{gathered} (x_1,y_1)=(-2,-1) \n (x_2,y_2)=(-1,-3) \end{gathered}$

similarly to the previous case, the distance between the endpoint for A'B' is

$d=\sqrt[]{(-1-(-2))^2+(-3-(-1))^2}$

which is equal to

$\begin{gathered} d=\sqrt[]{(-1+2)^2+(-3+1)^2} \n d=\sqrt[]{1^2+(-2)^2} \n d=\sqrt[]{1+4} \n d=\sqrt[]{5}\ldots..(B) \end{gathered}$

Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.

Then, the answer is B.

A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%. Testing at the 5% level the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%.a. Calculate the p-value for this test.
b. Find the p-value for this test and draw your conclusion.
c. Suppose that the alternative hypothesis in part b had been two-sided rather than one-sided. Conduct your test using either the critical value or the p-value approach.

Answers

The p-value for the given test is 0.0901.

Given that, a pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%.

What is a standard deviation?

Standard deviation is the degree of dispersion or the scatter of the data points relative to its mean, in descriptive statistics.

Given, Mean = 3.07, μ=3%, σ =0.4% and n=64.

Hypothesis test $H_(0)$ ;μ=3 and $H_(1)$ ;μ>3

We need to test the null hypothesis against the alternative hypothesis, we reject the null hypothesis and accept the alternative hypothesis.

When x>x critical

x critical = μ+Z+σ

Z = (x-μ)/(σ/√n)

= (3.07-3)/(0.4/√64)

= (0.07)/0.05

= 1.4

α = 5 and $z_{0.05$ = 1.645

If Z> $Z_{0.05$

1.4 > 1.645

Therefore, we do not reject null hypothesis at 5% significant level.

There is sufficient evidence that the mean impurity in concentration pills is 3% or less than 3%.

p-value

p−value=P(Z>1.4)

=1−P(Z<1.4)

=1−0.90988

=0.0901

Therefore, the p-value for the given test is 0.0901.

To learn more about the standard deviation visit:

brainly.com/question/14747159.

#SPJ2

Answer:

Step-by-step explanation:

Marl me as brainliest answer c

Find the measurement of angle A (round to the nearest tenth)

Answers

Answer:

B) θ = 17.1 degrees

Step-by-step explanation:

Here we have to use the tan ratio to find the answer.

tan = Opposite / Adjacent

Given: Opposite = 4, Adjacent = 13

tan θ = 4/13

θ = tan^-1 (4/13)

θ = 17.1 degrees

Answer: B) 17.1 degrees

Thank you.

Answer:

The correct answer option is 17.1°.

Step-by-step explanation:

We are given a right angled triangle with two known side lengths of perpendicular and base with respect to the unknown angle A for which we have to find the measure.

For that, we can use the formula of tan which by using the two given side lengths.

$tan A =(perpendicular)/(base)$