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3 years ago

The standard form of the equation of a parabola is y = x2 + 4x + 11.

Mathematics

2 answers:

RideAnS [48]3 years ago

8 0

A. You can get this through the process known as completing the square.

kondor19780726 [428]3 years ago

6 0

Answer:

Y=(x+2)^2+7

Step-by-step explanation:

You might be interested in

Sketch feda = 4pie/3 in standard position

rewona [7]

Since 4pi/3 = 3pi/3 + pi/3 = pi + pi/3, that means it goes past the angle of pi (the negative x-axis), and an additional pi/3 radians. So this gives you a diagonal line that passes through the origin, from the third quadrant through to the first quadrant, and makes an angle of 60 degrees with the negative x-axis.

7 0

3 years ago

Please answer, Thank you. Image below.

Bezzdna [24]

Answer:

88°

Step-by-step explanation:

The triangle is an isosceles triangle, so two of the angles are both 46°. We also know that the sum of all the angles in any triangle is 180°, so we can set up the following equation:

46° + 46° + e = 180°

Solving this gets e = 88°.

8 0

2 years ago

Need some help please...

Nesterboy [21]

Answer:

C: Starting at 1103 you gain 91 feet each additional hour of climing.

Step-by-step explanation:

4 0

3 years ago

A researcher planned a study in which a crucial step was offering participants a food reward. It was important that three food r

lbvjy [14]

Answer:

Step-by-step explanation:

Hello!

A pilot study was conducted to test if three food rewards are equally appealing to the participants.

Of 60 participants surveyed:

16 preferred cupcakes (CC)

26 preferred candy bars (CB)

18 preferred dried apricots (DA)

If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3

The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. $X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}$ Where k= number of categories of the variable.

For this example the statistical hypotheses are:

H₀: P(CC)=P(CB)=P(DA)= 1/3

H₁: At least one of the proportions isn't equal to the others.

To calculate the expected frequencies for each category you have to use the formula: $E_i= n* P_i$ where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.

$E_{CC}= n* P(CC)= 60*1/3= 20$

$E_{CB}= n*P(CB)= 60*1/3= 20$

$E_{DA}= n* P(DA)= 60* 1/3= 20$

The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:

Assuming α: 0.05

$X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378$

The rejection region is then X²₂ ≥ 7.378

$X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8$

I hope this helps!

5 0

3 years ago

Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following event

Paladinen [302]

Answer:

Step-by-step explanation:

The sample space is shown in the attached photo.

Probability = number of favourable outcomes/total number of outcomes.

Looking at the diagram, the total possible outcomes is 36.

A) from the diagram, the total number of events in which the sum of the numbers is odd is 18. Therefore, the probability that the sum of the numbers is odd is

18/36 = 1/2

B) the total number of events in which the sum of the numbers is 10 or more is 6. Therefore, the probability that the sum of the numbers is 10 or more is

6/36 = 1/6

C) the total number of events in which 3 appears on each of the two dice is 1. Therefore, the probability that 3 appears on each of the two dice is

1/36

7 0

3 years ago