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3 years ago

12

Graph the function. Then state the domain and range.

1 answer:

Marta_Voda [28]3 years ago

4 0

I think it's x=0 and f(x)= greater than or equal to, all real numbers

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Find the standard form of the equation of the hyperbola satisfying the given conditions: X intercept +/- 6; foci at (-10,0) and

uysha [10]

Answer:

$\frac{x^{2}}{36} - \frac{y^{2}}{64}=1$

Step-by-step explanation:

Given an hyperbola with the following conditions:

Foci at (-10,0) and (10,0)
x-intercept +/- 6;

The following holds:

The center is midway between the foci, so the center must be at (h, k) = (0, 0).

The foci are 10 units to either side of the center, so c = 10 and $c^2 = 100$
The center lies on the origin, so the two x-intercepts must then also be the hyperbola's vertices.

Since the intercepts are 6 units to either side of the center, then a = 6 and $a^2 = 36.$

$Then, a^2+b^2=c^2\\b^2=100-36=64$

Therefore, substituting $a^2 = 36.$ and $b^2=64$ into the standard form

$\frac{x^{2}}{a^2} - \frac{y^{2}}{b^2}=1\\We \: have:\\ \dfrac{x^{2}}{36} - \dfrac{y^{2}}{64}=1$

4 0

3 years ago

-2(3x - 4) + 7<br> divided by 3

kolbaska11 [484]

Answer:

-6x+31/3

Step-by-step explanation:

6 0

3 years ago

It is believed that the percentage of people who support candidate A is 56%. A sample of size 100 indicated that 40 people suppo

kondor19780726 [428]

Given data:

Sample size $=100$

Sample proportion of people support candidate A:

$p=\frac{40}{100}=0.40$

Population proportion of people support Candidate A :

$P=\frac{56}{100}=0.56$

Check the condition: $nP>10$ and $n(1-P)>10.$

$nP=100*0.40=40>10$

$n(1-P)=100*0.60=60>10$

Null Hyposthesis: $H_0: P=0.56$

Alternative Hypothesis: $H_\alpha :P\neq 0.40$

The test statistics:

$z=\frac{p-P}{\sqrt{\frac{P(1-P)}{n}}}$

Plug in p=0.56, P=0.40 and n=100 in the above formula,

$z=\frac{0.56-0.40}{\sqrt{\frac{0.40(1-0.40)}{100}}}$

$z=\frac{0.56-0.40}{\sqrt{\frac{0.40(1-0.40)}{100}}}=3.2659$

The table value of z at 10% of significance level is 1.28

Table value is less than the calculated value.

Hence $H_0$ is rejected at 10% level.

Therefore there is the evidence at an alpha level of 10% to conclude that the percentage of people who support candidate A has changed.

5 0

3 years ago

Organic sugar used to be sold at a bulk price of $4 per pound. The price was recently

MaRussiya [10]

Answer: $5

Step-by-step explanation:

Old price was $4

Increase of 25%

= 4 x 25/100 = 1

New price is 4+1 = $5

8 0

3 years ago

4/5 divided by 3/10=

erik [133]

Step 1. Apply this rule: a ÷ $\frac{b}{c} =a* \frac{c}{b}$

$\frac{4}{5} * \frac{10}{3}$

Step 2. Apply this rule: $\frac{a}{b} * \frac{c}{d} = \frac{ac}{bd}$

$\frac{4*10}{5*3}$

Step 3. Simplify 4 × 10 to 40

$\frac{40}{5*3}$

Step 4. Simplify 5 × 3 to 15

$\frac{40}{15}$

Step 5. Simplify

$\frac{8}{3}$

Done!

7 0

3 years ago