__________________________

Answer:

Step-by-step explanation:

[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]

[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]

[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]

Answer:

I believe the answer is C

Answer:

True

Step-by-step explanation:

from the scale 0-1, 2/8 is closer to 0 because you round 2 down to 0, which gives you 0.

Answer:

Normality assumptions are met.

The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356). The interpretation is that we are 90% sure that the true proportion of all adult drivers than ran at least one red light in the last month is between these bounds.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Out of 1251 adult drivers, 641 of them have run at least one red light in the last month.

This means that [tex]n = 1251, \pi = \frac{641}{1251} = 0.5124[/tex]

Normality assumptions:

We need that: [tex]n\pi[/tex] and [tex]n(1-\pi)[/tex] are 10 or greater. So

[tex]n\pi = 1251*0.5124 = 641[/tex]

[tex]n(1-\pi) = 1251*0.4876 = 610[/tex]

So the normality assumptions are met.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 - 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.4892[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 + 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.5356[/tex]

The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356). The interpretation is that we are 90% sure that the true proportion of all adult drivers than ran at least one red light in the last month is between these bounds.

9514 1404 393

Answer:

  $14.14

Step-by-step explanation:

The amount of interest earned is ...

  I = P((1 +r/365)^n -1) . . . . interest on principal P at annual rate r compounded daily for n days

  I = 3021(1 +0.055/365)^31 -1) ≈ 14.14

$14.14 in interest is earned in 31 days.

Answer:

it’s just 2x^2

it’s not factorable

Answer:

7

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

The height of the rock after t seconds is given by the following equation:

[tex]H(t) = -16t^2 + 96t + 112[/tex]

How long will it take in seconds for the rock to hit the ocean?

This is t for which:

[tex]H(t) = 0[/tex]

So

[tex]-16t^2 + 96t + 112 = 0[/tex]

Simplifying by -16

[tex]t^2 - 6t - 7 = 0[/tex]

So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]

[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]

[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]

[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]

Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.

Answer:

23% probability the family has at least 3 children under the age of 21.

Step-by-step explanation:

If a family is selected at random, what is the probability the family has at least 3 children under the age of 21?

15% have three children under the age of 21

5% have 4 children under the age of 21

3% have 5 or more children under the age of 21.

So:

15% + 5% + 3% = 23%

23% probability the family has at least 3 children under the age of 21.

Answer:

5

step by step explanation:

if she gets $10 off of her purchase that means she would have a little extra money to another shirt

Answer:2

Step-by-step explanation:

Answer:

they all go straight across

Step-by-step explanation:

Answer:

Go across from each

Step-by-step explanation:

Answer:

cos P = 71.09

Step-by-step explanation:

cos = [tex]\frac{adajcent}{hypotenuse}[/tex]

cos P = [tex]\frac{24}{74}[/tex]

cos P = 0.324

cos-1 of 0.324 is 71.09

cos P = 71.09

Answer:

C:140

Step-by-step explanation:

because 7 x 5 in the tiangle.

Answer:

4 is in the one thousands place. The 0 is in the hundredths place. The 7 is in the tenths place.

Answer:

Step-by-step explanation:

1)(-3x+10)(50-x)=180

-4x+60=180

-4x=120

x=-30

2)6x+2+2x=90

8x=88

x=11

larger angle: 68°

3) a=3x°

4)(7x-5)=-2x+22

9x=27

x=3

DBE=16°

5)(x-39)=2x-59)

x=20

Answer:

x equals 10, angle measure is 30°

Step-by-step explanation:

By using the Vertical Angles Theorem which states that opposite angles formed by 2 intersecting lines are congruent we can find that the measure of the angle with 3x is equal to the measure of it's opposite angle or 30°. Using this we can make an equation that can find us our answer.

3x = 30

Divide both sides by 3

3x/3 = 30/3

x = 10

Answer:

m = 4 + (2n)/(3)

Step-by-step explanation:

Move all terms that contain m to the right side and solve it.

Answer:

Yes

Step-by-step explanation:

Because you're multiplying by 1 so it stays the same value

Step-by-step explanation:

the answer is 576 cubic centimetre.

Answer:

Its 576 cubic centimeters

Step-by-step explanation:

Answer:

its true i cant pay attention in class cuz its boring but im

not failing it thank god

Answer:

sameeee but im currently not failing, lets hope it stays like that ;-;

Step-by-step explanation:

im smart

Answer:

There is sufficient evidence to support the claim.

Step-by-step explanation:

Given

[tex]\alpha = 0.10[/tex]

Make A

[tex]\bar x_1 = 41[/tex]

[tex]\sigma_1= 4.6[/tex]

[tex]n = 35[/tex]

Make B

[tex]\bar x_2 = 45[/tex]

[tex]\sigma_2 = 4.3[/tex]

[tex]n = 35[/tex]

First, we state the null and alternate hypothesis

[tex]H_0 : \mu_1 = \mu_2[/tex]

[tex]H_1 : \mu_1 \ne \mu_2[/tex]

Next, calculate test statistic:

[tex]z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]

[tex]z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}[/tex]

[tex]z = \frac{-4}{\sqrt{0.6046+0.5283}}[/tex]

[tex]z = \frac{-4}{\sqrt{1.1329}}[/tex]

[tex]z = \frac{-4}{1.0643}[/tex]

[tex]z = -3.7583[/tex]

The critical value at [tex]\alpha = 0.10[/tex] is: [tex]\±1.282[/tex]

[tex]-3.7583 < -1.282[/tex]

So, we reject [tex]H_0[/tex]

This implies that; there is sufficient evidence to support the claim.

Answer:

5.50 + 2.25 ≥ c

Step-by-step explanation

Movie = 5.50

Popcorn = 2.25

C = The total cost

5.50 + 2.25 = C

Answer:

i think y=2 and x=-7

Step-by-step explanation:

Answer:

B)

Step-by-step explanation:

A function is when every input has one output.

Easiest way is to do the "vertical line test" and "horizonal line test."

Basically you draw a vertical line and a horizontal line.

If either line passes through more than one point, then it is not a function.

The only one that passes them is B, the line.

Answer:

B

Step-by-step explanation:

A function is when every input has one output.

Easiest way is to do the "vertical line test" and "horizonal line test."

Basically you draw a vertical line and a horizontal line.

If either line passes through more than one point, then it is not a function.

The only one that passes them is B, the line.

Answer:

25

Step-by-step explanation:

Answer: x=2

Isolate the variable by dividing each side by the factors that don't contain variables.