a2 - ab + 8b + b2 - 1

Answer:

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Step-by-step explanation:

Before building the confidence intervals, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

In the morning:

Sample of 57, mean of 5.2, standard deviation of 0.6, so:

[tex]\mu_1 = 5.2[/tex]

[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]

In the afternoon/evening:

Sample of 70, mean of 4.5, standard deviation of 0.4, so:

[tex]\mu_2 = 4.5[/tex]

[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]

Confidence interval:

The confidence interval is:

[tex]\mu \pm zs[/tex]

In which

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

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower bound of the interval is:

[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Step-by-step explanation:

Lets break this word problem down:

"The difference" means we're going to be finding x - y ("difference" means we're finding how much one value "differs" from the other)

"a number and it's opposite" so we're doing x - y, where y = -x. So already, we can re-write this as x - (-x) or x + x

"is 28" so x + x = 28 ("is" always means "equals")

"Find the number" so we're finding x.

x - (-x) = 28  (I went back a step so I could write everything out more plainly)

simplify

x + x = 28

add

2x = 28

divide both sides by 2 to get x on its own

x = 14

Answer:

14

Answer:

√5/121

Step-by-step explanation:

formula: a^½=√a

(⁵/¹²¹)^½=√⁵/¹²¹

We need to find the percent, let's start but making the equation.

The price is 2.69

The tax cost is 0.13

So what percent of 2.69 is = 0.13.

Equation: X/100 x 2.69 = 0.13

Multiply each side by 100 so we can get x alone with the price: 2.69x = 13

Now to get x alone, we must divide both sides by 2.69: x = 4.8

Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.

I hope this helps! :)

Answer:

0.53%

Step-by-step explanation:

hope it is well understood

Answer:

Step-by-step explanation:

In order to find out how long it takes for the rocket to hit the ground, we only need set that position equation equal to 0 (that's how high something is off the ground when it is sitting ON the ground) and factor to solve for t:

[tex]0=-4.9t^2+112t+395[/tex]

Factor that however you are factoring in class to get

t = -3.1 seconds and t = 25.9 seconds.

Since time can NEVER be negative, it takes the rocket approximately 26 seconds to hit the ground.

Here we want to create algebraic expressions for different quantities.

i) Nazaneen has  3*m marbles.

ii) Karly has m + 4 marbles.

a) The given data is:

Shireen has m marbles.

Nazaneen has three times as many marbles as Shireen.

Knowing that Shireen has m marbles, we can conclude that Nazaneen has:

3*m marbles.

Karly has 4 more marbles than Shireen, then Karly has m + 4 marbles.

Then the equations for the number of marbles that each one has are:

Shireen = m

i) Nazaneen has  3*m marbles.

ii) Karly has m + 4 marbles.

If you want to learn more, you can read:

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(256⁴-1)

= (256-1)⁴

Using identity (a-b)⁴ = a⁴−4a³b+6a²b²−4ab³+b⁴

Let a be 256 and b be 1

Then

256⁴−4(256)³(1)+6(256)²(1)²−4(256)(1)³+(1)⁴

After solving

(256²-1)²

(a-b)² = a²-2ab+b²

256²-2×256×1+1²

= (256²-1)(256²+1)

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Answer:

Use identity:

Consider that:

Now factorize:

Answer:

D. Neither perpendicular nor parallel

Step-by-step explanation:

Let's find the slope (m) of both lines:

✔️Slope (m) of the line that passes through (6, -1) and (11, 2):

Slope (m) = change in y/change in x

Slope (m) = (2 -(-1))/(11 - 6) = 3/5

✔️Slope (m) of the line that passes through (5, -7) and (8, -2)

Slope (m) = change in y/change in x

Slope (m) = (-2 -(-7))/(8 - 5) = 5/3

✅The slope of both lines are not the same, therefore they are not parallel nor same line.

Also, the slope of one is not the negative reciprocal of the other, therefore they are not perpendicular.

Answer:

False

Step-by-step explanation:

The point that is equidistant from the vertices of a triangle is called the circumcenter.

9514 1404 393

Answer:

  False

Step-by-step explanation:

The incenter is the center of the inscribed circle, which is tangent to all of the sides of the triangle. The incenter is equidistant from the sides, not the vertices.

_____

Additional comment

The circumcenter is the center of the circumscribing circle. Each of the vertices of the triangle is on the circumcircle, so the circumcenter is equidistant from the vertices.

The incenter is located at the intersection point of the angle bisectors. The circumcenter is located at the intersection point of the perpendicular bisectors of the sides.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.

__

(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.

Answer:

Yes 7i is the answer

Step-by-step explanation:

they are equivalent.

Answer:

D

Step-by-step explanation:

if you draw any vertical line through a function it should have a max of one intersection point so if the graph, reading from left to right doubles back on itself, it is not a function

Answer:

The correct answer is B. It will take them 7.2 hours.

Step-by-step explanation:

Given that to collect data on the signal strengths in a neighborhood, Briana must drive from house to house and take readings, and she has a graduate student, Henry, to assist her, and Briana figures it would take her 12 hours to complete the task working alone, and that it would take Henry 18 hours if he completed the task by himself, to determine how long will it take Briana and Henry to complete the task together the following calculation must be performed:

1/12 + 1/18 = X

18 / (12 x 18) + 12 / (18 x 12) = X

30/216 = X

5/36 = X

36/5 = 7.2

Therefore, they will be able to finish the task in 7.2 hours.

Answer:

7/3 is the answer

Step-by-step explanation:

Answer: lol ez

B.

Step-by-step explanation: XD

Answer:

D

Step-by-step explanation:

The general formula for the sine or cosine function is

y = A*Sin(Bx + C) + D

C = 0 in this case

B = pi / 3

The period is given by the formula

P = 2 * pi / B

P = 2 * pi//pi/3

The 2 pis cancel and you are left with 2*3 = 6

Answer:

2 • (59x10 - 60)

 ————————————————

        5  

Step-by-step explanation:

Answer:

y=-4x-5

Step-by-step explanation:

The slope of the line is - 4, the equation of line is y=-4x-5

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

============================================

Explanation for part (a)

All distances mentioned are in feet.

We'll have a right triangle which allows us to apply the pythagorean theorem. Refer to the diagram below.

a^2+b^2 = c^2

x^2+y^2 = z^2

Apply the derivative to both sides with respect to t. We'll use implicit differentiation and the chain rule.

[tex]x^2+y^2 = z^2\\\\\frac{d}{dt}[x^2+y^2] = \frac{d}{dt}[z^2]\\\\\frac{d}{dt}[x^2]+\frac{d}{dt}[y^2] = \frac{d}{dt}[z^2]\\\\2x*\frac{dx}{dt}+2y*\frac{dy}{dt}=2z*\frac{dz}{dt}\\\\x*\frac{dx}{dt}+y*\frac{dy}{dt}=z*\frac{dz}{dt}\\\\[/tex]

Now we'll plug in (x,y,z) = (4000,3000,5000). The x and y values are given. The z value is found by use of the pythagorean theorem. Ie, you solve 4000^2+3000^2 = z^2 to get z = 5000. Or you could note that this is a scaled copy of the 3-4-5 right triangle.

We know that dx/dt = 0 because the horizontal distance, the x distance, is not changing. The rocket is only changing in the y direction. Or you could say that the horizontal speed is zero.

The vertical speed is dy/dt = 800 ft/s and it's when y = 3000. It's likely that dy/dt isn't the same value through the rocket's journey; however, all we care about is the instant when y = 3000.

Let's plug all that in and isolate dz/dt

[tex]4000*0+3000*800=5000*\frac{dz}{dt}\\\\2,400,000=5000*\frac{dz}{dt}\\\\\frac{dz}{dt} = \frac{2,400,000}{5000}\\\\\frac{dz}{dt} = 480\\\\[/tex]

At the exact instant that the rocket is 3000 ft in the air, the distance between the camera and the rocket is changing by an instantaneous speed of 480 ft/s.

-----------------------------------------------------------------------

Explanation for part (b)

Again, refer to the diagram below.

We have theta (symbol [tex]\theta[/tex]) as the angle of elevation. As the rocket's height increases, so does the angle theta.

We can tie together the opposite side y with the adjacent side x with the tangent function of this angle.

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\theta) = \frac{y}{x}[/tex]

Like before, we'll apply implicit differentiation. This time we'll use the quotient rule as well.

[tex]\tan(\theta) = \frac{y}{x}\\\\\frac{d}{dt}[\tan(\theta)] = \frac{d}{dt}\left[\frac{y}{x}\right]\\\\\sec^2(\theta)*\frac{d\theta}{dt} = \frac{\frac{dy}{dt}*x - y*\frac{dx}{dt}}{x^2}\\\\\sec^2(\theta)*\frac{d\theta}{dt} = \frac{800*4000 - 3000*0}{4000^2}\\\\\sec^2(\theta)*\frac{d\theta}{dt} = \frac{3,200,000}{16,000,000}\\\\\sec^2(\theta)*\frac{d\theta}{dt} = \frac{32}{160}\\\\\sec^2(\theta)*\frac{d\theta}{dt} = \frac{1}{5}\\\\[/tex]

Let's take a brief detour. We'll return to this later. Recall earlier that [tex]\tan(\theta) = \frac{y}{x}\\\\[/tex]

If we plug in y = 3000 and x = 4000, then we end up with [tex]\tan(\theta) = \frac{3}{4}\\\\[/tex] which becomes [tex]\tan^2(\theta) = \frac{9}{16}[/tex]

Apply this trig identity

[tex]\sec^2(\theta) = 1 + \tan^2(\theta)[/tex]

and you should end up with [tex]\sec^2(\theta) = 1+\frac{9}{16} = \frac{25}{16}[/tex]

So we can now return to the equation we want to solve

[tex]\sec^2(\theta)*\frac{d\theta}{dt} = \frac{1}{5}\\\\\frac{25}{16}*\frac{d\theta}{dt} = \frac{1}{5}\\\\\frac{d\theta}{dt} = \frac{1}{5}*\frac{16}{25}\\\\\frac{d\theta}{dt} = \frac{16}{125}\\\\\frac{d\theta}{dt} = 0.128\\\\[/tex]

This means that at the instant the rocket is 3000 ft in the air, the angle of elevation theta is increasing by 0.128 radians per second.

This is approximately 7.334 degrees per second.

The distance from the television camera to the rocket is changing at 480 ft/s while the camera's angle of elevation is changing at 0.128 rad/s

Let x represent the distance from the camera to the rocket and let h represent the height of the rocket.

a)

[tex]x^2=h^2+4000^2\\\\2x\frac{dx}{dt}=2h\frac{dh}{dt} \\\\x\frac{dx}{dt}=h\frac{dh}{dt} \\\\At \ h=3000\ ft, \frac{dh}{dt}=800\ ft/s;\\x^2=3000^{2} +4000^2\\x=5000\\\\\\x\frac{dx}{dt}=h\frac{dh}{dt} \\\\5000\frac{dx}{dt}=3000*800\\\\\frac{dx}{dt}=480\ ft/s[/tex]

b)

[tex]tan(\theta)=\frac{h}{4000} \\\\h=4000tan(\theta)\\\\\frac{dh}{dt}=4000sec^2(\theta)\frac{d\theta}{dt} \\\\\\At\ h=3000\ ft;\\\\tan\theta = \frac{3000}{4000}=\frac{3}{4} \\\\sec^2(\theta)=1+tan^2(\theta)=1+(\frac{3}{4})^2=\frac{25}{16} \\\\\\\frac{dh}{dt}=4000sec^2(\theta)\frac{d\theta}{dt}\\\\800=4000*\frac{25}{16}* \frac{d\theta}{dt}\\\\\frac{d\theta}{dt}=0.128\ rad/s[/tex]

Hence, The distance from the television camera to the rocket is changing at 480 ft/s while the camera's angle of elevation is changing at 0.128 rad/s

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Answer:

i still se question marks

Step-by-step explanation:

Answer:

The lowest percentage from all voters combined that must be unmarried in order for Candidate A to win the election is 53.85%.

Step-by-step explanation:

Proportion married:

x are married

1 - x are unmarried.

Will vote for candidate A:

15% of x

80% of 1 - x. So

[tex]0.15x + 0.8(1-x)[/tex]

Candidate A wins:

If his proportion is more than 50%, that is:

[tex]0.15x + 0.8(1-x) > 0.5[/tex]

[tex]0.15x+ 0.8 - 0.8x > 0.5[/tex]

[tex]-0.65x > -0.3[/tex]

[tex]0.65x < 0.3[/tex]

[tex]x < \frac{0.3}{0.65}[/tex]

[tex]x < 0.4615[/tex]

Highest percentage of married is 46.15%, so:

The lowest percentage of unmarried is:

100 - 46.15 = 53.85%.

The lowest percentage from all voters combined that must be unmarried in order for Candidate A to win the election is 53.85%.

144 x 1.25 = 180

Answer: 144

Answer:

144

Step-by-step explanation:

144 × 1.25 = 180

We add the 1 to .25 to represent the original value plus the 25% increase.

Or you could have divided 180 by 1.25 to find original price.

I dont know what you mean by the question but according to me.

If y=x^5

y=x^5+3

Then y+3=x^5+3

Answered by Gauthmath must click thanks and mark brainliest

Answer:

m∠F = 45°

Step-by-step explanation:

Notice the lengths of the given sides and the right angle. This is enough information to prove that this is a 45-45-90 triangle, or just basically a square cut diagonally.

Regardless if even just one side is given for a 45-45-90 triangle, all 45-45-90 triangles have one thing in common. The sides that form the right angle are equivalent and the hypotenuse is equal to one of the sides that form the right angle times the square root of two. I'm aware that it sounded confusing, as I'm awful at explaining, so just look at the picture I've attached instead of trying to understand my explanation that seemed like trying to learn a second language.

Look at the picture. See that FD = x times that square root of 2 and that DE = x. Now look back at your picture. It's connecting, now isn't it?

Now that we know that this is indeed a 45-45-90 triangle, we can confirm that m∠F = 45°

Answer:

34.5p-2.75

Step-by-step explanation:

First add -0.5p and 12p together which is 11.5p, then add 23p with 11.5p which is 34.5p And -2.75 remains the same

So the answer is 34.5p-2.75

Answer:

34.5p-2.75

Step-by-step explanation:

-0.5p+12p-2.75+23p=34.5p-2.75

Answer: This quadratic equation has two real solutions.

Step-by-step explanation:

[tex]y=x^{2} -11x+7\\\\D=(-11)^{2} -4 \cdot 7=121-28=93 \: > 0\\\\x=\dfrac{11 \pm \sqrt{93} }{2}[/tex]

I think its A) (f+g)(z)=|2x+4|-2

Step-by-step explanation:

21

12^2 = 144

144 - 123 = 21

11^2 = 121

12^2 = 144

Between these

Answered by Gauthmath must click thanks and mark brainliest