If a ball is thrown into the air with a velocity of 43 ft/s, its height (in feet) after t seconds is given by y = 43t - 16t^2. Find the velocity when t = 2.
Let h = s(t) = 50t − 16t2 give the height of the ball at time t. Then the ball's velocity at time t = a can be found by v(a) = lim t→a s(t) − s(a) t

Answer:

x-6+x

2x-6=14

2x=20

x=10

Answer:

x-6+x

2x-6=14

2x=20

x=10

Step-by-step explanation:

I tried hard... I really hope this helps!

Answer:

No

Step-by-step explanation:

If they were opposite, they would be equal.

But they are not, (on one of the spaces in between them is smaller and one is larger.)

Hope I have helped you, since it seems I haven't helped "other people" the last time :/

Answer:

No

Step-by-step explanation:

Answer:

i think is e or b

Step-by-step explanation:

[tex]7(b-2)[/tex]  Can be interpreted as letter E.

Answer:

After 25 years, Minneapolis will have 154,062 more residents than Anoka.

Step-by-step explanation:

First, let's write a function for each case.

For Anoka, the initial population is 18,000. The population grows 5.2% or 0.052 each year. Thus:

[tex]A(x)=18000(1.052)^x[/tex], where x represents the amount of years after 1994.

Inversely, for Minneapolis, the population decreases by 2.3% or 0.023. Another way to write this is that it in changes by 1-0.023 or .977 or 97.7%. Thus:

[tex]M(x)=390000(0.977)^x[/tex].

To find how many more people are living in Minneapolis than Anoka after 25 years, simply plug 25 into the functions and then subtract.

In Anoka, after 25 years, there will be:

[tex]A(25)=18000(1.052)^{25}\approx 63924[/tex] residents.

In Minneapolis, after 25 years, there will be:

[tex]M(25)=390000(.977)^{25}\approx217986[/tex] residents.

217986-63924=154,062 residents.

Answer:

g(x) = (x + 3)^2

Step-by-step explanation:

When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.

If we have a quadratic function

[tex]f(x)=x^2[/tex]

and the graph is shifted 3 units to the left, then we can think of a new unit u that is:

[tex]g(x)=u^2[/tex]

The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.

Then, the relation between u and x is:

[tex]u-x=0-(-3)=3\\\\u=x+3[/tex]

We can use this relation in the new graph and replace u as:

[tex]g(x)=(x+3)^2[/tex]

Answer:

g(x) = (x + 3)^2

Step-by-step explanation:

I took the practice test as well.

Answer: (1 and 22/45)

Step-by-step explanation:

I guess that we are working with mixed numbers here, and we have the equation:

(8÷2 2/9) − (2 11/15)

first we solve: 8÷2 = 4.

Now, we can write this as:

(4 + 2/9) - (2 + 11/15)

(4 - 2) + (2/9 - 11/15)

now, 9*5 = 45

        15*3 = 45

then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45

2 - 23/45

But in mixed numbers we also need to work with a positive rational, then we have:

2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45

then the solution is:

(1 and 22/45)

Answer :

percentage decrease = {(2.89-2.82)/2.89}x100 = 2.42%

Answer:

h = A ÷ ½(a - b)

Step-by-step explanation:

A = ½ah - ½bh

A = ½h( a - b)

Divide both sides by the coefficients of h

A ÷ ½(a - b) = h

Answer:

a

Step-by-step explanation:

Maybe: the SRS condition is OK but we need to look at the data to check Normality.

The normality inference is important in that the null compares the difference in the sample means to the difference that one would expect by random variation, or by chance, alone meaning that the sample is assumed to have being from a normal distribution with a mean and standards deviation.

Answer:

[tex]\boxed{\sf \ \ \ 11,464 \ \ \ }[/tex]

Step-by-step explanation:

hello

we need to compute the following

[tex]\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...[/tex]

hope this helps

Answer:

  (f-g)(x) = -x² +4x +6

Step-by-step explanation:

We assume you want to find (f -g)(x).

 [tex](f-g)(x)=f(x)-g(x)=(4x+1)-(x^2-5)\\\\\boxed{(f-g)(x)=-x^2+4x+6}[/tex]

Answer:

Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]

= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]

= [tex]\frac{13}{16}[/tex]

Answer:

Yeah, you got the answer right.

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

-5 is smaller than -2.

-2 is smaller than 1

1 is smaller than 3

Answer:

the 3 one

Step-by-step explanation:

the larger the negative number,the higher up the number line it goes

so -5 is the greatest negative number,-2 the next, the 1 and 3

Answer:

[tex]3{x}^{3} + 2x + 5[/tex]

Step-by-step explanation:

Sorry if my notes weren't very clear.

Answer:B

Step-by-step explanation: got it right

Answer:

C. (x + 3)(x − 8)

Step-by-step explanation:

We need two numbers that add to -5 and multiply to -24.

They are -8 and 3 since -8 + 3 = -5, and -8 * 3 = -24.

x^2 - 5x - 24 = (x - 8)(x + 3)

Answer:

[tex]-\frac{8}{3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex]

Required

Simpify

The very first step is to take LCM of the given expression

[tex]\frac{-10 -4 - 2}{6}[/tex]

Perform arithmetic operations o the numerator

[tex]-\frac{16}{6}[/tex]

Divide the numerator and denominator by 2

[tex]-\frac{16/2}{6/2}[/tex]

[tex]-\frac{8}{3}[/tex]

The expression can't be further simplified;

Hence, [tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex] = [tex]-\frac{8}{3}[/tex]

Answer: 0.8284 units²

Step-by-step explanation:

To find the area between curves, we need to use the integral. We can see that both sides of the shaded region are equal to each other. Therefore, we can find the area of one shaded part and multiply it by 2 for the 2 shaded regions. For the integral, we can find the area of the shaded region on the left side, on the interval from 0 to π/4.

Now that we know the integral, we can figure out the function. We do this by subtracting the top curve by the bottom curve. The top curve on the left shaded region, is y=cosx. The bottom curve on the shaded region is y=sinx. Therefore, we will subtract cosx-sinx.

[tex]2\int\limits^\frac{\pi }{4} _0 {cosx-sinx} \, dx[/tex]

Now that we have the integral, we can solve by splitting the integral into 2 separate integrals by the Sum Rule. Let's disregard the multiply by 2 for now, but we will make sure to multiply by 2 at the end.

[tex]\int\limits^\frac{\pi }{4} _0 {cosx} \, dx -\int\limits^\frac{\pi }{4} _0 {sinx} \, dx[/tex]

Now, we can solve each integral separately.

[tex]\int\limits^\frac{\pi }{4} _0 {cosx} \, dx =sinx]^\pi^ /^40[/tex]

*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.

[tex]sin(\frac{\pi }{4} )-sin(0)=\frac{\sqrt{2} }{2} -0=\frac{\sqrt{2} }{2}[/tex]

Now, we can find the integral of sinx.

[tex]\int\limits^\frac{\pi }{4} _0 {sinx} \, dx=-cos]^\pi ^/^40[/tex]

*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.

[tex]-cos(\frac{\pi }{4} )-(-cos(0))=-\frac{\sqrt{2} }{2} -(-1)=-\frac{\sqrt{2} }{2} +1[/tex]

Now that we have the integral of each integral, we can subtract them, and multiply by 2.

[tex]\frac{\sqrt{2} }{2} -(-\frac{\sqrt{2} }{2} +1)=\sqrt{2}+1[/tex]

[tex]2(\sqrt{2} +1)=0.8284 units^2[/tex]

Answer:

equilateral

Step-by-step explanation:

There are various types of triangles out there, each with its own unique characteristics that distinguish it from others.

One such triangle is called an equilateral triangle. Essentially, like its name suggests, this kind of triangle has all three angles equal (they're actually all equal to 60 degrees). Additionally, this triangle has all three sides that same, as well.

Thus, the answer is equilateral.

Just for future reference, here are a couple more types of triangles:

- Isosceles

These triangles have at least 2 sides equal to each other; in other words, an equilateral triangle is an example of an isosceles triangle. In addition, the two angles of an isosceles triangle opposite to the two equal sides are themselves congruent.

- Scalene

These triangles have all three sides different, which in turn means that all three angles are distinct.

- Acute

These triangles' angles are all less than 90 degrees. That's what "acute" means: less than 90 degrees.

- Obtuse

These triangles have exactly 1 angle that is larger than 90 degrees.

- Right

These triangles have exactly 1 angle that is equal to 90 degrees.

~ an aesthetics lover

Answer: Equilateral triangle

Step-by-step explanation: A triangle with 3 congruent sides is called an equilateral triangle or stated another way, an equilateral triangle is a triangle in which all 3 sides have the same length.

I have attached an example of this below.

Answer:

m∠1 = 91°

Step-by-step explanation:

Since ∠2 and ∠3 are Supplementary Angles, to find x:

5x + 14 + 7x - 14 = 180

12x = 180

x = 15

Now we plug in x as 15 in to find m∠2:

m∠2 = 5(15) + 14

m∠2 = 75 + 14

m∠2 = 89

Since ∠1 and ∠2 are also supplementary, to find m∠1, we simply subtract 180°:

m∠1 = 180 - m∠2

m∠1 = 180 - 89

m∠1 = 91°

Answer:

D.

Step-by-step explanation:

Answer:

Hello! :) The answer will be under “Explaination”

Step-by-step explanation:

The correct answer to your question is 4 1/3

Here is the work:

So if we simply 39/9 we will get 13/3

Than we divide 3 and 13

Which will leave us with 4 and 1 left over

So the answer is 4 1/3

Here is how to check your work, 4x3 =12 and 12+1=13 (13/3 which equals to 39/9

ANSWER: 4 1/3

Hope this helps! :)

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

                                              meadow voles     common voles      Row Total

apple slices                                     26                          32                      58

peanut butter-oatmeal                   35                          25                     60

Column Total                                   61                          57                     118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Answer:

[tex]6 \pm 2.861(0.3354)[/tex]

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.861.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.861\frac{1.5}{\sqrt{20}} = 2.861(0.3354)[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The format of the confidence interval is:

[tex]S_{M} \pm M[/tex]

In which [tex]S_{M}[/tex] is the sample mean

So

[tex]6 \pm 2.861(0.3354)[/tex]

Step-by-step explanation:

Answer:

729

Step-by-step explanation:

Replace x with 9. [tex]9^{2}[/tex] which is 9*9=81 than [tex]9^{1}[/tex] which is 9*1=9. Simplify 81*9=729.

Answer:

Step-by-step explanation:

There are 9 possible outcomes for (Bill, Ben)'s cards:

  (4, 4) total 8; (4, 5) total 9; (4, 6) total 10;

  (5, 4) total 9; (5, 5) total 10; (5, 6) total 11;

  (6, 4) total 10; (6, 5) total 11; (6, 6) total 12.

Of these 9 outcomes, 4 have an odd total; 6 are less than 11.

 P(odd) = 4/9

  P(sum < 11) = 2/3

Answer:

56.52 in

Step-by-step explanation:

Circumference Formula: C = 2πr

Since we are given radius r = 9, simply plug it into the formula:

C = 2π(9)

C = 18π

C = 56.5487

Answer:

56.5

Step-by-step explanation:

The circumference is the product of the diameter and PI

P = (9+9)*π = 18*3.14=56.52

Explanation:

The identity we'll use is cos(-x) = cos(x) for any value of x.

So cos(-150) = cos(150).

Then locate the angle 150 on the unit circle. The terminal point is [tex]\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]

The x coordinate of this terminal point is the value of cos(150).

Answer:

Cos(-150°)=-√3/2

Step-by-step explanation:

-150° is found at the third quadrant so the cost value at third quadrant is negative

Cos(-150°)= -cos(30)=-cos(210)

Cos(-150°)=- (√3/2)

Cos(-150°)=-√3/2

Hope it helps

Answer:

A.50-n=44, 6 shorts borrowed

Step-by-step explanation:

If her sister borrowed n shorts, that means Shelly now has n less shorts. Since her amount of shorts is 50, then 50-n must equal how many shorts she has now, meaning 50-n=44. Solving the equation we get n=6. This means that her sister borrowed 6 shorts.

Answer:

A

Step-by-step explanation:

50 minus the shorts Shawnie borrowed (n) equal to 44