50 points.........

A dolphin jumps from the water with an initial velocity of 44 feet per second at an elevation angle of 60°. Which parametric equations model the dolphin’s path through the air?

x(t) = sin(60°)t + 44 and y(t) = –16t2 + cos(60°)t + 44
x(t) = cos(60°)t + 44 and y(t) = –16t2 + sin(60°)t + 44
x(t) = 44sin(60°)t and y(t) = –16t2 + 44cos(60°)t
x(t) = 44cos(60°)t and y(t) = –16t2 + 44sin(60°)t

Answer:

∠1 = 36°

∠2 = 122°

∠3 = 122°

∠4 = 38°

Step-by-step explanation:

∠2 = 180°-58° (Supplementary angles add up to 180°)

    = 122°

∠2 = ∠3 (Vertically opposite angles are equal)

    = 122°

∠1 = 180°-122°-22° (Sum of angles in a triangle is 180°)

   = 36°

∠4 = 180°-122°-20° (Sum of angles in a triangle is 180°)

     = 38°

Answer:

D

Step-by-step explanation:

From the total 1000 students, 450 are male, so 1000 - 450 = 550 students are female.

117 students are both [enrolled in extracurriculars] and [female].

The total number of [female] students is equal to the total number of [female AND enrolled] students plus the total number of [female AND not enrolled] students. The events of being enrolled in extracurriculars and not being enrolled are mutually exclusive. So if x is the number of female students not enrolled in extracurriculars, then

550 = x + 117

x = 550 - 117

x = 433

and the answer is B.

Answer:

m<5 = 71 and m<8 = 109

Step-by-step explanation:

m<1 is equivalent to m<5 and m<2 is equivalent to m<8.

Answer:

∠5 = 71°

∠8 = 109°

Step-by-step explanation:

∠1 = 71°

∠5 = 71°  (the same as ∠1 = 71°) its a corresponding angle

∠8 = 180 - ∠5

∠8 = 180 - 71

∠8 = 109°

Answer:

A

Step-by-step explanation:

The mode describes the most frequently occurring score or observation in a distribution. The tallest bar would describe the most frequently occurring score. Hence, the mode can be inferred directly from a histogram.

Hence, the frequency distribution or histogram could be used to directly deduce the mode of a distribution.

Learn more : https://brainly.com/question/16785562

Answer:

We can't set up a proportion to solve for x in a percent equation. For example,   34/100=5/x

Step-by-step explanation:

Answer:

6/8

Step-by-step explanation:

Answer:

2688

Step-by-step explanation:

Answer:

7/40

Step-by-step explanation:

12-5=7

54-14=40

7/40

Answer:

(3, 60) (5, 100) (8, 160) (9, 180) (12, 240)

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

move x to the 3x side and move 5 to 9 side.

you get 2x=4

then you divide 2 from both sides and get 2

Answer:

x=2

Step-by-step explanation:

•Original Expression;

3x+5=x+9

•Group like terms;

3x-x=9-5

•Simplify

3x-x

=2x

Then

9-5

=4

Which is going to be;

2x=4

•Divide both sides by 2 to find x

4 can be divided by 2 two times so;

x=2

Answer:

2. Eunju is right

3. [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Step-by-step explanation:

Polynomial Remainder Theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

[tex]f(x)=(x+b)^3+(x+c)^2-(b-c)[/tex]

To find out if x+b is a factor of f(x), we find f(-b):

[tex]f(-b)=(-b+b)^3+(-b+c)^2-(b-c)[/tex]

Operating:

[tex]f(-b)=(-b+c)^2-(b-c)[/tex]

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex] without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

[tex]x^2+5x+6 =(x+2)(x+3)[/tex]

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

[tex]f(x)=x^4+5x^3+2x^2-20x-24[/tex]

Find f(-2):

[tex]f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24[/tex]

[tex]f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0[/tex]

Find f(-3):

[tex]f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24[/tex]

[tex]f(-3)=81-5*27+2*9+60-24[/tex]

[tex]f(-3)=81-135+18+60-24 =0[/tex]

Since both f(-2) and f(-3) are zero, [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Answer:

0.001 (one thousandth)

Step-by-step explanation:

hope this helps

Answer:

1 thousandth

Step-by-step explanation:

2 is in the ones place, 3 is in the tenths place, 9 is in the hundredths place, 1 is in the thousandths place.

Hope it helps!

Answer:

Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} - 5x - 20[/tex]

To find f(-9) , substitute the value of x that's - 9 into f (x). That is for every x in f(x) replace it with - 9

We have

[tex]f( - 9) = 2 ({ - 9})^{2} - 5( - 9) - 20 \\ = 2(81) + 45 - 20 \\ = 162 + 25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 187 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

Hope this helps you

Answer:

345 divided by 5, answer in standard form

69 ....

Answer:

69

Step-by-step explanation:

Standard: 69

word : sixty nine

Answer:

Each student will get 1/6 liters of soda.

Step-by-step explanation:

In order to do this, we need to divide 1/2 by 3.

All we had to do is multiply 2 by 3.

1/6 is smaller than 1/2, and because 6 is 2 x 3, it's 3 times smaller, or less.

Therefore, each student will get 1/6 liters of soda.

Hope this helps! :D

Answer:

The answer to this question is C. 40.274.

Answer:

The slope of UV = 4

Step-by-step explanation:

Given the points

Finding the slope of UV

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-1,\:1\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-3\right)[/tex]

[tex]m=\frac{-3-1}{-2-\left(-1\right)}[/tex]

[tex]m=4[/tex]

Thus, the slope of UV = 4

awnser

12;8

Step-by-step explanation:

i belive its that if its not then its prolly 12;20 if you get it wrong i will give you points-

Answer:

Step-by-step explanation:

147 x 23 = 3381

=>

Answer:

B: 3381

Step-by-step explanation:

147 X 23 = 3,381. if she drove 147 miles for 23 days that's 3381 miles in one month

Answer:

0.6818

Step-by-step explanation:

The first table shows a proportional relationship between x and y.

A proportional relationship exist between two entities if an increase in one causes an increase in another or vice versa.

x             y

7            28

14           35

x               y

1               2

4               4

7                5

The first table shows a proportional relationship between x and y, for every value of x, y increases by almost 2 times.

Learn more about proportional relationship here: https://brainly.com/question/2575222

Answer:

We have 92 % confidence that the true mean time a student sleeps per night is between (-0.25, 1.61).

Step-by-step explanation:

Compute the sample mean and sample standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum X=\frac{54.3 }{8}=6.788\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 11.8288}=1.299[/tex]

Since, the sample standard deviation is computed the t-statistics will be used for the confidence interval.

The critical value of t for (n - 1) degrees of freedom and 92% confidence level is:

[tex]t_{\alpha/2, (n-1)}=t_{0.04, 7}=2.046[/tex]

*Use a t-table.

Compute the 92% confidence interval for the true mean time a student sleeps per night as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]

     [tex]=6.788\pm 2.046\times\frac{1.299}{\sqrt{8}}\\\\=6.788\pm 0.9392\\\\=(-0.2504, 1.6080)\\\\\approx (-0.25, 1.61)[/tex]

We have 92 % confidence that the true mean time a student sleeps per night is between (-0.25, 1.61).

Answer:

the answer ur looking for

81 −11.7 ≈ 70

Answer:

Commutative property of multiplication is shown above. This is because no matter how you put them, the answer will still be 140  

Answer:

0.92

Step-by-step explanation:

Answer:

5x=3+7

5x=10

X=10/5

=2

Answer:

270

Step-by-step explanation:

First, to find how far the car will go in one hour, you do 180 divided by 4. We already know that the car drives at a constant rate. If you do 180 divided by 4, you get 45. Then you multiply 45 by the amount of hours (6) to get 270

Answer:

the line is inconsistent:)

Step-by-step explanation:

Answer:

The sum of all the external angles of a triangle is 360°.

Step-by-step explanation:

Let there are n sides in a polygon.

So, there are n internal angles in the polygon, let ∠i1, ∠i2, ∠i3, ..., ∠in are the measure of n internal angles of the polygon.

The measure of external angle corresponding to ∠i1,  ∠1= 180°-∠i1,

The measure of external angle corresponding to ∠i2, ∠2 = 180°-∠i2,

Similarly, the measure of external angle corresponding to ∠in, ∠n = 180°-∠in.

Now, the sum of all the external angles of the polygon,

(∠1+∠2+...+∠n)=(180°-∠i1)+(180°-∠i2)+...+(180°-∠in)

=(180°+180°+...n times)-(∠i1+∠i2+...+∠in)

=n x 180° - (∠i1+∠i2+...+∠in)

As ∠i1+∠i2+...+∠in is the sum of all the internal angles of the polygon.

So, the sum of all the external angles of the polygon =

(n x 180°) - (sum of all the internal angles of the polygon).

In the case of a triangle, n=3  and the sum of all the three internal angles, ∠i1+∠i2+∠i3 = 180°.

Therefore, the sum of all the external angles of a triangle,

∠1+∠2+∠3 =3x180°-(∠i1+∠i2+∠i3)

                 =540°=180°

                 =360°.

Hence, the sum of all the external angles of a triangle is 360°.