Hillel is juggling flaming torches to raise money for charity. His initial appearence raises $500, and he raises $15 for each minuter of juggling performance. The amount R of money Hillel raises is a function of t, the length of his performance in minutes. write the functions formula

Answer:

The rate of change of the Coyote population in 2002 is 32

Step-by-step explanation:

Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2

The formula is given as;

P(t) = (t^2 + 100) ln (t + 2)

The rate of change refers to the first integral of the formula;

Thus we need to calculate this by the use of product formula;

The first differential of t^2 + 100 is 2t

while that of ln(t + 2) is 1/(t + 2)

P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)

Now, we substitute 2 for the value of t here.

P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))

P’(2) = 4 ln 4 + 104(1/4)

P’(2) = 4ln 4 + 26

P’(2) = 5.55 + 26 = 31.55 which is approximately 32

Answer:

Step-by-step explanation:

84?

8+4 is 12, and 84 is greater than 80, and less than 90

Answer:

84

Step-by-step explanation:

Answer: 12 hours

Step-by-step explanation:

Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open

1/6 = portion of pool filled per hour by the inlet pipe

1/12 = portion of pool emptied per hour by the drain

1/x = portion of pool filled per hour if the inlet pipe and drain are both open

Then, 1/6 - 1/12 = 1/x

Multiply by the LCD, 12x, to obtain

2x - x = 12

x = 12 hours

Answer:

4over27

Step-by-step explanation:

8over9 divided by 6 equals 8over54 which simplifies to 4over27

Answer:

4 over 27

Step-by-step explanation:

she spent 6 day reading, there 7 day in a week so we have to change it to 7 and four pages.

Answer:

Approximately 23,433 children will have cancer.

Step-by-step explanation:

3/1500 can be simplified to 1/500, which can also be written as 0.002. To find the number of children who have cancer, we do 11,721,722 * 0.002, which gives us 23,433.444 which we can round to 23,433.

Answer:

[tex]\frac{1}{4} x-2=10[/tex]

Step-by-step explanation:

Let x be that number.

[tex]\frac{1}{4} x-2=10[/tex]

If you want to find the number..

[tex]\frac{1}{4} x=10+2[/tex]

[tex]0.25x=12[/tex]

[tex]x=12/0.25[/tex]

[tex]x=48[/tex]

The net outward flux across the boundary of the tetrahedron is: -4

What is the gradient of a function in a vector field?

The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).

Given vector field:

F = ( -2x, y, - 2 z )

[tex]\mathbf{\nabla \cdot F = ( i \dfrac{\partial }{\partial x }+ j \dfrac{\partial}{\partial y} + k \dfrac{\partial}{\partial z}) \langle -2x, y, -2z \rangle}[/tex]

[tex]\mathbf{ \nabla \cdot F = ( \dfrac{\partial }{\partial x }(-2x)+ \dfrac{\partial}{\partial y}(y) + \dfrac{\partial}{\partial z}(-2z))}[/tex]

= -2 + 1 -2

= -3

According to divergence theorem;

Flux [tex]\mathbf{=\iiint _v \nabla \cdot (F) \ dv}[/tex]

x+y+z = 2; [tex]1^{st}[/tex]  Octant

[tex]= \int\limits^2_0 \int\limits^{2-x}_0 \int\limits^{2-x-y}_0 -3dzdydx[/tex]

[tex]=-3 \int\limits^2_0 \int\limits^{2-x}_0 (2-x-y)dy dx[/tex]

[tex]= -3 \int\limits^2_0[(2-x)y - \dfrac{y^2}{2}]^{2-x}__0 \ \ dx[/tex]

[tex]= -3 \int\limits^2_0(2-x)^2 - \dfrac{(2-x)^2}{2} dx[/tex]

[tex]= -3 \int\limits^2_0\dfrac{(2-x)^2}{2} dx = - \dfrac{3}{2} \int\limits^2_0(4-4x+x^2) dx[/tex]

[tex]=- \dfrac{3}{2}(4x-x^2 + \dfrac{x^3}{3})^2_0[/tex]

[tex]=- \dfrac{3}{2}(8-8+\dfrac{8}{3})[/tex]

[tex]=- \dfrac{3}{2}(\dfrac{8}{3})[/tex]

= -4

Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: -4

Learn more about the gradient of a function here:

https://brainly.com/question/6158243

Answer:

 Slope = 4.000/2.000 = 2.000

 x-intercept = 6/2 = 3

 y-intercept = -6/1 = -6.00000

Step-by-step explanation:

Step by step solution :

Step  1  : Equation of a Straight Line

Graph of a Straight Line

Calculate the Y-Intercept

Calculate the X-Intercept

Calculate the Slope

Answer for y=2x-6  is below

Answer:  

Slope = 4.000/2.000 = 2.000

 x-intercept = 6/2 = 3

 y-intercept = -6/1 = -6.00000

Hope this helps.

Answer:

Correlation Coefficient

Step-by-step explanation:

The correlation coefficient (r) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.

Answer:

Hello

The answer is 3855'5

Step-by-step explanation:

At first change lbs to kg.

Then you'll change the kg to grkg×1000=gr

Answer:

3 1/2

Step-by-step explanation:

7 1/4 - 3 3/4

Borrow 1 from the 7 in the form of 4/4

6 + 4/4 + 1/4 - 3 3/4

6 5/4 - 3 3/4

3 2/4

Simplify the fraction

3 1/2

Answer:

[tex]3 \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]7 \frac{1}{4} - 3 \frac{3}{4} \\ \frac{29}{4} - \frac{15}{4} \\ = \frac{14}{4} \\ = \frac{7}{2} \\ = 3.5 = 3 \frac{1}{2} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

As you know, a year has around 365 + 1/4 days.

This means that in two years, we have:

365 + 356 + 1/4 + 1/4 = 730 + 1/2

and so on.

adding this up, when we have 4 years we have a full day extra, this is:

1460 + 1

When we divide 1461 by 4, we have 365 with a surpass of 1.

The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.

So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.

The "math rule" used to know if a year is leap or not is:

if a year is not divisible by 4, then it is a common year

else if the year is not divisible by 100 then it is a leap year,

else if the year is not divisible by 400, then it is a common year

if not, the year is a leap year.

Where "year" represents the number of the year.

Answer:

X probability = 0.02

Cumulative frequency at x ( 6 ) = 1

Step-by-step explanation:

X       P ( X )            Cf ( X )

1        0.58                0.58

2        0.18                0.58 + 0.18 = 0.76

3        0.10                0.76 + 0.10 = 0.86

4        0.07                0.86 + 0.07 = 0.93

5        0.05                0.93 + 0.05 = 0.98

6        0.02                0.98 + 0.02 = 1

Answer:

a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).

Step-by-step explanation:

a) Let is find first the velocity vector by differentiation:

[tex]\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j[/tex]

[tex]\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j[/tex]

[tex]\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)[/tex]

Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:

[tex]\|\vec u \| = 1[/tex]

Then,

[tex]\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }[/tex]

[tex]\| \vec u \| = \sqrt{1}[/tex]

[tex]\|\vec u \| = 1[/tex]

Hence, the particle has a constant speed of 4.

b) The acceleration vector is obtained by deriving the velocity vector.

[tex]\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j[/tex]

[tex]\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)[/tex]

Velocity and acceleration are orthogonal to each other only if [tex]\vec v \bullet \vec a = 0[/tex]. Then,

[tex]\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)[/tex]

[tex]\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t[/tex]

[tex]\vec v \bullet \vec a = 0[/tex]

Which demonstrates the orthogonality between velocity and acceleration vectors.

c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: [tex]t \geq 0[/tex]

And cosine decrease and sine increase inasmuch as t becomes bigger.

d) Let evaluate the vector in [tex]t = 0[/tex].

[tex]r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j[/tex]

[tex]r(0) = 0\,i + 1 \,j[/tex]

False, the particle begin at the point (0,1).

Answer:

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Answer:

[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]    

[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]    

The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]

Step-by-step explanation:

Information given

[tex]\bar X=2.9[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =1.4[/tex] represent the population standard deviation

n=2092 represent the sample size  

Confidence interval

The confidence interval is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Since the Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]

Replacing the info we got:

[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]    

[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]    

The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]

Answer:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic would be given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]

Step-by-step explanation:

Information given

[tex]n_1 = 60 [/tex] represent the sample size 1

[tex]n_2 =40[/tex] represent the sample size 2

[tex]s^2_1 = 8[/tex] represent the sample variance 1

[tex]s^2_2 = 10[/tex] represent the sample variance 2

The statistic to check the hypothesis is given by:

[tex]F=\frac{s^2_2}{s^2_1}[/tex]

Hypothesis to test

We want to test if the two variances are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic would be given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]

Answer:

V(speed)=3.5 mile per hour

Step-by-step explanation:

[tex]V=mile per hour[/tex]

[tex]V=\frac{7}{8}/ \frac{1}{4}[/tex]

[tex]V=\frac{7}{8}*\frac{4}{1}[/tex]

[tex]V=\frac{7}{8}*4[/tex]

[tex]V=3.5[/tex]

Answer:

  75% reduction

Step-by-step explanation:

The price dropped by $120. As a percentage of the original price, that is ...

  -$120/$160 × 100% = -75%

The price changed by -75%.

Answer:

75% decrease.

Step-by-step explanation:

The original price is $160 and we went to $40.

That means the price got reduced by $120 in the process.

$120/$160 = 0.75 = 75%.

So in other words, we lost 75% of the price ($120) and got left with 25% of the price ($40).

I hope this helps!

Answer:

 A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.

Step-by-step explanation:

When the x-values are evenly spaced, a linear function will have evenly-space y-values.

In the first table, the y-differences are all +8.

In the second table, the y-differences are 0, 1.5, 1.5, so are not all the same.

In the third table, the y-differences are all -3.

The second table represents a non-linear function.

__

In the graph, you can see that the points from the second table (purple) are not on a straight line.

Answer:

B

Step-by-step explanation:

Answer:

The answer is true

Step-by-step explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2

Answer:

10 cm

Step-by-step explanation:

نستخدم فيثاغورس

ٲب²+ب ج²=ج ٲ²

ج ٲ²= 6²+8²

ج ٲ²= 100

ج ٲ= 10 سم

Answer:

Step-by-step explanation:

1. 6w*2v + 3*6w= 12vw + 18w

2. 7(-5v) - 7(8)= -35v - 56

3. 2x*(-2x) - 3(2x) = -4x^2 - 6x

4. -4*v - 4(1)= -4v - 4

5. 2n*6n + 2n + 2*6n + 2= 12n^2 + 14n + 2

6. 4n(2n) + 4n(6) + 2n + 6= 8n^2 + 26n + 6

7. x(6x) - 2x - 18x + 6 = 6x^2 - 20x + 6

8. 8p(6p) + 8p(2) - 2(6p) - 4 = 48p^2 + 16p - 12p - 4= 48p^2 + 4p - 4

9. 6p(5p) - 6p(8) + 8(5p) - 40= 30p^2 - 48p + 40p - 40= 30p^2 - 8p - 40

10. 3m(8m) + 3m(7) - 8m - 7 = 24m^2 + 21m - 8m - 7= 24m^2 + 13m - 7

11. 2a(8a) - 2a(5) - 8a + 5 = 16a^2 - 10a - 8a + 5 = 16a^2 - 18a + 5

12. 5n(5n) - 5n(5) + 6(5n) - 6(5)= 25n^2 - 25n + 30n - 30= 25n^2 + 5n - 30

13. 4p(4p) - 4p - 4p + 1 = 16p^2 - 8p +

14. 7x(5x) + 7x(6) -6(5x) - 6(6)= 35x^2 + 42x - 30x - 36= 35x^2 + 12x - 36

Answer:

A and D

Step-by-step explanation:

Either rotate the dilated circle 180° about point C or Translate the dilated circle so that it's centre is at point B so that we come to know that the circles are similar

Answer:

[tex] \frac{19}{20} [/tex]

Step-by-step explanation:

[tex] \frac{7}{10} + \frac{1}{4} \\ \frac{14 + 5}{20} \\ = \frac{19}{20} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Bottom prism: 126*11=1386    

Top Prism: 2*45=90

Total volume: 1386+90= 1746 cubic cm

Answer:

I think that it would be A

Step-by-step explanation:

If it were not a sailor, I would say B, but a sailor can face a hurricane at sea.

Answer:

Option (2)

Step-by-step explanation:

Option (1).

Time taken by Tina to walk = 56 minutes

Time taken by her sister to walk the same distance = x minutes

If both the sisters take the same time to walk, then

x = 56 minutes

Option (2).

Let the height of Tina = x inches

and the height of her brother = 56 inches

if Tina is shorter than her brother then,

x < 56 inches

Option (3).

Tina's dog weighed two months ago = 56 pounds

If the dog gained the weight in two months then weight before 2 months will be less than the present weight.

Let the weight of her dog is x pounds now,

x > 56 pounds

Option (4).

Amount with Tina = $x

Cost of the camera = $56

If the money with Tina has enough money to buy the camera, then the amount of money with her will be higher than the cost of the camera.

x > $56

Option (2) will be the answer.

Answer:

x = 23

Step-by-step explanation:

2x + 5y = 35 * (-3) ------>  -6x -15y = -105 (A)

x = -10 - 15y -----> x + 15y = -10 (B)

(A) + (B)

-5x = -115

x = 23

Answer:

a

Step-by-step explanation:

The difference between a rational number and an irrational number is always an irrational number. The correct option is B.

A Rational Number is a number of the form p/q, p & q are integers, and q ≠ 0.  An irrational number is all real numbers except rational numbers i.e. it is a non-repeating and non-terminating decimal number or it can not be expressed in a ratio of two integers.

Further, natural numbers can be rational numbers. Also, all repeating and terminating decimals are rational.

The difference between a rational number and an irrational number is always an irrational number. For example:

2 - √3 is always an irrational number where 2 is rational and √3 is an irrational number.

Hence addition and subtraction of rational and irrational numbers is always an irrational number.

To know more about an irrational number follow

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