A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving the rabbit sees it and starts running away at a speed of 40 feet per second. What should the fox's speed be to catch up to the rabbit.

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

Read more on the Sine function:

https://brainly.com/question/21902442

https://brainly.com/question/29529184

https://brainly.com/question/23214084

Answer:

<

Step-by-step explanation:

The height of the right triangle which is the value of x is determined as 8.

Option C.

We can use the Pythagorean theorem to solve for the height of the right triangle.

In this case, the hypotenuse has a length of 17 and one of the other sides (the base) has a length of 15. Let x be the length of the height of the triangle.

Then we have:

17² = 15² + x²

Simplifying this equation, we get:

289 = 225 + x²

Subtracting 225 from both sides, we get:

64 = x²

Taking the square root of both sides, we get:

x = 8

Learn more about right triangle here: https://brainly.com/question/1248322

#SPJ1

The simplification if the expression "9 × d x e × 6" involving whole number and variable is 54de

9 × d x e × 6

Given the task content, this implies multiplying of all variables and whole numbers in the expression in order to arrive at a common result.

9 × d x e × 6

= 54de

It is very possible to simplify a mathematical statement whether or not the variables are letters, numbers, numbers and letters, like terms and unlike terms. So from the simplification above, 9 × d x e × 6 gives 54de.

Therefore, the simplification if the expression "9 × d x e × 6" involving whole number and variable is 54de

Learn more about simplification:

https://brainly.com/question/723406

#SPJ1

Answer:

16.48

Step-by-step explanation:

The round off of 16.4829 to the nearest hundredth is 16.48.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

16.4829

You rounded to the nearest hundredths place.

The 8 in the hundredths place rounds down to 8, or stays the same,

because the digit to the right in the thousandths place is 2.

and, When the digit to the right is less than 5 we round toward 0.

So, 16.4829 was rounded down toward zero to 16.48.

Learn more about round off here:

https://brainly.com/question/13391706

#SPJ2

The investment after 10 years becomes $1,343.9.

Given that,
Melanie invests a principal of $1,000 at 3% interest. To find the value of her investment after 10 years if the interest is compounded monthly.

Interest is defined as the charges levied by the institution on the consumer on money lending and borrowing.

Principal = $1000
TIme = 10 years
Rate = 3 %

\(Amount = principal (1 + r/100)^n\\Amount = 1000 (1 + 3/100)^{10}\\Amount = 1343.9\)

Amount = $1343.9

Thus, the investment after 10 years becomes $1,343.9.

Learn more about interest here:
https://brainly.com/question/13324776
#SPJ1

Answer:

y = 2x +5

X=2y + 5

X-5 =2y

X-5 / 2 = y

f-1 (x) = x-5/2

Step-by-step explanation:

Answer

This is correct for sure

Step-by-step explanation:

Answer:

The right answer is B.

Step-by-step explanation:

To be sure if three sides could be used to form a triangle, you need to remember that two sides of a triangle added together is always greater than the final side. B is the only selection that does not work for the law, 3 + 5 = 8 which is smaller than 10, so the corrct answer is B.

The value of every variable in the parallelogram is: a = 9 HK = 27.0 GK = 46 G = 63.5°

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.These shapes include squares, rectangles, rhombuses, and rhomboids. All of these shapes have four sides, four corners, and four angles

We know that sides of a parallelogram are parallel and congruent, as opposite angle

According to question  that GA equals HK, as:

46 is equal to 3a plus 19 When we subtract 19 from both sides, we get:

27 x 3a is the result of dividing both sides by 3:

we know that opposite angles in a parallelogram are congruent, we can use a = 9. Since angle H is 56 degrees, angle K must also be 56 degrees. The length of side HK can be determined using the Law of Cosines:

HK2 = GA2 + GK2 - 2(GA)(GK)cos(H) When we substitute the values we are familiar with, we obtain:

After solving the equation we obtain: HK2 = 462 + (3a + 19)2 - 2(46)(3a + 19)cos(56°).

HK2 = 2112 + 9a2 + 342a - 2764cos(56°) HK2 = 2112 + 9(9)2 + 342(9) - 2764cos(56°) HK2  732.4 By taking the square root of both sides, we obtain the following results:

∵ GA = 46, we can use the parallelogram's opposite sides being congruent to determine the length of side GK: HK  27.0

Then, we can use the Law of Cosines to determine the angle G's measurement:

cos(G) = (HK2 + GA2 - GK2) / (2(HK)(GA)) Using the values we are familiar with, we get,

cos(G) = (27.02 + 462 - 462) / (2(27.0)(46)) cos(G)  0.465 Using the inverse cosine, we get the following:

G ≈ 63.5°

Hence, the worth of every variable in the parallelogram is:

a = 9 HK = 27.0 GK = 46 G = 63.5°

Learn more about Quadrilateral here

https://brainly.com/question/29934440

SPJ1

Answer:

Vishwas Gulati

Step-by-step explanation:

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

Learn more about constant of proportionality at:

https://brainly.com/question/27598477

#SPJ1

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

For more such questions on event probability visit:

https://brainly.com/question/30390037

#SPJ8

Answer:

the answer is D

Step-by-step explanation:

i got it right and so would you ;)

The confidence interval for the mean of the population is (40.5, 41.5). Option D is correct.

If the sample size is given to be n >30, then for finding the confidence interval for the mean of the population from this small sample, we use t-statistic.

Then, we get the confidence interval in between the limits;

\(\rm CI= \overline{x} \pm t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}\\\\ CI=41+0.95\times \frac{3}{\sqrt{144} } \\\\ CI= 41+0.7125 \\\\ CI=41.7\\\\ CI=41-0.7125\\\ CI=40.5\)

The confidence interval for the mean of the population is (40.5, 41.5).

Hence,option D is correct.

Learn more about confidence interval refer;

https://brainly.com/question/23008823

#SPJ2

Answer:I think 3 years

Step-by-step explanation:

sorry if im wrong

Answer:

C and E

Step-by-step explanation:

Expressions does not contain any equal or less than greater than sign

So C and E are the right answers

The measure of angle B is given as follows:

m < B = 49.2º.

Two angles are said to be complementary angles when the sum of their measures is of 90º.

The measures are given as follows:

As the angles are complementary, the value of x is obtained as follows:

x + 21 + 4x - 30 = 90

5x - 9 = 90

5x = 99

x = 19.8.

Hence the measure of angle B is obtained as follows:

m < B = 4 x 19.8 - 30

m < B = 49.2º.

The measures are given as follows:

The angles are complementary, and it asks for the measure of angle B.

More can be learned about complementary angles at brainly.com/question/98924

#SPJ1

The domain for f(x) is all real numbers greater than or equal to -4

The equation of the function is given as

g(x) ≥ -2√(1/2x + 2)

For the function to have real values,

We need to set the radical to at least 0

This means that we set 1/2x + 2 to greater than or equal to 0

So, we have the following representation

1/2x + 2 ≥ 0

Subtract 2 from both sides

1/2x ≥ -2

Multiply both sides by 2

x ≥ -4

Hence, the domain is all real numbers that are at least -4

Read more about domain at

brainly.com/question/2264373

#SPJ1

Answer:

\(d=3\ units\)

Step-by-step explanation:

The distance formula is:

\(d = \sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2\)

We can plug in the given coordinate pairs into the formula:

\(d = \sqrt {\left( {5-5\right)^2 + \left( {4-(-1) } \right)^2\)

\(d = \sqrt {\left( {0 } \right)^2 + \left( {-4+1} \right)^2\)

\(d=\sqrt{0+(-3)^2}\)

\(d=\sqrt{0+9}\)

\(d=\sqrt{9}\)

\(d=3\ units\)

Answer:

3 or b

Step-by-step explanation:

EDGE 2022

Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

To learn more about constraint refer to:

https://brainly.com/question/24279865

#SPJ9

Answer:

in my wisdom i think x=60 and y=60

The number of index cards that Paquita has now is 6.

Given that,

Paquita has 63 index cards.

She uses 57 of them for a project.

We have to find the number of cards left with her.

It is clear that, we have to subtract the total number of cards with the number of cards she used for the project.

Total number of index cards that Paquita has= 63

Number of cards she used for the project = 57

Number of cards left with her = 63 - 57

                                                  = 6

Hence the number of cards that Paquita has now is 6.

Learn more about Subtraction here :

https://brainly.com/question/28381779

#SPJ1

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

For more questions on trigonometric form

https://brainly.com/question/31744474

#SPJ8

Answer:

0.062147906

Step-by-step explanation:

log 15 - log 3

=0.062147906

Answer:

A. Nerve cells

Step-by-step explanation:

Answer:

nerve cells

Step-by-step explanation:

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.