A car travels 500 meters the first minute. Each minute after,the car travels 160meters .if this pattern continues ,what is the distance the car travels in 15 minutes?
An=a1+d(n-1)

A. 2740
B. 2900
C. 7660
D. 7160

Answer:

c

Step-by-step explanation:

c

the expression that represents both sin(57°) and cos(33°) is 15/x

To determine the expression that represents both sin(57°) and cos(33°), we need to use the given information about the triangle.

Let's label the angle opposite the perpendicular side as angle A and the angle opposite the base as angle B.

Since the perpendicular is 15 and the base is 17, we can use the Pythagorean theorem to find the length of the hypotenuse (x):

x² = 15² + 17²

x² = 225 + 289

x² = 514

x = √514

Now, let's analyze the angles. The angle A (opposite the perpendicular) is 33°, while the angle B (opposite the base) is 57°.

Therefore, sin(57°) is represented by 15/x, and cos(33°) is represented by 15/x.

Thus, the expression that represents both sin(57°) and cos(33°) is 15/x

Learn more about Pythagorean theorem here

https://brainly.com/question/28361847

#SPJ6

The average value of a continuous function f on the closed interval [a, b] is equal to the definite integral of f over [a, b], divided by the length of the interval [a, b].

Let f(x) be a continuous function on the interval [a, b]. The average value of f on [a, b] is given by:

AVG = (1/(b-a)) * ∫[a, b] f(x) dx

where ∫[a, b] f(x) dx denotes the definite integral of f(x) over [a, b]. The length of the interval [a, b] is given by (b-a). Therefore, the average value of f on [a, b] is the ratio of the definite integral of f over [a, b] to the length of the interval [a, b]. This formula holds for any continuous function f on [a, b].

For more questions like Integral click the link below:

https://brainly.com/question/22008756

#SPJ11

Answer:

C. 15/16

Step-by-step explanation:

A. Divide by 3

B. Divide by 5

C. Can't divide by anything.

D. Divide by 4

Answer:

C

Step-by-step explanation:

21/24 = 7/8

35/40 = 7/8

7/8 ≠ 15/16

14/16 ≠ 15/16

28/32 = 7/8

Answer:

(x + 3)(x - 3)

Step-by-step explanation:

\( {x}^{2} - 9 \\ = {x}^{2} - {3}^{2} \\ = (x + 3)(x - 3)\)

The answer is:5.56 seconds (rounded to the nearest 100th of a second).Given,The equation that describes the height of the rocket, y in feet, as it relates to the time after launch, x in seconds, is as follows: y = − 16x² + 89x+ 50.

To find the time that the rocket will hit the ground, we must set the height of the rocket, y to zero. Therefore:0 = − 16x² + 89x+ 50. Now we must solve for x. There are a number of ways to solve for x. One way is to use the quadratic formula: x = − b ± sqrt(b² − 4ac)/2a,

Where a, b, and c are coefficients in the quadratic equation, ax² + bx + c. In our equation, a = − 16, b = 89, and c = 50. Therefore:x = [ - 89 ± sqrt( 89² - 4 (- 16) (50))] / ( 2 (- 16))x = [ - 89 ± sqrt( 5041 + 3200)] / - 32x = [ - 89 ± sqrt( 8241)] / - 32x = [ - 89 ± 91] / - 32.

There are two solutions for x. One solution is: x = ( - 89 + 91 ) / - 32 = - 0.0625.

The other solution is:x = ( - 89 - 91 ) / - 32 = 5.5625.The time that the rocket will hit the ground is 5.5625 seconds (to the nearest 100th of a second). Therefore, the answer is:5.56 seconds (rounded to the nearest 100th of a second).

For more question on equation

https://brainly.com/question/17145398

#SPJ8

The time that the rocket would hit the ground is 2.95 seconds.

Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the​ ground is related to time by the following quadratic function:

h(t) = -16x² + 89x + 50

Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:

0 = -16x² + 89x + 50

16t² - 89 - 50 = 0

\(t = \frac{-(-80)\; \pm \;\sqrt{(-80)^2 - 4(16)(-50)}}{2(16)}\)

Time, t = (√139)/4

Time, t = 2.95 seconds.

Read more on time here: brainly.com/question/26746473

#SPJ1

Answer:

a

Step-by-step explanation:

raise to five

less than

ten times

Answer:

Step-by-step explanation:

This is called "solving an inequality".

The inequality can flip:

< becomes >

> becomes <

≤ becomes ≥

≥ becomes ≤

This only happens when we multiply or divide both sides by a negative number, or when we swap everything from either sides.

The thing to remember if there are two of the inequalities, we have to do everything to both sides. The goal stays the same. Get the "X" by itself in the middle.

-17 < 5 - 2x <= 9

-5    -5            -5

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

-22 < -2x <= 4

Now we have to divide the -2 on both sides. Remember! Dividing by a negative means we have to FLIP THE SIGNS!

-22 < -2x <= 4

/-2        /-2      /-2

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

11 > x >= -2

And your final answer would be that.

It can also be written this way:

-2 <= x < 11

Answer:

11 > x >= -2

Step-by-step explanation:

Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

heres the answer with work

The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

To know more about solutions:

https://brainly.com/question/30089986

#SPJ4

Sin(300°) = -√3 / 2 .

The cosine model is y = - 7 + 10 · cos (π · x/30 - π).

The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).

Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:

\(y = A \cdot \cos (B\cdot x + C) + D\)     (1)

\(y = A\cdot \sin (B\cdot x + C) + D\)      (2)

Where:

First, we find the amplitude and the midpoint:

A = [3 - (- 17)]/2

A = 10

D = [3 + (- 17)]/2

D = - 7

Now we find the angular phase and the angular frequency for each model:

Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)

- 17 = 10 · cos C - 7     (3)

3 = 10 · cos (30 · B + C) - 7      (4)

By (3):

- 10 = 10 · cos C

cos C = - 1

C = acos(- 1)

C = - π

And by (4):

3 = 10 · cos (30 · B - π) - 7

10 = 10 · cos (30 · B - π)

cos (30 · B - π) = 1

30 · B - π = acos 1

30 · B - π = 0

30 · B = π

B = π/30

The cosine model is y = - 7 + 10 · cos (π · x/30 - π).

Sine model

Obtain the sine model by using trigonometric expressions:

cos θ = sin (θ + π/2)     (5)

By (5):

y = - 7 + 10 · sin (π · x/30 - π + π/2)

y = - 7 + 10 · sin (π · x/30 - π/2)

The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).

To learn more on sinusoidal functions: https://brainly.com/question/12060967

#SPJ1

Answer:

$14.10

Step-by-step explanation:

Answer:

$14.10

Step-by-step explanation:

this is the full answer for you're Q

please give me good

The time taken by the object to hit the ground will be 9 seconds.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that an object is launched at 9.8 meters per second (m/s) from a 308.7-meter tall platform. The function that represents the object's height s at time t seconds after launch is

s(t) = −4.9t²+ 9.8t + 308.7

To find the time taken put the function equal to zero.

−4.9t²+ 9.8t + 308.7 = 0

t² - 2t - 63 = 0

t² - 9t + 7t - 63 = 0

t ( t - 9 ) +7 ( t - 9 ) = 0

( t - 9 ) ( t + 7 ) = 0

t = 9 and -7(ignore)

t = 9 seconds

Therefore, the time taken by the object to hit the ground will be 9 seconds.

To know more about a quadratic equation follow

https://brainly.com/question/2264627

#SPJ2

Answer:

15

Step-by-step explanation:

I got this answer because I just added up all the x's.

1=3

2=2

3=5

4=3

5=2

3+2= 5

5+5=10

10+3=13

13+2=15

Answer:

Amount in account after one year = £241.5

Step-by-step explanation:

Given:

Amount deposit into bank = £230

Rate of yearly interest = 5% Simple interest per year

Number of year = 1 year

Find:

Amount in account after one year

Computation:

Simple interest = Amount deposit x Rate of yearly interest x Number of year

Simple interest = 230 x 5% x 1

Simple interest = 230 x 0.05

Simple interest = £11.5

Amount in account after one year = Amount deposit into bank + Simple interest

Amount in account after one year = 230 + 11.5

Amount in account after one year = £241.5

1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.

2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.

3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.

4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.

The approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6

To find the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches, we will first calculate the surface area (SA) and volume (V) of the ball, and then divide the surface area by the volume.

Step 1: Calculate the surface area (SA) using the formula for the surface area of a sphere:

\(SA = 4 πr^2\)
\(SA = 4 π5^2\)
\(SA = 4 π(25)\)
\(SA=100π\)

Step 2: Calculate the volume (V) using the formula for the volume of a sphere:

\(V = \frac{4}{3} π (r)^{3}\)
\(V = \frac{4}{3} π (5)^{3}\)
\(V = \frac{4}{3} π (125)\)
V = 166.67 π cubic inches

Step 3: Calculate the surface-area-to-volume ratio (SA/V)
\(\frac{SA}{V} = \frac{100}{166.67}\)
\(\frac{SA}{V}=\frac{100}{166.67}\)

\(\frac{SA}{V}= 0.6\)

So the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6. The best answer from the choices provided is A.

To know more about "volume of a sphere" refer here:

https://brainly.com/question/30522025#

#SPJ11

The probability that the tile he pulled has the number 18 is,

⇒ 1 / 3

We have to given that;

Jacob put six numbered tiles into a bag.

And, The tiles are shown below.

19  12  18  17  18  9

Since, He reaches into the bag and pulls out.

Hence, Total number of tiles = 6

So, The probability that the tile he pulled has the number 18 is,

⇒ 2 / 6

Because there are 2 tile for number 18.

⇒ 1 / 3

Thus, The probability that the tile he pulled has the number 18 is,

⇒ 1 / 3

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

(a) To sketch the surface S, we consider the upper half of the sphere of radius 3. b) The boundary curve C is x² + y² = 9. c) the parameterization of C is r(t) = (3cosθ, 3sinθ, 0). d) The line integral is -9sin²θ - 3cosθ. e) The original flux integral is -9π/4.

(a) To sketch the surface S, we consider the upper half of the sphere of radius 3. The orientation is upwards, indicating that the normal vectors are pointing outward. The surface S can be represented as the portion of the sphere with z ≥ 0.

(b) The boundary curve C is the circle of radius 3 in the xy-plane, given by the equation x² + y² = 9. The orientation of C is counter-clockwise when viewed from above.

(c) To parameterize C, we can use polar coordinates. Let's choose θ as the parameter ranging from 0 to 2π. Then, the parameterization of C is:

r(t) = (3cosθ, 3sinθ, 0)

(d) To evaluate the line integral, we need to find the dot product F(r(t)) · r'(t) and simplify it:

F(x, y, z) = (y, -1, 3y)

r(t) = (3cosθ, 3sinθ, 0)

Substituting these values into F and r'(t):

F(r(t)) = (3sinθ, -1, 3(3sinθ))

r'(t) = (-3sinθ, 3cosθ, 0)

Taking the dot product:

F(r(t)) · r'(t) = (3sinθ)(-3sinθ) + (-1)(3cosθ) + (3(3sinθ))(0)

= -9sin²θ - 3cosθ + 0

= -9sin²θ - 3cosθ

(e) To evaluate the line integral, we need to compute:

∫[F(r(t)) - r'(t)] dt

Substituting the expressions for F(r(t)) and r'(t):

∫[-9sin²θ - 3cosθ] dt

To evaluate this integral, we need to specify the limits of integration, which correspond to the range of θ. Since we're considering the full circle, the limits are 0 to 2π:

∫[F(r(t)) - r'(t)] dt = ∫[-9sin²θ - 3cosθ] dθ (from 0 to 2π)

Integrating term by term:

= [-9∫sin²θ dθ] - [3∫cosθ dθ] (from 0 to 2π)

Using trigonometric identities, we have:

= [-9(θ/2 - sin(2θ)/4)] - [3sinθ] (from 0 to 2π)

Plugging in the limits of integration:

= [-9(2π/2 - sin(4π)/4)] - [3sin(2π)] - [-9(0/2 - sin(0)/4)] - [3sin(0)]

Simplifying, we get:

= [-9π + 9π/4] - [0] - [0] - [0]

= -9π/4

Therefore, the line integral is -9π/4.

According to Stokes' Theorem, this tells us that the original flux integral ∬curl F · dS is also equal to -9π/4.

To learn more about curve here:

https://brainly.com/question/32524810

#SPJ4

In a nutshell, pi is the ratio of a circle's diameter to its circumference. It is written as the Greek letter p, or. This ratio will always equal pi, no matter how big the circle is. The value of pi is around 3.14 in decimal notation.

Circumference and diameter of a circle are related by the Pi formula. If the diameter and circumference of a circle are known, it can be used to compute the value of pi. Pi is a Greek letter with the symbol, and in geometry, it represents the proportion of a circle's diameter to its circumference.

The Greek word perimitros, which means "perimeter," begins with the letter pi, which is why [the Welsh mathematician] William Jones gave it the name "pi" in 1706.

A circle is used to calculate the ratio known as pi. The value of pi is given by = Circumference/Diameter if the diameter and circumference of a circle are known.

Therefore pi of this is \(30.3 cm^{2}\) .

To learn more about pi value refer to :

https://brainly.com/question/15962176

#SPJ1

Answer:

196 miles

Step-by-step explanation:

To find the distance that the bus drives, we can use the formula:

distance = rate x time

where rate is the average speed and time is the duration of the trip.

In this case, the average speed of the bus is 56 mph and the duration of the trip is 3 1/2 hours. However, it is easier to work with time in terms of a single unit, so let's convert 3 1/2 hours to 7/2 hours:

3 1/2 hours = (2 x 3) + 1/2 hours = 7/2 hours

Now we can plug in the values into the formula:

distance = rate x time

distance = 56 mph x 7/2 hours

We can simplify by multiplying 56 by 7 and then dividing by 2:

distance = (56 x 7) / 2 = 196 miles

Answer:

y = 5/3x + 9

Step-by-step explanation:

y = 5/3x + b

4 = 5/3(-3) + b

4 = -5 + b

9 = b

Answer:

10 sec

Step-by-step explanation:

Answer:

I already said b in the comment area so I'm just putting it here now

Step-by-step explanation:

(B) The value of the correlation coefficient will move closer to 0.

Therefore, the correct option is (B) The value of the correlation coefficient will move closer to 0.

Know more about Data here:

https://brainly.com/question/19243813

#SPJ2

Answer:

D

Step-by-step explanation:

If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle?

A triangle with two equal sides is said to be an isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

As we know that in an isosceles triangle set of two angles is equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

Learn more about the Isosceles triangle from the link below

brainly.com/question/2456591

#SPJ4

Control limits are based on multiples of the sample statistic's standard deviation, hence the assertion is false that "control limits are based on multiples of the process standard deviation".

A control chart is made up of many different parts. There are two control limitations. The top dashed line represents the upper control limit (UCL), and the bottom dashed line represents the lower control limit (LCL).The solid middle line denotes the statistic's average for the plot.

The horizontal lines known as control limits in a control chart show the upper and lower limits of the acceptable range of results for a process. When plotted data goes over a control limit, a process is out of control and requires management action. The control limits are defined as three standard deviations on either side of the mean.

Visit here to learn more about Standard deviation: https://brainly.com/question/23907081

#SPJ4

Answer:

20.

|3 + 10| = |13| = 13

|3| + |10| = 3 + 10 = 13

Both equal 13.

The student answered 27 out of 30 questions correctly on the history test, achieving a 90% accuracy rate.

To calculate the number of questions the student answered correctly, we can multiply the total number of questions (30) by the percentage of questions answered correctly (90%). The calculation is as follows:

Number of questions answered correctly = Total number of questions × Percentage of questions answered correctly

= 30 × 0.90

= 27

Therefore, the student answered 27 questions correctly on the history test.

To learn more about Percentage  click here :

brainly.com/question/14318030

#SPJ11