PLEASE HELP ME!!
let g be the function given by g (x) = 3x^4 - 8x^3. At what value of x on the closed interval [ -2,2 ] does g have an absolute maximum

Answer:

96 oz

Step-by-step explanation:

There are 16 oz in a pound, so you do 16 * 6 = 96

Answer:

Options B, D and E

Step-by-step explanation:

Given equation is,

-4x + 5y - 12 = 8

-4x + 5y = 20

If a point given in the options lie on the line, point will satisfy the equation.

Option A.

For a point (5, 0),

-4(5) + 5(0) = 20

-20 = 20

False

Therefore, (5, 0) will not lie on the given line.

Option B

For (-2, 2.4)

-4(-2) + 5(2.4) = 20

8 + 12 = 20

20 = 20

True.

Therefore, (-2, 2.4) will lie on the given line

Option C

For (8, 5),

-4(8) + 5(5) = 20

-32 + 25 = 20

-7 = 20

False

Therefore, (8, 5) will not lie on the line.

Option D

For (10, 12)

-4(10) + 5(12) = 20

-40 + 60 = 20

20 = 20

True.

Therefore, (10, 12) will lie on the line.

Option E

For (0, 4)

-4(0) + 5(4) = 20

20 = 20

True.

Therefore, (0, 4) will lie on the line.

Options B, D and E are correct.

Answer:

14% of the seats are empty

Step-by-step explanation:

7/50 = ?/100

50×2=100

so 7×2=?

?=14

14/100=14%

The percent of seats that are empty in the hall of 50 seats with 43 being occupied is; 14%

We are given;

Total number of seats in hall = 50

Number of occupied seats = 43

Number of empty seats = 7

Now, we want to find the percent of seats were empty.

This is gotten by;

% of empty seats = (number of empty seats/total number of seast) * 100%

% of empty seats = (7/50) * 100%

% of empty seats = 14%

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The factor of the expression using linear interpolation is 208.12 and 11,110.41

Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.

Now, The linear interpolation is given as:

1. (F/P,17%,34)

2. (A/G,23%,45)

Now, According to the question:

The factor is then calculated as:

\(Factor=(1+17\)%\()^3^4\)

Express 17% as decimal

\(Factor=(1+0.17)^3^4\)

Take the sum of 1 and 0.17

\(Factor=(1.17)^3^4\)

Evaluate the exponent

Factor = 208.12

2.The factor is then calculated as:

\(Factor=(1+23\)%\()^4^5\)

Express 23% as decimal

\(Factor=(1+0.23)^4^5\)

Take the sum of 1 and 0.23

\(Factor=(1.23)^4^5\)

Evaluate the exponent

Factor = 11,110.41

Hence, the factor of the expression using linear interpolation is 208.12 and 11,110.41

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By applying this pattern to the sixth term, we can see that it is obtained by multiplying 6 by -3.2 and then adding 1 to the result. This results in -18.2.

To find the sixth term of the sequence, we can substitute the value of n as 6 into the given formula:

aₙ = -3.2n + 1

Now, let's substitute n = 6 into the formula:

a₆ = -3.2(6) + 1

Simplifying the expression:

a₆ = -19.2 + 1

a₆ = -18.2

Therefore, the sixth term of the sequence is -18.2.

In the given sequence, the value of each term is obtained by substituting the value of n into the formula -3.2n + 1. The general pattern of the sequence is that each term is 3.2 times the corresponding value of n, with 1 added to it.

By applying this pattern to the sixth term, we can see that it is obtained by multiplying 6 by -3.2 and then adding 1 to the result. This results in -18.2.

It's important to note that the given formula assumes that the sequence starts at n = 1. If the sequence starts at a different value of n, the corresponding term will need to be adjusted accordingly.

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To complete the race in 113 minutes, David must maintain an average speed of a certain number of miles per minute from mile marker 9 to the finish line.

To find David's average speed from mile marker 9 to the finish line, we first need to determine the distance he has to cover in that segment of the race. Since he passed mile marker 9 after 73 minutes, he has 113 - 73 = 40 minutes left to complete the race.

Next, we need to know the distance between mile marker 9 and the finish line. Let's assume that distance is d miles.

To calculate David's average speed, we divide the distance he needs to cover (d miles) by the time remaining (40 minutes):

Average speed = d miles / 40 minutes

Therefore, to complete the race in 113 minutes, David's average speed from mile marker 9 to the finish line must be d miles / 40 minutes.

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From the given triangle ABC, the measure of side BC is 9 yards.

From the given triangle ABC, AB=12 yards and AC=15 yards.

By using Pythagoras theorem, we get

AC²=AB²+BC²

15²=12²+BC²

225=144+BC²

BC²=225-144

BC²=81

BC=√81

BC=9 yards

Therefore, from the given triangle ABC, the measure of side BC is 9 yards.

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Therefore, the area of the region enclosed by one loop of the curve is approximately 3.339 square units.

We can start by sketching the graph of the polar curve r = 5 cos(7θ). It has seven loops, each with a maximum radius of 5 and a minimum radius of -5.

The area enclosed by one loop can be found by integrating 1/2 r^2 dθ from θ = 0 to θ = π/7, since the curve completes one loop in this interval.

So, the area of one loop is:

A = 1/2 ∫[0,π/7] (5 cos(7θ))^2 dθ

= 1/2 ∫[0,π/7] 25 cos^2(7θ) dθ

= 1/2 (25/2) ∫[0,π/7] (cos(27θ) + 1) dθ

= 25/4 [sin(27θ)/14 + θ] from θ = 0 to θ = π/7

= 25/4 [(sin(2π/7)/14 + π/7) - (sin(0)/14 + 0)]

= 25/4 [(sin(2π/7) + 2π/7)/14]

≈ 3.339

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To calculate your earnings for 5 years, we can use the given information that you will receive a 3% raise each year.

In the first year, your earnings are $38,900. For the subsequent years, we can calculate the raise amount and add it to the previous year's earnings. Year 2: $38,900 + 3% of $38,900, Year 3: (Year 2 earnings) + 3% of (Year 2 earnings), Year 4: (Year 3 earnings) + 3% of (Year 3 earnings), Year 5: (Year 4 earnings) + 3% of (Year 4 earnings). Calculating each year's earnings: Year 2: $38,900 + 0.03 * $38,900,  Year 3: (Year 2 earnings) + 0.03 * (Year 2 earnings),  Year 4: (Year 3 earnings) + 0.03 * (Year 3 earnings), Year 5: (Year 4 earnings) + 0.03 * (Year 4 earnings).

Using these calculations, we find the earnings for each year: Year 1: $38,900,  Year 2: $40,067, Year 3: $41,240,  Year 4: $42,422,  Year 5: $43,613.

Therefore, if you work for the company for 5 years, you will earn approximately $43,613.

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Answer:

I believe it's an abtusr triangle

sorry if wring

Answer:

judging from the list of numbers i would pick a

In this scenario, we can use the concept of relative velocity to determine the speed of the car.

The police officer's speed is given as 120 mph, and the rate at which the distance between the helicopter and the car is decreasing is given as 190 mph. We can consider the horizontal motion for simplicity.

Let's denote the speed of the car as Vc. Since the radar detects that the distance between the car and the helicopter is decreasing, the relative velocity between them is the difference between their velocities.

Relative velocity = Speed of the car - Speed of the helicopter

190 mph = Vc - 120 mph

To find the speed of the car, we rearrange the equation:

Vc = 190 mph + 120 mph

Vc = 310 mph

Therefore, the speed of the car, as detected by the radar, is 310 mph.

Answer: y > x + 4

Step-by-step explanation:

First lets find a linear equation for the dividing line, in the form:

y = mx + b

We know that b is 4, since this is the y-intercept

lets use any point on the graph, I'll use (-4, 0):

y = mx + 4

0 = m(-4) + 4

-4 = -4m

m = 1

So the slope is 1. Our completed formula for the line is:

y = x + 4

Since the left side of this graph is shaded, we know it will either be > or ≥. Since the line is also dotted we know it is denoted by a simple ">" sign.

So our completed inequality equation is: y > x + 4

Hope this helped!

Answer:

\(\sf y > x+4\)

Step-by-step explanation:

Choose 2 points on the line:  (-4, 0) and (0, 4)

\(\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-0}{0-(-4)}=1\)

point-slope form of linear equation:  \(\sf y-y_1=m(x-x_1)\)

\(\implies \sf y-0=1(x-(-4))\)

\(\implies \sf y=x+4\)

Solid line : ≤ or ≥

Dashed line: < or >

Therefore as the line is dashed, and the shading is above the line,

\(\implies \sf y > x+4\)

Answer:

60 ft

Step-by-step explanation:

a² + b² = c²

20² + 15² = c²

c = √625

c = 25

total distance = 20 ft + 15 ft + 25 ft = 60 ft

Answer:

The boutique charges $64 for a wallet, and $25 for a belt.

Step-by-step explanation:

We can write two equations using the information we are given. The we solve the system of equations to find the prices.

Let w = price of 1 wallet.

Let b = price of 1 belt.

"Last month, the company sold 25 wallets and 62 belts, for a total of $3,150."

25w + 62b = 3150

"This month, they sold 78 wallets and 19 belts, for a total of $5,467."

78w + 19b = 5467

We now have the following system of 2 equations in 2 unknowns.

25w + 62b = 3150

78w + 19b = 5467

We will use the substitution method.

Solve the first equation for w.

25w + 62b = 3150

25w = -62b + 3150

w = -62/25 b + 126

Now substitute w with -62/25 b + 126 in the second equation, and solve for b.

78w + 19b = 5467

78(-62/25 b + 126) + 19b = 5467

-4836/25 b + 9828 + 19b = 5467

-4836/25 b + 19b = -4361

Multiply both sides by 25.

-4836b + 475b = -109,025

4361b = 109,025

b = 25

Now we substitute 25 for b in the first original equation and solve for w.

25w + 62b = 3150

25w + 62(25) = 3150

25w + 1550 = 3150

25w = 1600

w = 64

Answer: The boutique charges $64 for a wallet, and $25 for a belt.

The total area bounded between the curves f(x)=-2x^2 -1 and g(x)=-x+3 on the interval [0,1] is 13/6 square units.

To determine the total area bounded between the curves f(x)=-2x^2 -1 and g(x)=-x+3 on the interval [0,1], we need to find the area of the region enclosed by these two curves. We can do this by integrating the difference between the two functions with respect to x over the interval [0,1]:

∫[0,1] (g(x) - f(x)) dx

= ∫[0,1] (-x+3 - (-2x^2 -1)) dx

= ∫[0,1] (2x^2 - x + 4) dx

= [2/3 x^3 - 1/2 x^2 + 4x] from 0 to 1

= (2/3 - 1/2 + 4) - 0

= 13/6

Therefore, the total area bounded between the curves f(x)=-2x^2 -1 and g(x)=-x+3 on the interval [0,1] is 13/6 square units.

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Answer:

We know that 6² = 36 , which is very close to 37 . Thus square root of 37 will be very close to 6

Answer:

Step-by-step explanation:

16.50 × m = 99

m = 6

Answer:

To determine its convergence, we can use the comparison test. We consider two series for comparison:

Series 1: $\sum_{k=0}^\infty \frac{k^8}{5(3-6k+3k^6)^2}$

Series 2: $\sum_{k=0}^\infty \frac{k^8 + k^3 + 4k}{5(3-6k+3k^6)^2}$

We notice that Series 2 is always greater than or equal to Series 1.

Next, we use the p-test, which states that if the ratio of consecutive terms in a series approaches a value less than 1, then the series converges. For Series 1, the ratio of consecutive terms approaches 1, which means Series 1 diverges.

Since Series 1, which is smaller than Series 2, diverges, we can conclude that Series 2 also diverges.

Therefore, based on the comparison test, the given series also diverges.

Step-by-step explanation:

If you take the point on the bridge directly beneath the lowest point on the cable to be the origin, then the parabola has equation

\(y = ax^2+bx+10\)

300 ft to either side of the origin, the parabola reaches a value of y = 90, so

\(a(300)^2+b(300)+10 = 90 \implies 4500a+15b = 4\)

\(a(-300)^2+b(-300)+10 = 90 \implies 4500a-15b = 4\)

Adding these together eliminates b and lets you solve for a :

\((4500a+15b)+(4500a-15b)=4+4 \\\\ 9000a = 8 \\\\ a = \dfrac1{1125}\)

Solving for b gives

\(4500\left(\dfrac1{1125}\right)+15b=4 \\\\ 4+15b = 4 \\\\ 15b=0 \\\\ b=0\)

So the parabola's equation is

\(y = \dfrac{x^2}{1125}+10\)

150 ft away from the origin, the cable is at a height y of

\(y = \dfrac{150^2}{1125}+10 = \boxed{30}\)

ft above the bridge.

Solution to the given linear system of differential equations {x′y′==10x−6y9x−5y} is given by x = 6e^{3t} and y = 8e^{2t}.Let's solve the given system of differential equations {x′y′==10x−6y9x−5y} :Given system of differential equations is {x′y′==10x−6y9x−5y}

Differentiating both the sides of the equation w.r.t. "t", we get: x′y′ + xy′′ = 10x′ − 6y′ + 9xy′ − 5y′′ …(1)Putting the value of x′ from the first equation of the system into (1), we get: y′′ − 9y′ + 5y = 0 …(2)This is a linear homogeneous differential equation, whose auxiliary equation is given by: r^2 - 9r + 5 = 0(r - 5)(r - 1) = 0 => r = 5, 1Hence, the general solution to the differential equation (2) is given by: y = c1e^{5t} + c2e^{-t}Let's solve for the constants c1 and c2:Given initial conditions are: x(0) = 6 and y(0) = 8Putting t = 0 in the first equation of the system, we get: x′(0)y′(0) = 10x(0) - 6y(0)=> 6y′(0) = 40 => y′(0) = 20/3Putting t = 0 and y = 8 in the general solution of the differential equation (2), we get:8 = c1 + c2 …(3)Differentiating the general solution and then putting t = 0 and y′ = 20/3, we get:20/3 = 5c1 - c2 …

Solving equations (3) and (4), we get: c1 = 16/3 and c2 = 8/3Hence, the solution to the differential equation (2) is given by: y = (16/3)e^{5t} + (8/3)e^{-t}Putting this value of y in the first equation of the system, we get: x = (6/5)e^{3t}Putting both the values of x and y in the given system of differential equations {x′y′==10x−6y9x−5y}, we can verify that they satisfy the given system of differential equations.Hence, the required solution to the given linear system of differential equations {x′y′==10x−6y9x−5y} is given by x = 6e^{3t} and y = 8e^{2t}.

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The ladder is 13 m long and leans against a window 5 m high, then the ladder leaned to the other side without moving its feet to reach the 12 m high window.

if we imagine a leaning ladder it will look like a right triangle and it will remind us of the Pythagorean theorem. do you remember the pythagorean theorem?

The Pythagorean theorem explains the relationship or relationship between the lengths of the sides of a right triangle.

The Pythagorean theorem reads: "The square of the length of the hypotenuse (hypotenuse) in a right triangle is equal to the sum of the squares of the lengths of the other sides".

in the picture, let's say if the width of the street is a, the height of the window is b and the length of the stairs is c.

in this case we will find the width of the street, namely a, then we use formula a² = c² - b² .

then it will be

b = 12

c = 13

a² = c² - b²

a² = 13² - 12²

a² = 169 - 144

a² = 25

a = 5

The perimeter of the rhombus FGHJ is 20 units

The coordinates are given as:

F = (-2, -2)

G = (-2, 3)

H = (2, 6)

From the question, we understand that vertex J is directly below vertex H.

This means that vertices H and J have the same x coordinate.

So, we have

J = (2, y)

The distance between F and G is 5 units,

So, we have

J = (2, y - 5)

Where

y = 6 i.e. the y coordinate of H

This gives

J = (2, 6 - 5)

Evaluate

J = (2, 1)

See attachment for the graph of the rhombus

In (a), we have:

The distance between F and G is 5 units,

This means that

FG = 5

The side lengths of a rhombus are equal.

So, the perimeter is

P = 4 * FG

This gives

P =4 * 5

Evaluate

P = 20

Hence, the perimeter of the rhombus is 20 units

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Answer:

8

Step-by-step explanation:

Answer:

x^2 +11x +30

Step-by-step explanation:

(x+6) * ( x+5)

The blue area is x^2

pink is 6x

green is 5x

orange is 5*6 = 30

Add them together

x^2 +6x+5x+30

x^2 +11x +30

True. The values that can be entered into a field are determined by the data type of the field.

The data type specifies what type of data can be stored in the field, such as text, numbers, dates, or boolean values. This helps ensure data consistency and accuracy within the field.
Field values that may be entered into a field are determined by the data type of the field. The data type defines the kind of values that can be stored in that specific field, ensuring that the information entered is consistent and accurate.

Data are collected by techniques such as measurement, observation, interrogation or analysis and are often represented as numbers or symbols that can be further processed. Data fields are data stored in unmanaged fields. Test data is data created during the execution of the test. Data analysis uses techniques such as computation, reasoning, discussion, presentation, visualization, or other post-mortem analysis. Before analysis, raw data (or raw data) is usually cleaned: outliers are removed and obvious devices or incorrect input data are corrected.

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Therefore, the correct choice is A, and the expression can be written as: 2 sin 15° cos 15° = sin(30°) = 1/2

The given expression is 2 sin 15° cos 15°. This expression can be written using the double angle formula for sine, which is sin(2θ) = 2 sinθ cosθ. In this case, θ is 15°.
So, 2 sin 15° cos 15° can be rewritten as sin(2 * 15°), which simplifies to sin(30°).
Now, we can find the exact value of sin(30°) using the properties of a 30-60-90 right triangle. In such a triangle, the side ratios are 1:√3:2, where the side opposite the 30° angle has a length of 1, the side opposite the 60° angle has a length of √3, and the hypotenuse has a length of 2. The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse. So, sin(30°) = 1/2.
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Answer:

4.27985 and 14.72015

Step-by-step explanation:

4.27985 x 14.72015 = 63

4.27985 + 14.72015 = 19

Answer:

I believe A is the answer.

Step-by-step explanation:

Looking at the building which is 160 ft tall, the tree is about half that size which is 80 feet.