please help <3 it would mean the world to me

The average velocity of the projectile from 1.2 seconds to 13 seconds is approximately 419.40 feet per second.

To find the average velocity of the projectile, we need to calculate the change in height over the given time interval and divide it by the duration. The height of the projectile at time t is given by the function f(t) = 162 + 432t + 4.

First, we need to find the height at the initial time, t = 1.2 seconds, by substituting t = 1.2 into the function: f(1.2) = 162 + 432(1.2) + 4 = 622.4 feet.

Next, we find the height at the final time, t = 13 seconds, using the same process: f(13) = 162 + 432(13) + 4 = 5882 feet.

The change in height over the time interval from 1.2 seconds to 13 seconds is the difference between the final and initial heights: 5882 - 622.4 = 5259.6 feet.

To calculate the average velocity, we divide the change in height by the duration: 5259.6 / (13 - 1.2) = 419.40 feet per second.

Therefore, the average velocity of the projectile from 1.2 seconds to 13 seconds is approximately 419.40 feet per second.

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Answer:

Step-by-step explanation:

Just a simple manipulation question: rearrange for so all but the (y) is on the other side.

\(4x+3y=7\\ 3y=7-4x\\ y=7-4x/3\)

Answer:

5

Step-by-step explanation:

11x+x=60

12x=60

x=60/12

x=5

Answer:

The slope is 4/5 and the y intercept is -3

Step-by-step explanation:

The equation is in slope intercept form

y= mx+b where m is the slope and b is the y intercept

y = 4/5x -3

The slope is 4/5 and the y intercept is -3

The possible outputs of the function for different values of [x] are given below.

Given is the following function -

h(x) = 32x - 1

We can write the output for the given function as -

[x]            h(x) = 32x - 1                   h(x)                             

1               {32 x 1 - 1 = 31}                   31

2              {32 x 2 - 1 = 63}                 63  

3              {32 x 3 - 1 = 95}                 95

4              {32 x 4 - 1 = 127}                127

Therefore, the possible outputs of the function for different values of [x] are given above.

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Answer:

Start with the parent function y=1/x^2.

Add 3 to x in the denominator, because the graph is shifted left 3. Add 1 to the fraction, because the graph is shifted up 1 unit.

Step-by-step explanation:

When a function is transformed, it means the function is either rotated, dilated, rotated or translated.

The equation of the function whose graph is sketched is:

\(f(x) = \frac{1}{(x + 3)^2} + 1\)

The parent function is an inverse function of the form:

\(y = \frac 1{x^2}\)

The parent function is shifted in two ways.

When a function is shifted to the left, the rule is:

\((x,y) \to (x + h,y)\)

Where:

\(h \to\) number of units.

So, we have:

\((x,y) \to (x + 3,y)\)

The function becomes

\(y' = \frac{1}{(x + 3)^2}\)

When a function is shifted up, the rule is:

\((x,y) \to (x ,y+b)\)

Where:

\(b \to\) number of units.

So, we have:

\((x,y) \to (x ,y+1)\)

The function becomes

\(y'' = \frac{1}{(x + 3)^2} + 1\)

So, the graph of the function in the given graph (see attachment) is:

\(f(x) = \frac{1}{(x + 3)^2} + 1\)

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We estimate that there are approximately 43 horse beads in the bag.

We can use the method of proportion to estimate how many horse beads are in the bag. We know that Neil randomly selected 14 beads out of a total of 200 beads, which represents 7% of the total.

We can assume that the proportion of horse beads in the bag is the same as the proportion of horse beads in the sample of 14 beads that Neil selected.

Out of the 14 beads that Neil selected, 3 were horse beads. Therefore, we can estimate that the proportion of horse beads in the bag is:

3/14 = 0.214

To estimate how many horse beads are in the bag, we can multiply the proportion by the total number of beads:

0.214 * 200 = 42.8

Rounding to the nearest whole number, we estimate that there are approximately 43 horse beads in the bag.

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Answer: 400 points

Step-by-step explanation:

500 x 80 =  40,000

40,000/100 = 400 points

The sum of the exterior angle of the pentagon is 360 degrees.

The polygon above is a pentagon. A pentagon is a polygon with 5 sides.

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The sum of the exterior angles of a polygon is 360°.

Therefore, the sum of the measure of the exterior angles of the pentagon as shown is 360 degrees.

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Answer:

5 dollars

Step-by-step explanation:

Answer:

The price of an adult ticket is $5

Step-by-step explanation:

5*5=25

31-25=6

4*5=20

62-20=42

42÷7=6

The total area of the shaded region is 352 square feet (352ft²).The area of the shaded region is calculated by adding the area of the individual shapes within the region.

A right triangle is a triangle with one right angle, which is an angle that measures 90 degrees. The other two angles in a right triangle must measure less than 90 degrees and together must add up to 90 degrees.

The first shape is a right triangle with sides of 25ft, 8ft, and 8ft. The area of this triangle is calculated using the formula A = (1/2)bh, where b is the base and h is the height. In this case, the base is 25ft and the height is 8ft, so the area of the triangle is 80 square feet (80ft²).

The second shape is a rectangle with sides of 8ft and 8ft. The area of this rectangle is 64 square feet (64ft²).

The third shape is a square with sides of 8ft. The area of this square is 64 square feet (64ft²).

The fourth shape is a rectangle with sides of 8ft and 18ft. The area of this rectangle is 144 square feet (144ft²).

The total area of the shaded region is 352 square feet (352ft²). This is calculated by adding the area of each individual shape: 80ft² + 64ft² + 64ft² + 144ft² = 352ft².

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The area of the shaded region is 322 ft² which is the calculated by subtracting the area of squares from area of rectangle.

Area is a measure of the size of a two-dimensional surface. It is calculated by multiplying the length of a surface by its width.

We can calculate the area of the shaded region by subtracting the area of the two squares from the area of the rectangle.

The area of the rectangle is given by the formula A = l x w, where l and w are the length and width of the rectangle respectively.

The area of the rectangle=

A= 25 x 18

A= 450 ft²

The area of each square is given by the formula A = s², where s is the length of one side.

The area of each square:

A= 8²

A= 64 ft²

Now, the area of the shaded region=

Area of rectangle - (Area of square 1 + Area of square 2).

A= 450 - (64 + 64)

A= 450 - 128

A= 322 ft²

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The complete question is as follows:

The mass of the thin bar is \((\pi/2) - 1\).

To find the mass of the thin bar with the given density function, we need to integrate the density function over the length of the bar.

The length of the bar is given as L = SA - SX = \(\pi/2 - 0 = \pi/2.\)

So, the mass of the bar is given by the integral:

M = ∫(SX to SA) p(x) dx

Substituting the given density function, we get:

M = ∫(0 to \(\pi/2\)) (1 + sin x) dx

Using integration rules, we can integrate this as follows:

M = [x - cos x] from 0 to \(\pi/2\)

M = \((\pi/2) - cos(\pi/2) - 0 + cos(0)\)

\(M = (\pi/2) - 1\)

Therefore, the mass of the thin bar is \((\pi/2) - 1.\)

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\( = \frac{1}{9} \times 9\\\)

\( = \frac{9}{9} \\\)

\( = \frac{1}{1} \\\)

\( = 1\\\)

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The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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In this scenario, we have a budget constraint and an indifference curve representing preferences. By analyzing the given information, we can determine the optimal bundle of goods and how it changes with a decrease in income.

a. The budget constraint can be represented graphically. The X-intercept is found by setting Y = 0, giving us X = I/Px = 100/2 = 50. The Y-intercept is found by setting X = 0, giving us Y = I/Py = 100/4 = 25. The slope of the budget constraint is determined by the ratio of the prices, giving us -Px/Py = -2/4 = -1/2. Thus, the budget constraint line can be drawn connecting the X and Y intercepts with a slope of -1/2.

b. The optimal bundle of X and Y can be found by maximizing utility subject to the budget constraint. Given the marginal rate of substitution (MRS) of Y/(2X), we set the MRS equal to the slope of the budget constraint, -Px/Py = -1/2. Solving for X and Y, we can find the optimal bundle.

c. Labeling the optimal bundle found in part b as "A," we can draw an indifference curve passing through this point on the graph. The indifference curve represents the combinations of X and Y that provide the same level of utility.

d. If the income decreases to $80, the new budget constraint can be drawn with the same slope but a lower intercept. We can find the new optimal bundle, labeled "B," by maximizing utility subject to the new budget constraint. Similarly, we can draw another indifference curve passing through point B to represent the new optimal bundle.

If X is a normal good and Y is an inferior good, a decrease in income will generally lead to a decrease in the optimal amount of Y and an increase in the optimal amount of X. This is because as income decreases, the demand for inferior goods like Y tends to decrease, while the demand for normal goods like X remains relatively stable or may even increase. The specific changes in the optimal amounts of X and Y would depend on the specific preferences and income elasticity of the goods.

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Answer:

x= -2; x=0

Step-by-step explanation:

-5+6|2x+2|=7

6|2x+2|=12

|2x+2|=2

x= -2; x=0

Answer:

16.) 126=(5+x)+(10+x)

17.) It states that the width added x feet and so did the width

Step-by-step explanation:

On the rectangle, you can see that they added x feet to both sides.

I hope this helps. Let me know if you have any questions!

Answer:

The symbol 'n,' represents the total number of individuals or observations in the sample.

Answer:

The principal quantum number, n, describes the energy of an electron and the most probable distance of the electron from the nucleus. In other words, it refers to the size of the orbital and the energy level an electron is placed in. The number of subshells, or l, describes the shape of the orbital.

Answer:

y = \(\frac{1}{4}\) x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-4}\) = \(\frac{1}{4}\) , then

y = \(\frac{1}{4}\) x + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y = \(\frac{1}{4}\) x + 6 ← equation of perpendicular line

Answer:

Step-by-step explanation:

height of post ÷ length of shadow = 2/10 = ⅕

height of tower is ⅕ the length of its shadow.

⅕×125 = 25

The tower is 25 feet tall

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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N is congruent to k+1 modulo 3, and since k+1 is not divisible by 3, N is not divisible by 3. Hence, we have shown that if the sum of the digits of a natural number is divisible by 3, then the number itself is not divisible by 3. This can be answered by the concept of Polynomial.

Suppose we have a natural number N = d_k * 10^k + d_{k-1} * 10^{k-1} + … + d_1 * 10 + d_0, where each d_i is a digit between 0 and 9 inclusive, and k is the number of digits in N minus 1. We can recognize N as the evaluation of the polynomial f(x) = d_k * x^k + d_{k-1} * x^{k-1} + ... + d_1 * x + d_0, evaluated at x = 10. Note that f(x) has integer coefficients and degree k, and thus satisfies the conditions of the theorem.

For example, let's consider a natural number N represented as a polynomial f(x) = a_nx^n + a_(n-1)x^(n-1) + … + a_0. To determine if N is divisible by 3, we can check if f(a) ≡ f(b) (mod 3) for integer values of a and b. Similarly, to determine if N is divisible by 9, we can check if f(a) ≡ f(b) (mod 9) for integer values of a and b. Using this theorem, we can deduce divisibility criteria for natural numbers by 3 or 9.

Now, suppose the sum of the digits of N is divisible by 3. Then we can write N = 3m for some integer m. Note that 10 is congruent to 1 modulo 3, so by the theorem, we have f(10) is congruent to f(1) modulo 3. But f(10) = N and f(1) = k+1, since the sum of the coefficients of f(x) is equal to k+1.

Therefore, N is congruent to k+1 modulo 3, and since k+1 is not divisible by 3, N is not divisible by 3. Hence, we have shown that if the sum of the digits of a natural number is divisible by 3, then the number itself is not divisible by 3.

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Using the value of x in tan θ = y/x, we can find the value of tan θ which is -12/5.

Given that P(x, y) denote the point where the terminal side of an angle θ meets the unit circle and P is in Quadrant IV and x = 5/13.

We need to find the value of tan θ.

Tan θ = y/x

As P is in Quadrant IV, x is positive and y is negative.

Thus, \(y = -\sqrt{(1-x^2)}\).

\(tan\theta = y/x\\= -\sqrt{(1-x^2)/5/13} \\= -13\sqrt{(1-x^2)/5} \\= -12/5\).

Hence, the value of tan θ is option (c) -12/5.

The given problem can be solved using the concept of trigonometry and geometry.

First, we need to understand the unit circle and its quadrants.

Unit circle is a circle of radius 1 centered at the origin of a coordinate plane.

It is used to understand the properties of angles in trigonometry.

It has 4 quadrants,

Quadrant I, II, III, and IV which are numbered in an anti-clockwise direction from 1 to 4.

The coordinates of P are given as \((5/13, -\sqrt{1-x^2})\).

As x is positive and y is negative, it is in the Quadrant IV.

Using the value of x in tan θ = y/x, we can find the value of tan θ which is -12/5.

Therefore, option (c) -12/5 is the correct answer.

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Answer:

There are no questions below .

Answer:

Step-by-step explanation:

Let the length of the smaller piece be l inches. Then the larger piece is 3*l = 3l inches. But l + 3l = 72. Hence, 4l =72. l= 72/4 = 18. Therefore, the smaller piece has a length of 18 inches.