The water in a pool evaporates at a rate of 16 gallons per week. What interger represents the change in the number of gallons of water in the pool after 24 weeks.



Just answer the question please don’t play with me rn I have 2 hours to submit my goddam assignment.

Answer: y = -f(x+1)

when adding in paratheses, graph moves negatively, and when subtracting it moves positively

the function also flips so it is entirely negated

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Step-by-step explanation:

you can find it using this formula

√ (x2 − x1)2 + (y2 − y1)2

√(-1--73)^2 + (9-30)^2

= 3√527

= 68.8694417

Answer:

(0, 9)

Step-by-step explanation:

y = 9 is the same as (0, 9)

The power series representation of 1/(1 + x⁴) is 1 - x⁴ + x⁸ - x¹² + ..., and the interval of convergence is -1 < x < 1.

To express 1/(1+x⁴) as the sum of a power series, we can use the geometric series formula:

1/(1 - r) = 1 + r + r² + r³ + ...

In this case, we have r = -x⁴.

Substituting into the formula, we get:

1/(1 + x⁴) = 1 + (-x⁴) + (-x⁴)² + (-x⁴)³ + ...

Simplifying:

1/(1 + x⁴) = 1 - x⁴ + x⁸ - x¹²+ ...

The power series representation of 1/(1 + x⁴) is the sum of the terms: 1, -x⁴ + x⁸ - x¹², ...

To find the interval of convergence, we need to determine for which values of x the series converges. For a power series, the interval of convergence is the range of x values for which the series converges.

The convergence of a power series can be determined using the ratio test:

lim (n→∞) |aₙ₊₁ / aₙ|

If the limit is less than 1, the series converges. If the limit is greater than 1 or infinite, the series diverges.

Applying the ratio test to our series:

lim (n→∞) |-x(4(n+1)) / (-x(4n))|

Simplifying:

lim (n→∞) |x⁴| = |x⁴|

For the series to converge, |x⁴| must be less than 1:

|x⁴| < 1

Taking the fourth root:

|x| < 1

Therefore, the interval of convergence for the power series representation of 1/(1 + x⁴) is -1 < x < 1.

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Answer: x^2+3x+5

Step-by-step explanation:

Substitute (x+4) in so that you get f(x)=(x+4)^2-5(x+4)+9. Then expand so you get x^2+8x+16-5x-20+9. Now simplify and you get x^2+3x+5. That is your final answer.

Answer:

1. 8:15

2. 6

3. 32

4. 12.4

Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

An Edgeworth box is used to represent the initial allocation of goods between David and Wilson based on their endowments of onion rings and chips.

An Edgeworth box is a graphical representation used to analyze the allocation of goods between two individuals.

In this case, we consider David and Wilson's initial endowments of onion rings and chips.

To draw the Edgeworth box, we create a rectangular box where the horizontal axis represents the quantity of onion rings (q1) and the vertical axis represents the quantity of chips (q2). The box is divided into four quadrants, representing the allocation of goods to each individual.

Based on their initial endowments, David has 35 onion rings and 10 chips, while Wilson has 5 onion rings and 20 chips.

We label the initial allocation of goods as point "e" within the Edgeworth box, indicating the quantities of onion rings and chips for each person.

By visually representing the initial allocation in the Edgeworth box, we can analyze the potential for trade and the possibility of mutually beneficial exchanges between David and Wilson based on their preferences and utility functions.

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Lines x + 5 = 0 and y = 4x + 4 intersect on a standard (x, y) coordinate plane.

To find the y-coordinate of the point where the two lines intersect.

given lines  are x +5 =0 and y=4x+4

we need to find point of intersection at point of intersection both line will have same point

Let point of intersection be (a,b)

then

a+5 = 0 and b = 4a+4

from 1st equation we have

a = -5

from the 2nd

b = 4a+4

b = 4(-5)+4

b = -20+4

b = -16

Hence y coordinate of point of intersection is -16

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Answer:

she put 131

Step-by-step explanation:

is she took out 45 from 176 she would have put in 131 I'm the account

The gradient of the normal to the curve of h at x =3 is 1/20.

The provided is that h(x) = f(g(x))

Also provided,

g(3) = 7

g'(3) = 4

And f'(7) = -5

Taking,

h(x) = f(g(x))

Differentiating with respect to x,

h'(x) = f('g(x)).g'(x)

h'(x) is the gradient of the curve at x,

Now, putting the value of x = 3,

h'(x) = f('g(3)).g'(3)

We know, g(3) = 7 and g'(x) = 4,

h'(x) = f'(7).4

We know, f'(x) = -5

h'(x) = -5(4)

h'(x) = -20

The slope to the curve at x = 3 is -20.

We know the slope of the normal M1 and the slope at the curve M2 at the same point has their product value as -1,

So,

M1.M2 = -1

M1(-20) = -1

M1 = 1/20

So, the slope of the normal at the curve at x = 3 is 1/20.

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The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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Answer:

12

(If needed explanation ask in the comments! ty)

Hope This Helps! •v•

Answer:

15) 30°

16) 49.5°

Step-by-step explanation:

15) We solve using the Trigonometric function of Sine

sin θ = Opposite/Hypotenuse

Opposite = 12

Hypotenuse = 24

sinθ = 12/24

θ = arc sin(12/24)

= 30°

Approximately = 30°

16)We solve using the Trigonometric function of Cosine

cos θ = Adjacent/Hypotenuse

Adjacent = 13

Hypotenuse = 20

cos θ = 13/20

θ = arc cos (13/20)

= 49.458398126°

Approximately = 49.5°

Answer:

105 Bowls

Step-by-step explanation:

6.825 ÷ 0.065 = 105 Bowls

The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

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The function p(x) = 5x³ + 3 grows at the fastest rate for increasing values of x.

A function is a relation between two sets one is called domain and the other one is range.

Given functions are:

h(x) = 2x

f(x) = 8x² − 3x

g(x) = 19x

p(x) = 5x³ + 3

Here, p(x) = 5x³ + 3 is the only cubic function.

As the degree of the function p(x) is highest among all.

Therefore, this function p(x) grows at the fastest rate for increasing values of x.

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If P(A)=. 75, P(A∪B)=.86, and P(A∩B)=.56, then P(B) is b) 0.67.

The probabilities in this problem are as follows: P(A) is the likelihood of event A occurring, P(A∪B)is the probability of either event A or event B occurring, and P(A∩B) is the probability of events A and B occurring simultaneously.

We must compute the probability of event B occurring, denoted as P(B).

The probability of either event A or event B is stated by the general addition rule of probability.

The likelihood of event B occurring is equal to the sum of the probabilities of events A and B multiplied by the probability of events A and B occurring simultaneously. This rule can be represented as follows:

P(A∪B) = P(A) + P(B) − P(A∩B),

​The likelihood of event B occurring can be calculated using the general addition rule of probability. We must solve the following equation for P(B), as shown below.

0.86 = 0.75 + P(B) − 0.56,

0.86 = 0.19 + P(B),

P(B) = 0.86 − 0.19,

P(B) = 0.67.

​

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Correct question:

If P(A)=. 75, P(A∪B)=.86, and P(A∩B)=.56, then P(B) is equal to what?

a) 0.25

(b) 0.67

(c) 0.56

(d) 0.11

It is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.

To determine the number of participants expected to receive a coupon for sleigh rides, we need to divide the total number of participants (900) by the number of coupon options (3) since each option has an equal chance of being received.

The expected number of participants receiving a coupon for sleigh rides can be calculated as follows:

Total participants / Number of coupon options = Expected number of participants receiving a sleigh ride coupon

900 participants / 3 coupon options = 300 participants.

Therefore, it is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.

It's important to note that this calculation assumes an equal chance of receiving each type of coupon and does not consider any specific preferences or biases that participants may have.

The calculation is based on the assumption of a random distribution of coupons among the participants.

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Answer:

1x27

3x9

Comment me below if I need to have each possible factor.

Step-by-step explanation:

Answer:

Step-by-step explanation:

20

Answer:

  $12

Step-by-step explanation:

You want to know the price increase per 100 meters if the fee for climbing d meters is ...

  f = 110 + 0.12d

The rate of change indicated by the coefficient of d in the equation is 0.12 for each unit of d. Then the amount of change for 100 units of d is ...

  0.12(100) = 12

The price increases by $12 for every 100 meters climbed.

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Answer:

15.13 units

Step-by-step explanation:

Answer: x - 4

The missing dimension of the prism is A

because the volume of the rectangular prism equals the product of the sides, we have:

V = (x - 1)(x - 3)A

but V = x³ - 8x² + 19x - 12

=> x³ - 8x² + 19x - 12 = (x - 1 )(x - 3)A

⇔ x²(x - 1) - 7x(x - 1) + 12(x - 1) = (x - 1)(x - 3)A

⇔ (x² - 7x + 12)(x - 1) = (x - 1)(x - 3)A

⇔ (x² - 3x - 4x + 12)(x - 1) = (x - 1)(x - 3)A

⇔ (x - 3)(x - 4)(x - 1) = (x - 1)(x - 3)A

⇒ A = x - 4

Step-by-step explanation:

Answer: The maximum number of solutions is four.

Step-by-step explanation: To find the number of solutions of a system containing a circle and a parabola, we need to find the points of intersection between the two curves. The points of intersection are the solutions of the system of equations that represent the circle and the parabola. For example, if the circle has the equation \ce {x^2 + y^2 = r^2} x^2 + y^2 = r^2 and the parabola has the equation \ce {y = ax^2 + bx + c} y = ax^2 + bx + c, then we can substitute \ce {y} y from the second equation into the first equation and get a quadratic equation in \ce {x} x:

\ce {x^2 + (ax^2 + bx + c)^2 = r^2} x^2 + (ax^2 + bx + c)^2 = r^2

This equation can have at most two real roots for \ce {x} x, which correspond to at most two points of intersection. However, this is not the maximum number of solutions possible, because we can also substitute \ce {x} x from the second equation into the first equation and get another quadratic equation in \ce {y} y:

\ce {(y - c - bx)^2 / a^2 + y^2 = r^2} (y - c - bx)^2 / a^2 + y^2 = r^2

This equation can also have at most two real roots for \ce {y} y, which correspond to at most two more points of intersection. Therefore, the maximum number of solutions is four, when both quadratic equations have two real roots each. This happens when the circle and the parabola intersect in four distinct points, as shown in this example1:

\ce {x^2 + y^2 = 25} x^2 + y^2 = 25

\ce {y = x^2 - 4x + 4} y = x^2 - 4x + 4

The points of intersection are (5, 0), (-5, 0), (3, 4), and (-3, 4).

Hope this helps, and have a great day! =)

Answer:

y = 33.94 mm

x = 19.80 mm

Step-by-step explanation:

Because AC = CB, then ∠ABC = 45°

cos ∠ABC = 24/y

cos 45° = 0.7071 = 24/y

y = 33.94 mm

EF/BC = x/y

14/24 = x/33.94

24x = 475.16

x = 19.80 mm

Answer:

The slope is -1

Step-by-step explanation:

Use the formula m=y2-y1/x2-x1