How many seconds does the ball reach its maximum height using the equation
h(t)= -0.2t^2 + 2t

A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

To estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.

σ = population standard deviation ($800 in this case)

E = margin of error ($100 in this case)

Plugging in the values, we get:

n = (2.33 * 800 / 100)²

n ≈ 432.64

Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

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The solution of the trigonometric equation on the interval (, 360) is

A trigonometric equation is an equation that contains trigonometric ratios.

Given the trigonometric equation

2sinx = 1 - cosx, we proceed to solve for x as follows.

Since 2sinx = 1 - cosx

Using sin²x = 1 - cos²x

⇒ sinx = √(1 - cos²x )

Substituting this into the equation, we have that

2sinx = 1 - cosx

2√(1 - cos²x ) = 1 - cosx

Squaring both sides, we have that

[2√(1 - cos²x )]² = (1 - cosx)²

4(1 - cos²x ) = (1 - cosx)²

4 - 4cos²x = 1 - 2cosx + cos²x

Collecting similar terms, we have that

1 - 4 - 2cosx + 4cos²x + cos²x = 0

- 3 - 2cosx + 5cos²x = 0

Re-arranging the equation, we have that

5cos²x - 2cosx - 3 = 0

Let cosx = y

So, we have that

5y² - 2y - 3 = 0

Factorizing, we have that

5y² - 2y - 3 = 0

5y² - 5y + 3y - 3 = 0

5y(y - 1) + 3(y - 1) = 0

(5y + 3)(y - 1) = 0

⇒ 5y + 3 = 0 or y - 1 = 0

⇒ 5y = -3 or y = 1

⇒ y = -3/5 or y = 1

Since y = cosx, we have that

cosx = -3/5 or cosx = 1

cos(180° - x) = 3/5 or cos(270° - x) = 3/5 or cosx = 1

Taking inverse cosine, we have that

180° - x = cos⁻¹(3/5) or 270° - x = cos⁻¹(3/5) or x = cos⁻¹(1)

180° - x = 53.13° or 270° - x = 53.13° or x = 90°

x = 180° - 53.13° or x = 270° - 53.13° or x = 90°

x = 126.87° or x = 216.87 or x = 90°

So, the solution is

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Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, about 650 units of plastic will be produced. (Option C)

This is because, when the market forces are left to play out, competition drives efficiency upwards, which enable suppliers to produce at lower price thus offering consumers more quantity demanded for lower prices.

Hence, without government intervention, the unit produced will be 650 at the price of 7.

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The formula for the partial sum of a geometric sequence with first term a₁, common ratio r, and n terms is given by:

Sₙ = a₁(1 - rⁿ)/(1 - r)

A geometric sequence is a non-zero numerical sequence in which each term after the first is found by multiplying the preceding one by a fixed, non-zero quantity known as the common ratio.

In the formula, Sₙ is the sum of the first n terms of the sequence.

Alternatively, the formula can be expressed as:

Sₙ = (a₁(rⁿ - 1))/(r - 1)

Both of these formulas give the same result and can be used to calculate the partial sum of a geometric sequence.

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The equation that models the balance y after t months is y = -75t + 1,500

To write an equation that models the balance y after t months, we need to use the given information to determine the rate at which the balance is decreasing. We can use the formula for a straight line, y = mx + b, where m is the slope and b is the y-intercept.

We can start by finding the change in the balance over the three-month period from four to seven months after the purchase:

Change in balance = $1,200 - $975 = $225

The rate of change can be calculated by dividing the change in the balance by the number of months:

Rate of change = $225 / 3 months = $75 per month

We can use this rate of change as the slope of the equation:

y = -75t + b

To find the y-intercept b, we can use the fact that the balance was $1,200 four months after the purchase:

1,200 = -75(4) + b

b = 1,500

Therefore, the equation that models the balance y after t months is:

y = -75t + 1,500

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Answer:

23098376=890754730.0%

Step-by-step explanation:

Standard form of circle with    center  (h.k) and radius r :

( x-h)^2 + (y-k)^2 = r^2

FOr the data given:

(x + 4)^2  + ( y-3)^2 = 81             (81 is the radius, 9, squared)

Answer:

13in :)

Step-by-step explanation:

KJASJDAJK its oki! The formula for the area of a square is Side x Side= Area, meaning you can just square root the area (since its a square all sides should be the same length) sqrt of 169 would give you 13!

The value of the variable x is -4

First, we need to know that line segments are described as a section of a line that is bounded by two points or connecting two points.

From the information given, we have that;

Line SA and SD are equal segments

But  SA =3x+19 and SD=5x-11

Now, equate the expressions since they are of equal lengths, we have;

3x + 19 = 5x - 11

collect the like terms

3x - 5x = -11 + 19

Add or subtract the like terms, we have;

-2x = 8

Divide both sides by the coefficient, we have;

x = -4

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The appropriate diagram to illustrate the cube is given.

A cube is a three-dimensional shape featureing six equal square faces, with its edges and vertices being of congruent length. It counts as one of the five platonic solids distinguished by all of its features having matching sizes.

The cube can be perceived as a special instance of a rectangular parallelepiped where all six are perfectly square in shape. In order to calculate the volume of such an ordinary cube, the number of its edge needs to be multiplied by itself thrice (V = a³).

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The matrix after the row operation is given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

The row operation is given as follows:

Division by 7 = multiplication by 1/7, as the element at the desired position is of 7.

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

We want to have element 1 into row 1 and column 1, that is, the element of 7 at row 1 and column 1 of the matrix must assume a value of -1.

An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:

7/k = 1

k = 7.

Dividing every element of the first row by 7, the resulting matrix is then given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

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The single transformation that maps shape A to shape B is: Reflection about the line x = -2

There are different ways of carrying out transformation of objects and they are:

Reflection whereby  all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection

Rotation whereby all points are rotated about a point.

Dilation where the object is reduced or increased by a scale factor.

Translation where the object is moved from one point to another.

Looking at the given image, we can tell that this denotes a reflection because it is the exact same shape and looks like a mirror image which was reflected over the line x = -2

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Our table looks like this:
x | y
--|--
1 | 3
2 | 6
-2 | -6
0 | 0

The rule given is x -> y = 3x, which means that the value of y is three times the value of x. To fill in the table with at least 4 points, we can choose any four values of x and calculate their corresponding values of y using the rule.

Let's start with x = 1. Plugging this value into the rule, we get y = 3(1) = 3. So the first point in our table is (1, 3).

Next, let's try x = 2. Using the rule, we get y = 3(2) = 6. So the second point in our table is (2, 6).

Moving on, let's choose x = -2. Using the rule, we get y = 3(-2) = -6. So the third point in our table is (-2, -6).

Lastly, let's try x = 0. Using the rule, we get y = 3(0) = 0. So the fourth point in our table is (0, 0).
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Answer:

Step-by-step explanation:

The formula for the volume of a triangular prism is:

V = Bh, where B is the base area and h is the height of the prism.

Substituting the given values, we get:

V = 37.4 x 5

V = 187 yd^3

Therefore, the volume of the ramp is 187 cubic yards.

Answer: 0.12

Step-by-step explanation:

just divide whatever is under 5 with the total amount of frequency

so then you do 12/100 which is 0.12

In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.

The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.

Rounded to the nearest hundredth, this is approximately 10.68 units.

To find the width of the suitcase, we need to use the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

Given the volume of the suitcase as 8,556 cubic inches, the length as 32 inches, and the height as 15.5 inches, we can write the equation:

8556 = 32 × w × 15.5

Simplifying this equation, we can divide both sides by the product of 32 and 15.5:

8556 ÷ (32 × 15.5) = w

Solving for w, we get:

w ≈ 16.50 inches

Therefore, the width of the suitcase is approximately 16.50 inches.

Answer:

160

Step-by-step explanation:

The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp)

Adjacent = 80

Hypotenuse = x

therefore, cos(60) = 80/x

1/2 = 80/x

x = 80 x 2 = 160

There are 29 degrees of freedom for this repeated-measures t-test.

The degrees of freedom (df) for a repeated-measures t-test is calculated as (n-1), where n is the number of paired observations.

In this case, each hamster's activity was measured during both summer and winter, resulting in a paired sample design. Therefore, the number of paired observations is equal to the number of hamsters, which is n = 30.

Hence, the degrees of freedom for this repeated-measures t-test is:

df = n - 1 = 30 - 1 = 29

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Answer:

CA - 144

AD - 98

ABD - 49

BC - 134

C - unsure

Step-by-step explanation:

When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.

The expression 2w⁻²z⁰ can be simplified as follows:

2w⁻²z⁰ = 2/w² * z⁰

Since z⁰ = 1 for any non-zero value of z, we can simplify further:

2w⁻²z⁰ = 2/w² * 1

Now we can substitute w = 10 into the expression:

2(10)⁻² * 1 = 2/100 = 1/50

In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.

So, correct option is A.

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The value of p in the expression is 45

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5

this means,

a+5-5 = 2-5

a = 2-5

a = -3

Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,

p-42+42 = 3+42

p = 3+42

p = 45

therefore the value of p is 45

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(a) The shape of sampling distribution is not too close to 0 or 1 (b) The mean of standard deviation = 0.033

(c) [tex]P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)[/tex]

(a) The sampling distribution of p-p is approximately normal by the Central Limit Theorem because both sample sizes are large enough (n₁ = n₂ = 240) and the sample proportions of orange candies are not too close to 0 or 1.

(b) The mean of the sampling distribution of p-p is equal to the difference between the population proportions, which is 0.20 - 0.23 = -0.03. The standard deviation of the sampling distribution of p-p is given by:

sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]

= sqrt[(0.200.80/240) + (0.230.77/240)]

= 0.033

The standard deviation represents the amount of variation we expect to see in the differences between sample proportions of orange candies from multiple random samples of the same size.

(c) To find P(P-P>0), we need to standardize the difference between the sample proportions and the population difference and then find the probability that the standardized difference is greater than 0. That is:

(P-P - (p₁ - p₂)) / sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]

= (P-P - (-0.03)) / 0.033

= (P-P + 0.03) / 0.033

Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is greater than this value. For example, if we use a calculator, we get:

P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)

where Z is a standard normal variable. The probability is approximately 0.18. This means that if we take many random samples of 240 M&M's milk chocolate candies and 240 peanut M&M's and calculate the difference between the sample proportions of orange candies, about 18% of the time we would expect to see a difference of 0.03 or greater (favoring M&M's milk chocolate candies).

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Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].

In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.

Here,

The linear approximation of sin⁻¹(x) at a = 0 is given by:

sin⁻¹(x) ≈ x

To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:

d/dx(sin⁻¹(x)) = 1/√(1-x²)

d/dx(sin⁻¹(x))|x=0 = 1

Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.

To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.

Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:

-0.099 ≤ x ≤ 0.099

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Answer:

Step-by-step explanation:

c

The list that shows all the combinations is given as follows:

{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.

The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.

This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The options are given as follows:

The total number of options is given as follows:

3 x 2 = 6.

Hence the list is:

{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.

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The area of the shaded part is 42.14 ft² .

Area of the shaded part of the figure = area of square - area of quarter circle

Area of shaded part of the figure = s² - 1/4πr²

Where s = 14 ft and r = 14 ft

Substitute into the formula:

Area of shaded part = 14² - 1/4(3.14)(14²)

                                  = 42.14 ft²

Therefore, the area of the shaded part is: 42.14 ft² .

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