The water level of certain body of water is changing at a rate of W(t) = 1/2cos(3 - t/2) inches per hour; where represents hours since 12ampart c: use your calculator to evaluate your integral from part b. explain the meaning of the answer in terms of the context. (3 points)

The value of Standard Deviation is needed to calculate the minimum sample size accurately. If you have the value of Standard Deviation, you can substitute it into the equation to find the minimum sample size.

To determine the minimum number of CEOs that the journalist must survey to be within $50,000 of the true average annual salary, we need to consider the margin of error in the confidence interval.

The margin of error is determined by the z-value associated with the desired confidence level and the standard deviation of the population.

Given that the z-value associated with a 95% confidence interval is 1.96, we can use the following formula to calculate the margin of error:

Margin of Error = z-value * (Standard Deviation / sqrt(sample size))

To be within $50,000 of the true average annual salary, we can set up the equation:

$50,000 = 1.96 * (Standard Deviation / sqrt(sample size))

Solving for the sample size (number of CEOs):

sqrt(sample size) = (1.96 * Standard Deviation) / $50,000

sample size = (($50,000)^2 * (Standard Deviation)^2) / (1.96)^2

The value of Standard Deviation is needed to calculate the minimum sample size accurately. If you have the value of Standard Deviation, you can substitute it into the equation to find the minimum sample size.

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Answer:8.24

Step-by-step explanation:

When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3

The product of 6 and the square of a number

Consider the number as x

Then the product of 6 and the square of a number = \(6x^2\)

The product of 6 and the square of a number is increased by 5 times the number, the result is 4

Then the equation will be

\(6x^2\) + 5x = 4

Move 4 to the left hand side of the equation

\(6x^2\) + 5x - 4 = 0

We have to solve the quadratic equation

Split the middle terms

\(6x^2\) + 8x - 3x -4 = 0

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

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

Then the value of x will be

2x- 1 = 0

2x = 1

x = 1/2

Similarly

3x+4 = 0

3x = -4

x = -4/3

Hence, when the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3

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The amplitude of the graph of h(x) = (f+g)(x) is 2.

To find the amplitude of the graph of the function h(x) = (f+g)(x), we need to first determine the individual amplitudes of f(x) and g(x), and then take the maximum value between them.

The amplitude of a sinusoidal function is the absolute value of the coefficient multiplying the trigonometric function. In this case, the amplitude of f(x) is 2, and the amplitude of g(x) is 1.

Now, for the function h(x) = (f+g)(x), we add the two functions f(x) and g(x) together. Since we are interested in the maximum amplitude, we take the larger amplitude between the two functions, which is 2.

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The calculated value of x in the figures a and b is 12 units

From the question, we have the following parameters that can be used in our computation:

The similar triangles

Where

Ratio =  1 : 3

Figure a is smaller than figure b

So, we have

a : b = 1 ; 3

Figure a to the right has a 4

So, we have

4 : x = 1 ; 3

This means that

x/4 = 3/1

So, we have

x = 4 * 3/1

Evaluate

x = 12

Hence, the value of x is 12

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Question

Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:3

Both figures are triangles

Figure a is smaller than figure b

Figure a to the right has a 4

Figure b to the right has a x

This is an algebraic word problem and it has a solution of $120 which is Jonathan's pocket money for each month.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent Jonathan's pocket money for each month with the letter x so that;

In July he saved: x - $80 and in August he saved x - $72

Since his savings increased by 20%, then;

x - $72 + x - $80 = (20/100)(x - $80)

2x - $252 = (1/5)(x - $80)

5(2x - $252) = x - $80 {cross multiplication}

10x - $1260 = x - $80

10x - x = $1260 - $80 {collect like terms}

9x = $1080

x = $1080/9 {divide through by 9}

x = $120.

Therefore, the agebraic word problem have a solution of $120 which is Jonathan's pocket money for each month.

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The information is not enough to prove that triangles DEF and OPQ are congruent through SAS, as we need two equal side lengths and one angle measure.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The parameters given for this problem are given as follows:

As we are given only one side, instead of the two sides needed, we have that the information given is not enough to prove that the two triangles are congruent by the SAS congruence theorem.

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The exact x-coordinate of the point  is frac{1163}{291}6

The curve is given by {x = t² + 1, y = t² - t}.

Let's find dy/dx in terms of t as follows:

frac{dy}{dx} = frac{dy/dt}{dx/dt} = frac{(2t - 1)}{(2t)} = 1 - frac{1}{2t}

Therefore, when dy/dx = 27, we have:

1 - frac{1}{2t} = 27

Rightarrow 2t - 1 = frac{2}{27}

Rightarrow t = frac{29}{54}

The x-coordinate is given by x = t² + 1, therefore, we have:

x = left(frac{29}{54}right)^2 + 1

= frac{1163}{2916}

Hence, the exact x-coordinate of the point on the curve where the tangent line has slope 27 is frac{1163}{291}6

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a). We have proved all the given conditions.

b). It is true that condition 3 holds for all regular languages L1 and L2.

(a) Regular languages L1 and L2 can be suggested as follows:

Let \(L_1={0^{(n+1)} | n\geq 0}\)

and

\(L_2={1^{(n+1)} | n\geq 0}\)

We have to prove three conditions:1. L1 ⊈ L2:

The given languages L1 and L2 both are regular but L1 does not contain any string that starts with 1.

Therefore, L1 and L2 are distinct.2. L2  L1:

The given languages L1 and L2 both are regular but L2 does not contain any string that starts with 0.

Therefore, L2 and L1 are distinct.3. (L1 ∪ L2)* = L1* ∪ L2*:

For proving this condition, we need to prove two things:

First, we need to prove that (L1 ∪ L2)* ⊆ L1* ∪ L2*.

It is clear that every string in L1* or L2* belongs to (L1 ∪ L2)*.

Thus, we have L1* ⊆ (L1 ∪ L2)* and L2* ⊆ (L1 ∪ L2)*.

Therefore, L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Second, we need to prove that L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Every string that belongs to L1* or L2* also belongs to (L1 ∪ L2)*.

Thus, we have L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Therefore, (L1 ∪ L2)* = L1* ∪ L2*.

Therefore, we have proved all the given conditions.

(b)It is true that condition 3 holds for all regular languages L1 and L2.

This can be proved by using the fact that the union of regular languages is also a regular language and the Kleene star of a regular language is also a regular language.

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Answer:

15%

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

\(\frac{99}{660} =\\\\\frac{3}{20} =\\\\\frac{15}{100}\)

99 is 15% of 660

Answer:

It's A and the answer is 4^x

Step-by-step explanation:

The exponential function that models the data is f(x) = \(4^x\).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

We have a table.

The given function is not a linear because the difference of two consecutive term is not constant.

Now, the ratio

1/(1/12)= 12

12/1= 12

144/12= 12

1728/ 144= 12

If the ratio is same then the function is Exponential.

So, the exponential function is

f(x) = \(4^x\)

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Answer:

b Superscript positive

Step-by-step explanation:

Negative exponents in the denominators can be evaluated by moving the function from the denominator to the numerator and changing the power from negative to the positive.

We have

1/b⁻² = b²

Moving the function with a power from denominator to numerator or from numerator to denominator changes the sign of the power. It is not equal to zero.

This is the property of exponents.

Answer:

40

Step-by-step explanation:

15/40 divided by 5= (15 divided by 5)/(40 divided by 5)= 3/8

Answer:

a = 40

Step-by-step explanation:

Cross multiply, then divide:

I hope this helps!

Answer:

5

-5

13

-5

-13

13

5

-13

Step-by-step explanation:

Answer:

5, -5, 13, -5, -13, 13, 5, -13

Step-by-step explanation:

Hope this helped and have a good day

The absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.

According to the question.

We have solutions of a absolute value equation.

As we knoaw that, the non-negative value of a real number x without regard to its sign is known as its absolute value or modulus equation  in mathematics and is indicated by the symbol |x|.

To find the absolute value equation whose solution are x = -10 and x = -5 we need to add some previous steps, which make the equation an absolute value equation.

|(x+10)(x+5)|=0,

x=-10 and x=-5

Hence, the absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.

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Answer: 1+17r is your answer

Step-by-step explanation: Combine like terms

Answer:

1+17r

Step-by-step explanation:

The probability that exactly 4 of the 8 diamonds picked from the bag are real diamonds is 28/256 or 11.1%.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning the event is impossible and 1 meaning the event is certain to occur. Probability theory is used to make predictions and calculate the chances of different outcomes in order to make decisions. Probability theory can also be applied to understand the behavior of complex systems.

This is calculated by first determining the total amount of possible outcomes. Out of the 8 diamonds picked, there are 8C4 = 70 ways in which the 4 real diamonds can be chosen. With 8 real diamonds and 7 fake diamonds, the probability of a real diamond being chosen is 8/15, and the probability of a fake diamond being chosen is 7/15. Therefore, the probability of having exactly 4 real diamonds is 70 x (8/15)^4 x (7/15)^4 = 28/256.

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A) the probability that the month selected for the annual sale will be September or October is 1/6.

A) Since we are interested in the probability of selecting September or October, which are two out of the 12 months, the probability can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 months / 12 months

Probability = 1/6

Therefore, the probability that the month selected for the annual sale will be September or October is 1/6.

B) To calculate the probability, we need to sum the number of days in September and October and divide it by the total number of days in a year (365 or 366 in a leap year).

Probability = (30 + 31) days / 365 or 366 days

Probability ≈ 61/365 or 366

The exact probability will depend on whether it is a leap year or not.

Comparing the answers from part A and part B, we can see that the probability of selecting September or October using days is slightly different from the probability calculated assuming each month has an equal probability of being selected.

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The derivatives of the given functions with respect to x are as follows:

i) For y = \(ln(x^4 + 3x^2 + 6)\), the derivative is dy/dx = \((4x^3 + 6x)/(x^4 + 3x^2 + 6)\).

This is obtained using the chain rule and the derivative of ln(u) = (1/u)(du/dx).

ii) For y =\(2x - 12x^2 - x +\)4, the derivative is dy/dx = 2 - 24x - 1. This is obtained by taking the derivative of each term separately, as the derivative of a constant is zero and the derivative of \(x^n is nx^(n-1)\).

iii) For y = \(4(x^2 - 4x + 6)^3\), the derivative is dy/dx = 1\(2(x^2 - 4x + 6)^2(2x - 4)\). This is obtained using the chain rule and the power rule, where the derivative of \((u^n) = n(u^{n-1})(du/dx)\).

In summary, the derivative of \(ln(x^4 + 3x^2 + 6)\) with respect to x is \((4x^3 + 6x)/(x^4 + 3x^2 + 6)\). The derivative of \(2x - 12x^2 - x + 4\) with respect to x is 2 - 24x - 1. The derivative of\(4(x^2 - 4x + 6)^3\) with respect to x is \(12(x^2 - 4x + 6)^2(2x - 4)\).

i) The derivative of \(ln(x^4 + 3x^2 + 6\)) is obtained by applying the chain rule. The derivative of ln(u) is (1/u)(du/dx), where \(u = x^4 + 3x^2 + 6\). By finding the derivative of u with respect to x and substituting it into the chain rule formula, we get\((4x^3 + 6x)/(x^4 + 3x^2 + 6)\).

ii) The derivative of \(2x - 12x^2 - x + 4\) is obtained by taking the derivative of each term separately. The derivative of 2x is 2, the derivative of \(-12x^2 is -24x\) (using the power rule), and the derivative of -x is -1. The derivative of a constant term is zero. Combining these derivatives, we get dy/dx = 2 - 24x - 1.

iii) The derivative of \(4(x^2 - 4x + 6)^3\) is obtained using the chain rule and the power rule. We first apply the power rule by multiplying the exponent (3) by the expression inside the parentheses, resulting in \((x^2 - 4x + 6)^2\). Then, using the chain rule, we multiply by the derivative of the expression inside the parentheses, which is 2x - 4. Combining these results, we get dy/dx = \(12(x^2 - 4x + 6)^2(2x - 4).\)

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Answer:

22 and 15

Step-by-step explanation:

22+15=37

22-15=7

Answer:

Formula = pn × 3

which means previous number × 3

Step-by-step explanation:

\(3 \times 3 = 9 \\ 9 \times 3 = 27 \\ 27 \times 3 =81 \\ 81 \times 3 = 243 \\ 243 \times 3 = 729\)

Answer:

$6,900+ per month

Step-by-step explanation:

The rent she is paying should be 1/3 or less than her income. Therefore she has to earn 3 times or more of her income. The least she could earn every month is:

2,300 × 3 = $6,900

As for the equation, if we assume the rent is x, the equation for her income will be 3x.

Answer:

2,300 x 3 = 6,900

which is a needed income for a condo

Step-by-step explanation:

downtown

The equation m = 2s + $5 allows us to determine Marisol's earnings based on the amount Sophia earns babysitting, taking into account that Marisol earns $5 more than twice Sophia's earnings.

Let's break down the information given. Sophia earns s dollars babysitting. Marisol earns $5 more than twice what Sophia earns.

Twice what Sophia earns can be represented as 2s, and $5 more than that is 2s + $5. Therefore, the equation that represents how much money Marisol earns, m, is:

m = 2s + $5

In this equation, 2s represents twice what Sophia earns, and adding $5 to that gives us Marisol's earnings.

For example, if Sophia earns $10 babysitting, we can substitute s = $10 into the equation:

m = 2($10) + $5

m = $20 + $5

m = $25

So in this case, Marisol would earn $25.

Therefore, the equation m = 2s + $5 allows us to determine Marisol's earnings based on the amount Sophia earns babysitting, taking into account that Marisol earns $5 more than twice Sophia's earnings.

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Answer:

Beatrice age = 34 years

Step-by-step explanation:

Given:

Andrew age = Beatrice age + 2 year

Chris age = Beatrice age - 3 year

Sum of Andrew's age and Chris' age = 67

Find:

Beatrice age

Computation:

Assume;

Beatrice age = b

So,

Andrew age = Beatrice age + 2 year

Andrew age = b + 2

Chris age = Beatrice age - 3 year

Chris age = b - 3

So,

Andrew's age and Chris' age = 67

b + 2 + b - 3 = 67

2b - 1 = 67

2b = 68

b = 34

So,

Beatrice age = b

Beatrice age = 34 years

After 8 seconds the ball height was 42 units.

It is given that on a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.

It is required to find how high was the ball after 8 seconds.

It is defined as the graph of a quadratic function that has something bowl-shaped.

The orbit of the ball will be a parabola.

We know the standard form of a quadratic function:

\(\rm y=ax^2+bx+c\)      where \(\rm \\a\neq 0\)

At x = 0 and y = 10, we get:

\(\rm 10 =a(0)^2+b(0)+c\\\rm 10= c\\\rm c=10\)

At x = 2 and y=24, we get:

\(\rm 24= a(2)^2+b(2)+c\\\rm 24=4a+2b+10\\\rm 4a+2b=14\)....(1)

At x = 16 and y = 10, we get:

\(\rm 10= a(16)^2+b(16)+c\\\rm 10=256a+16b+10\\\rm 256a+16b=0 \\\)....(2)

By solving equations (1) and (2), we get;

a = - 1/2, b = 8 and c = 10

Putting these values in the standard form of a quadratic function, we get:

\(\rm y = - \frac{1}{2} x^2+8x+10\\\)

Now, after 8 seconds means when x = 8, we get:

\(\rm y=-\frac{1}{2}\times 8^2 +8\times8+10\\\rm y = -32+64+10\\\rm y= 42\)

Thus, after 8 seconds the ball height was 42 units.

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Answer:

b

Step-by-step explanation:

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

Interpreting as: circle 8.5 inches.

Assuming

"circle"

is a geometric object

circle | radius 8.5 inches

Equation:

(x - x_0)^2 + (y - y_0)^2 = 72.

(assuming center (x_0, y_0))

Properties:

diameter | 17 inches

area enclosed | 227 in^2 (square inches)

circumference | 53.4 inches

answer is D. 17/C

Answer:

Yes

Step-by-step explanation:

Let the numbers be p q r such that p>q>r

So p + q + r = 3q

2q = p+ r

And q< p but q> c,

So by Solving this would give

q= (p+ r)/2

so q is the mean of p & r.

Since the only other number that fits is q,

Then q is the mean of the numbers p,q,r

As so q is also the median of this set

Thus proving that the mean is the same as the median.

Answer:

28

Step-by-step explanation

28 times 25 is 700

Answer:

28

Step-by-step explanation: