Estimate:
556
X 4
Estimate and then find the product

The average angular velocity during the dive is option b, 3 π/ √2=rad/s.

The height of the platform, h = 10 m

The number of revolutions made by the diver = 2.5 revolutions = 5π radThe initial velocity of the diver = 0

The final velocity of the diver:

We know,

The formula for final velocity in terms of initial velocity, acceleration, and distance is given as;

v² = u² + 2

Here, Initial velocity, u = 0

Final velocity, v =

Acceleration due to gravity, a = 9.8 m/s²

Distance, s = h = 10 m

Therefore, v² = 0 + 2 × 9.8 × 10v²

   = 196v = √196v = 14.00 m/s

We know, the formula for average angular velocity is given as;

ω = θ/t

Here, angular displacement, θ = 5π rad

Time taken, t

We know, the formula for time taken is given as;

t = √2h/g

Here, height of the platform, h = 10 m

Acceleration due to gravity, g = 9.8 m/s²

Therefore,t = √2 × 10/9.8t = 1.427 s

Substituting the values of θ and t in the formula for average angular velocity, we get;

ω = θ/tω = 5π/1.427ω = 3.5 π/ √2rad/s

Therefore, the average angular velocity during the dive is option b, 3 π/ √2=rad/s.

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Answer:

Step-by-step explanation:

Since the figure is a right angled triangle we can use trigonometric ratios to find measure of ∠A.

To find ∠A we use sine

sin ∅ = opposite / hypotenuse

From the question

the opposite is 13

the hypotenuse is 15

So we have

\( \sin(∠A) = \frac{13}{15} \\∠A = \sin ^{ - 1} ( \frac{13}{15} ) \\ ∠A = 60.0735651...\)

We have the final answer as

∠A = 60.07°

Hope this helps you

Step-by-step explanation:

Hey there!

Here;

As the figure shown is a Right angled triangle. Taking refrence angle as angle A, we get,

p= 13

h = 15

In ratio of sin there is p and h, So using sin ratio.

\( \sin( \alpha ) = \frac{p}{h} \)

Put all values.

\( \sin( \alpha ) = \frac{13}{15} \)

Simplify it.

\( \sin( \alpha ) = 0.86666666\)

\( \alpha = { \sin}^{ - 1} (0.8666666)\)

\( \alpha = 60.0732°\)

Therefore the measure of angle A is 60°.

Hope it helps ...

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r\)

Answer:

The radius is approximately 21.33 cm.

Step-by-step explanation:

Using the formula V = 4/3 πr³, we can just substitute the value of the given volume and solve for r.

V = 40664cm³

Substitute the given and solve for r

V = 4/3 πr³

40664cm³ = 4/3πr³

\(\frac{3(40664cm^3)}{4\pi}=r^3\\9707.81 = r^3\\ r = 21.33\)

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

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Answer:

a) = -8

b) 1 - (-7) = 8

b) -7 - 1 = -8

c) for both they are still the same answer so  

[1- (-7)] = 8

[-7 - 1] = -8

I'm pretty sure these are the answers hope this helped

Step-by-step explanation:

Answer:

388.8

Step-by-step explanation:

Thats correct i think

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Answer:

x>4

Step-by-step explanation:

3x - 2 >10  add 2 to both sides

3x > 12  Divide both sides by 3

x >4

Answer:

\(x > \bf 4\)

Step-by-step explanation:

To find a solution to this inequality, we have to rearrange this equation to make \(x\) its subject:

\(3x - 2 > 10\)

⇒ \(3x - 2 + 2 > 10 + 2\)      [Add 2 to both sides]

⇒ \(3x > 12\)

⇒ \(\frac{3x}{3} > \frac{12}{3}\)                         [Divide both sides by 3]

⇒ \(x > \bf 4\)

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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Answer:108 feet

Step-by-step explanation:

In calculus and mathematics in general, when a symbol has a subscript and a superscript, it provides additional information or context about the symbol or variable being represented.

The subscript typically indicates the index or position of the variable. It is a smaller number or symbol written below and to the right of the main symbol. For example, in the expression "xn," the subscript "n" represents the index or position of the variable "x."

The superscript, on the other hand, often represents an exponent or power to which the variable is raised. It is a smaller number or symbol written above and to the right of the main symbol. For instance, in the expression "x2," the superscript "2" represents the exponent, indicating that "x" is raised to the power of 2.

In calculus, subscripts and superscripts are frequently used to denote different variables, indices, or operations in functions, sequences, series, and equations. They help provide clarity and convey specific meanings or relationships within mathematical expressions. It is essential to understand the conventions and notations used in specific contexts to interpret the subscripts and superscripts correctly.

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Answer:

A C and D

Step-by-step explanation:

A P E X

jrjfjfjfjfjfjfjf jfjfjf jfjfjf jfjfjf

Answer:

\({ \tt{178 = 293 > (k \times 115)}}\)

A graph which represents the linear function y = -2x is: graph B.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Generally speaking, the graph of any proportional relationship is characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) either increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in the graph of y = -2x is proportional as it passes through the origin (0, 0).

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The area of the regular octagon is 522.8 inches².

The polygon below is an octagon. An octagon is a polygon with 8 sides. The octagon is a regular octagon.

A regular octagon has all its sides equal to each other. Therefore, let's find the regular polygon with the given apothem and sides.

Therefore,

area of an octagon = 1 / 2 × apothem × perimeter

perimeter = 10 × 8 = 80 inches

apothem = 13.07 inches

Therefore,

area of an octagon = 1 / 2 × 13.07 × 80

area of an octagon = 40 × 13.07

area of an octagon = 522.8 inches²

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it A

Step-by-step explanation:

Answer

whats the question

Step-by-step explanation:

If a plane is 111 mi north and 189 mi east of an airport, the pilot should turn 31.4 degrees to fly directly to the airport.

To find the angle that the pilot should turn in order to fly directly to the airport, we can use the trigonometric functions sine, cosine, and tangent. Specifically, we will use the tangent function, which relates the opposite side (in this case, the distance north) to the adjacent side (in this case, the distance east) of a right triangle:

tan(x) = opposite/adjacent

We can rearrange this formula to solve for x:

x = arctan(opposite/adjacent)

where arctan is the inverse tangent function.

In this case, the opposite side is 111 miles (the distance north) and the adjacent side is 189 miles (the distance east). Plugging these values into the formula, we get:

x = arctan(111/189)

x = 31.4 degrees

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A type I error occurs when we reject the null hypothesis (H0) when it is actually true.

b) The significance level (α) is the probability of making a type I error. Since the rejection region is {y ≤ 12} and the null hypothesis is p = 0.8, we need to find the probability of getting a sample proportion (y/20) less than or equal to 0.6 (12/20) under the null hypothesis. Using a normal approximation to the binomial distribution, we have:

z = (0.6 - 0.8) / sqrt(0.8 * 0.2 / 20) ≈ -1.79

From a standard normal distribution table, we find that the area to the left of z = -1.79 is approximately 0.0367. Therefore, α = 0.0367 or 3.67%.

c) A type II error occurs when we fail to reject the null hypothesis (H0) when it is actually false.

d) To find β when p = 0.6, we need to find the probability of not rejecting the null hypothesis (H0: p = 0.8) when the true proportion is p = 0.6. Using a normal approximation to the binomial distribution, we have:

z = (0.6 - 0.8) / sqrt(0.8 * 0.2 / 20) ≈ -1.79

We want to find the probability that z is greater than -1.79, which is the area to the right of z = -1.79 under the standard normal distribution. From a standard normal distribution table, we find that the area to the right of z = -1.79 is approximately 0.9637. Therefore, β ≈ 0.9637.

e) To find β when p = 0.4, we again need to find the probability of not rejecting the null hypothesis (H0: p = 0.8) when the true proportion is p = 0.4. Using a normal approximation to the binomial distribution, we have:

z = (0.4 - 0.8) / sqrt(0.8 * 0.2 / 20) ≈ -3.58

We want to find the probability that z is greater than -1.79, which is the area to the right of z = -3.58 under the standard normal distribution. From a standard normal distribution table, we find that the area to the right of z = -3.58 is approximately 0.9997. Therefore, β ≈ 0.9997.

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Answer:

Mrs. Reed bought 4 boxes of paper clips and 6 bags of M&Ms.

Explanation:

4 x 4 = 16

3 x 6 = 18

16 + 18 = 34

Answer:

Step-by-step explanation:

The cash flow to stockholders for 1998 is -$4 million.

To calculate the cash flow to stockholders for 1998, follow these steps:

Identify the dividends paid: Brandy's Candies paid $23 million in dividends during 1998.

Determine the net common stock repurchases: Brandy's Candies made net common stock repurchases of $27 million during 1998.

Subtract the net common stock repurchases from the dividends paid: $23 million - $27 million = -$4 million.

The resulting cash flow to stockholders for 1998 is -$4 million, indicating a net outflow of cash from stockholders.

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Answer:

$10000 Total cost to transport 14 tons

Step-by-step explanation:

The total cost C(S) = $6500 + ($250/ton)S.  This is a linear function with initial value $6500 and slope $250/ton.

C(14) = $6500 + ($250/ton)(14) = $10000 = Total cost to transport 14 tons

Answer:

hello! the answer is below!

Step-by-step explanation:

Let's write the equation.

6500 + 250s = c

Now put in our value for s.

6500 + 250 · 19 = 4750

The answers are

6500 + 250s = c

And

4750

Hope this helps! :)

Answer:

1. volume = 1243.44ft^3

2. volume = 54259.2ft^3

Answer:

Step-by-step explanation:

Outlier

False. Cronbach's alpha is a measure of internal consistency reliability, not a measure of the correlation between scale items.

It assesses the extent to which the items in a scale or questionnaire are measuring the same underlying construct.

Cronbach's alpha is calculated based on the inter-item correlations among the items in a scale. It provides a measure of the average correlation between all possible pairs of items in the scale. The range of Cronbach's alpha is between 0 and 1, with higher values indicating greater internal consistency or reliability.

Essentially, Cronbach's alpha quantifies the extent to which the items in a scale are consistently measuring the same construct or concept. It assesses how well the items "hang together" as a reliable measurement tool.

While correlation between scale items is related to internal consistency, Cronbach's alpha specifically measures the degree to which the items are interrelated and provides a single coefficient that reflects the overall reliability of the scale. It does not directly indicate the extent of item-item correlations or the strength of individual item contributions to the scale.

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We are given that:

Circumference = 19.4 cm

Formula:

2πr = Circumference

Rewrite the equation:

The "r" variable represents the radius of the circle. Thus, we need to isolate it on one side to determine the radius. This can be done with the four mathematical operations (+  -  ×  ÷). Since the "÷" is included, we can divide both sides by 2π to isolate the "r" variable.

Divide both sides by 2π:

Substitute the radius as 22/7: