A hummingbird beats its wings about 75 times in one second. Based on this rate, what is the number of times a hummingbird beats its wings one minute?

Answer:

235 workers

Step-by-step explanation:

Factory operates on a standard work week shift for 5 days = 8 hours per day

In one week working hours are = 8 × 5 = 40 hours.

Company has an order for 7,500 new cars to be delivered in one week.

One car requires time to be fitted with a new hood ornament that requires to install = 1 hour and 15 minutes ( 1.25 hours )

In 40 hours (one week) cars will install with one worker = [tex]\frac{40}{1.25}[/tex] = 32 cars

To fulfill the order of 7,500 cars, Company needs workers = 7,500 ÷ 32 = 234.375 ≈ 235 workers.

235 workers must be assigned this job to meet the deadline.

Final answer:

To show that the differential equation M(x) + N(y)dy/dx=0 is separable, we must demonstrate that M and N can be expressed as functions of x and y respectively, without overlap, leading to an equation of the form f(y)dy/dx + g(x) = 0. Explanation of separable equations through specific cases and integration methods.

Explanation:

Separable equations involve the relationship M(x) + N(y)dy/dx = 0. To show this, you can use specific cases where M and N can be separated into functions of only x or y.

For example, if M/N can be expressed as f(y)/g(x), then the separable equation becomes f(y)(dy/dx) + g(x) = 0.

Integrating M(x, y) with respect to x can lead to finding a function f(x, y) that satisfies the given differential relationship.

1.D ,square root of 2

2.C, undefined

3. A

4. A, about -1

5. D, 12.3 feet

Using the exchange rate $1 U.S. = 0.678 euros, the cost of the souvenirs in US dollars is calculated by dividing the total in euros (44 euros) by the exchange rate (0.678). The result is approximately $64.89.

To find the cost of the souvenirs in US dollars, we must first understand the exchange rate provided $1 U.S. = 0.678 euros. This means that one dollar buys 0.678 euros. To convert the euros to dollars, we divide the amount in euros by the exchange rate. Here's how you can do it:

When you carry out the calculation, you'll get approximately $64.89. Therefore, the cost of the souvenirs in US dollars is around $64.89.

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To find out the number of toothpicks required to form 100 adjacent squares, one can use the formula 4 + 3(n - 1), resulting in 301 toothpicks.

To determine how many toothpicks are required to form 100 adjacent squares, we must first understand the pattern established by the initial set of squares. When forming three adjacent squares, 10 toothpicks are used. This is because the first square requires 4 toothpicks, and each subsequent square shares a side with the previous square, thus requiring only 3 additional toothpicks for each new square.

For n adjacent squares, the number of toothpicks required can be calculated with the formula: 4 + 3(n - 1), since the first square uses 4 toothpicks and each additional square uses 3 more toothpicks.

Now, let's apply this to 100 adjacent squares:

Therefore, 301 toothpicks are required to form 100 adjacent squares.

The relationship is that for each square, we need 4 toothpicks (1 new side for each square). So, for 100 adjacent squares, we require 400 toothpicks.

Let's analyze the pattern to determine the relationship between the number of squares and the toothpicks required. Consider the formation of 3 adjacent squares:

For the first square, we need 4 sides (4 toothpicks).

For the second square, we have 3 shared sides with the first square and 1 new side (3 + 1 = 4 toothpicks).

For the third square, we have 3 shared sides with the second square and 1 new side (3 + 1 = 4 toothpicks).

So, for 3 adjacent squares, we need a total of 12 toothpicks (4 + 4 + 4).

Now, let's generalize this pattern. For each additional square beyond the third, we are adding 4 toothpicks (1 new side for each square). Therefore, the toothpicks required to form n adjacent squares can be expressed as 4n.

For 100 adjacent squares:

Toothpicks=4×100=400

Hence, 400 toothpicks are required to form 100 adjacent squares.

The question probable may be:

To form 3 adjacent squares, 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?

To find the coordinates of the points common to the graphs of f and g, set f(x) equal to g(x) and solve for x. The zeros of f(x) are approximately x = -1, 2, and 2.98. The range of f when the domain is limited to [0,2] is approximately [-1,9].

To find the coordinates of the points common to the graphs of f and g, we will set f(x) equal to g(x) and solve for x.

f(x) = g(x)

[tex]x^3-6x^2+9x = 4\\x^3-6x^2+9x-4 = 0[/tex]

Using a graphing calculator or software, we can find that the zeros of f(x) are approximately x = -1, 2, and 2.98.

The range of f when the domain is limited to the closed interval [0,2] is the set of y-values that f(x) takes on within that interval.

By using the First Derivative Test, we can determine that the range of f in the interval [0,2] is approximately [-1,9].

Answer:

C just did this

Step-by-step explanation:

The expression for adding 8 to the sum of 23 and 10 is (23 + 10) + 8. This is due to the commutative property of addition, which states that the order in which you add numbers does not change the result.

The question asks for an expression to calculate adding 8 to the sum of 23 and 10. The first step is to add 23 and 10 together, which equals 33. Then add 8 to that sum. You can represent this process mathematically as (23 + 10) + 8. So if you need to write an expression for adding 8 to the sum of 23 and 10, it would be (23 + 10) + 8. Remember, adding numbers together (a process called addition) is commutative, meaning you can add numbers in any order and still get the same result.

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-Line

Two adjacent, supplementary angles form a straight line

Answer:

[tex]DA=3[/tex]

Step-by-step explanation:

We have been given an image of a circle and we are told that Secant DB intersects secant DZ at point D.    

We will use intersecting secants theorem to solve our given problem.  

Intersecting secants theorem states that if two secants say MN  and KL intersect at a point 'X' outside the circle, then product of XN and MX equals the product of XL and KX.

Using intersecting secants theorem we can set an equation as:

[tex]DA\cdot DB=DY\cdot DZ[/tex]

Upon substituting our given values in above equation we will get,

[tex]3x\cdot (3x+8)=x\cdot (32+x)[/tex]

Upon dividing both sides of our equation by x we will get,

[tex]\frac{3x\cdot (3x+8)}{x}=\frac{x\cdot (32+x)}{x}[/tex]

[tex]3\cdot (3x+8)=32+x[/tex]

Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex]9x+24=32+x[/tex]

[tex]9x-x+24-24=32-24+x-x[/tex]

[tex]8x=8[/tex]

Upon dividing both sides of our equation by 8 we will get,

[tex]\frac{8x}{8}=\frac{8}{8}[/tex]

[tex]x=1[/tex]

Since the length of DA is 3x, so upon multiplying 3 by 1 we will get,

[tex]\text{Length of DA}=3\cdot 1=3[/tex]

Therefore, the length of DA is 3 units.

Answer: The number of successful throw made in that season in total is 30

Step-by-step explanation:

On average the player successfully made 5 out of 6 free throws .

Thus if number of free throws is x then number of successful throw will be [tex]\frac{5}{6}\times x[/tex] .

The basketball player attempted 36 free trials in a season .

Here x=36

Therefore No of successful throws [tex]=\frac{5}{6}\times 36=30[/tex]

Thus the number of successful throw made in that season in total is 30

The correct initial velocity (v) for the basketball to go through the hoop is approximately 0.0406 ft/s.

To find the initial velocity v, we can use the given information and set up the equation using the height of the hoop and the distance away from the hoop. The equation of the path of the basketball is given by:

y = -16x^2/(0.434v^2) + 1.15x + 8

Given that the hoop is 10 feet high and located 17 feet away, we can substitute these values into the equation:

10 = -16(17)^2/(0.434v^2) + 1.15(17) + 8

Now, we can solve this equation for the initial velocity v. First, simplify the equation:

10 = -16(17)^2/(0.434v^2) + 19.55 + 8

Combine the constant terms on the right side:

10 = -16(17)^2/(0.434v^2) + 27.55

Now, isolate the term with v on one side:

(16(17)^2)/(0.434v^2) = 17.55

Next, multiply both sides by (0.434v^2)/(16(17)^2) to solve for v^2:

v^2 = (16(17)^2)/(0.434 * 17.55)

Now, take the square root of both sides to find v:

v = sqrt((16(17)^2)/(0.434 * 17.55))

Calculating this expression will give you the initial velocity v. Let's calculate:

v ≈ 0.0406 ft/s

The initial velocity v of the basketball should be approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] for it to go through the hoop.

To find the initial velocity v required for the basketball to go through the hoop, we utilize the parabolic model [tex]\(y = -\frac{16x^2}{0.434v^2} + 1.15x + 8\)[/tex]. Given that the height of the hoop (y) is 10 feet and the distance away from the hoop (x) is 17 feet, we substitute these values into the equation:

[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]

First, simplify the equation:

[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]

Combine like terms:

[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 19.55.\][/tex]

Isolate the fraction:

[tex]\[\frac{16 \cdot 17^2}{0.434v^2} = 9.55.\][/tex]

Now, solve for v²:

[tex]\[v^2 = \frac{16 \cdot 17^2}{0.434 \cdot 9.55}.\][/tex]

Finally, find v by taking the square root:

[tex]\[v \approx \sqrt{\frac{16 \cdot 17^2}{0.434 \cdot 9.55}} \approx 14.86 \, \text{ft/sec}.\][/tex]

The calculation shows that an initial velocity of approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] is required for the basketball to follow the modeled path and successfully go through the hoop.

The number -9 is a rational number as it can be written as a fraction of two integers, specifically -9/1.

The number -9 is a rational number because it can be expressed as a fraction of two integers: -9/1 where -9 is the numerator and 1 is the denominator. By definition, rational numbers include all integers, as each integer can be written as a fraction with a denominator of 1. This is different from irrational numbers, which cannot be written as a simple fraction. An example of an irrational number is the square root of 2, which cannot be precisely expressed as a fraction of two integers.

Answer:

ANswer is D on edgeunity

Step-by-step explanation: