An insect flies 20 feet in 1 second. how fast does the insect fly in miles per hour?

Answer:

[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]

Step-by-step explanation:

The given complex number is:

[tex]2+2i[/tex]

Now, the polar from of the complex number [tex]z=a+ib[/tex] is [tex]z=r(cos{\theta}+isin{\theta})[/tex].

Finding the absolute value of r:

[tex]r=|z|={\sqrt{2^2+2^2}[/tex]

[tex]r=\sqrt8[/tex]

[tex]r=2\sqrt{2}[/tex]

Now, find the value of argument,

Using formula, [tex]{\theta}=tan^{-1}(\frac{b}{a})[/tex]

[tex]{\theta}=tan^{-1}({\frac{2}{2})[/tex]

[tex]{\theta}=tan^{-1}(1)[/tex]

[tex]{\theta}={\frac{\pi}{4}}[/tex]

Thus, the polar form is:

[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]

which is the required polar form.

Answer:

Value of x is 4.0

Step-by-step explanation:

Given:

[tex]4^x=243[/tex]

To find: Value of x.

We use the following rule,

[tex]log\,x^a=a.log\,x[/tex]

Consider,

[tex]4^x=243[/tex]

Take log on both sides.

[tex]log\,4^x=log\,243[/tex]

[tex]x\times log\,4=log\,243[/tex]

[tex]x=\frac{log\,243}{log\,4}[/tex]

[tex]x=\frac{2.386}{0.602}[/tex]

x = 3.962

x = 4.0   (nearest tenth)

Therefore, Value of x is 4.0

Final answer:

To find the volume of a sphere with a given great circle area, solve the equation 4πr² = 201.06 to find the radius, then use the formula V = (4/3)πr³ to calculate the volume. The volume is approximately 267.97 cubic inches.

Explanation:

To find the volume of a sphere with a given great circle area, we first need to find the radius of the sphere. The great circle area is equal to the surface area of the sphere, which is 4πr², where r is the radius of the sphere. In this case, the great circle area is 201.06 square inches, so we can solve the equation 4πr² = 201.06 to find the radius. Once we have the radius, we can use the formula for the volume of a sphere, V = (4/3)πr³, to calculate the volume.

First, let's solve the equation 4πr² = 201.06 for r:

4πr² = 201.06

r² = 201.06 / (4π)

r² ≈ 16.06

r ≈ √16.06 ≈ 4.01

Now that we have the radius, we can calculate the volume using the formula V = (4/3)πr³:

V ≈ (4/3)π(4.01)³ ≈ 267.97 cubic inches

Answer:

the answer is 775.3

Answer : The volume of sphere will be, [tex]775.3\text{ inches}^3[/tex]

Step-by-step explanation :

To calculate the volume of sphere, we use the formula:

[tex]V=\frac{4}{3}\pi r^3[/tex]

where,

r = radius of sphere  

Given :

Radius of sphere = 5.7 inches

Now put all the given values in the above formula, we get:

[tex]V=\frac{4}{3}\pi r^3[/tex]

[tex]V=\frac{4}{3}\times 3.14\times (5.7inches)^3[/tex]

[tex]V=775.3\text{ inches}^3[/tex]

Thus, the volume of sphere will be, [tex]775.3\text{ inches}^3[/tex]

To solve the problem, we can set up a system of equations. The solution is 12 dimes and 16 quarters.

To solve this problem, we can set up a system of equations. Let's say the number of dimes is x and the number of quarters is y. We know that the total number of coins is 28, so we can write the equation:

x + y = 28

We also know that the value of the dimes is 10 cents and the value of the quarters is 25 cents. The total value of the change is 520 cents, so we can write the equation:

10x + 25y = 520

We can solve this system of equations using substitution or elimination. Let's use substitution:

From the first equation, we can express x in terms of y:
x = 28 - y

Substitute this value of x into the second equation:
10(28 - y) + 25y = 520

Simplify and solve for y:
280 - 10y + 25y = 520
15y = 240
y = 16

Now substitute this value of y back into the first equation to find x:
x + 16 = 28
x = 12

Therefore, the man has 12 dimes and 16 quarters.

Answer:

Scatterplot

Step-by-step explanation:

Bivariate data means that the data is in two variables. For example, if the height of the students is plotted against their age, this data will be the bivariate data.

A bivariate data is represented using the graph known as Scatter Plot. One variable is plotted along x-axis and second variable is plotted against y-axis. After plotting the two variables we can observe the relation(association) between the two variable using the line of best-fit which models the relation between the two variables.

So, the answer to this question is Scatterplot.

A graph that displays bivariate data is called a Scatterplot. It represents two variables and can indicate Positive Association, Negative Association, or No Association, based on the scatter pattern.

In the field of Statistics, a graph that displays bivariate data is referred to as a Scatterplot. Bivariate data represents two different variables, and a scatterplot is a graphical representation that uses dots to show the relationship, if any, between these two sets of data.

When looking at a scatterplot, the patterns of the dots can indicate associations. Positive Association is when as one variable increases, so does the other. Negative Association is when one variable decreases as the other increases. If the dots seem randomly scattered, it exhibits No Association.

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Answer:

The correct answer is D

Step-by-step explanation:

I got it right on Edge.2020. Have a great day!

If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.

So option D) $48,000 is correct.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Mr. and Mrs. Yeager want to buy a home valued at $320,000.

If they have 15% of this amount saved for a down payment, then

15% =15/100=0.15

Therefore, we get;

0.15 (320000)=48000

If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.

So option D) $48,000 is correct.

Learn more about multiplications;

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The height of the cylinder with a given volume of 1323
cmcubed and a radius of 7 cm, divide the volume by the area of the base. The correct height is 27 cm.

The height of a cylinder given its volume and the radius of its base. To find the height, we'll use the formula for the volume of a cylinder, which is V = ()h, where V is the volume,  is the radius and h is the height.

Step-by-step calculation:

The volume of the cylinder is given as 1323cmcubed.

The radius (r) of the base of the cylinder is given as 7 cm.

Plugging these values into the formula: 1323cm³= (7 cm)²  imes h.

Simplify the equation: 1323cm³ = 49cm²  imes h.

Divide both sides by 49cm² to find the height: h = 1323cm³ / 49cm².

The resulting height is therefore 27 cm, which is the solution to the problem.

The height of the cylinder is 27 cm.

To find the sales price, multiply $99.50 by 35% to get the discount amount of $34.83, then subtract that from the original price, resulting in a sales price of $64.67.

To calculate the sales price of a video game that has a discount of 35%, first determine the amount of the discount by multiplying the original price by the percentage of the discount. The original price of the video game is $99.50. Therefore, you calculate $99.50 × 0.35 to find the discount amount.

The discount amount is $34.825. Next, subtract the discount amount from the original price to find the sales price: $99.50 - $34.825 equals the sales price.

It's also important to round the discount to the nearest cent as currency, resulting in a discount of $34.83. Thus, the sale price of the video game will be $99.50 - $34.83, which equals $64.67.

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The scenario of cancelling a dance class due to student injuries is an example of the 'risk avoidance' strategy in risk management, which aims to avoid potential harm.

Canceling a dance class due to multiple students getting injured is a risk management strategy known as risk avoidance. This strategy eliminates the risk by not participating in the activity that could lead to the risk. In this context, the dance class risks injury to the students. In such a scenario, the dance instructor or school chooses to avoid the risk (moral hazard) by cancelling the activity (i.e., the dance class), thereby protecting the students from further harm. This is a common approach employed in situations where the potential adverse outcomes of risk outweigh any potential benefits of the activity.

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A positive relation between two things means that they are proportional to each other. One affects the other thing.

1) Smoking and cases of lung cancer. This is positive. As smoking affects lungs and can cause lung cancer. So, with increased smoking comes the increased risk of lung cancer thus increasing cases of lung cancer.

2) Amount of time spent at school each day and number of text sent per day - These two events are independent of each other. They are not based on each other. Hence, no relationship here.

A negative relation implies that if one thing increases, the other decreases.

3) The number of licks taken and the size of the Tootsie Pop. This is negative. As the number of licks increases, the size of the pop decreases.

Since one of the seven performers insists on being the first act, the remaining six performers can be arranged in '6!' (factorial of 6) ways. Therefore, there are 720 different ways to schedule the appearances of the variety show.

This problem is a permutation problem. Since one performer insists on being the first act of the evening, this leaves 6 other acts that can be arranged in any order. In permutation, if you have 'n' different items, they can be arranged in 'n!' (n factorial) ways. The factorial of a number n, denoted as 'n!', is the product of all positive integers less than or equal to n.

In this case, 6 performers can be arranged in '6!' ways. The factorial of 6 (6!) is 6 * 5 * 4 * 3 * 2 * 1 = 720. Therefore, there are 720 different ways to schedule the appearances of the remaining 6 acts after the first performer has gone on.

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The correct answer is 3192 cm3. I just did the test.

The predicted vital capacity of a 20-year-old, 5'5" female, using the provided equation, is approximately 3.97 liters.

To predict the vital capacity of this 20-year-old 5'5" female who weighs 120 pounds using the given equation, we first need to convert the height from feet to centimeters since standard medical measurements are usually in metric units. The conversion is 1 foot = 30.48 cm. Therefore, 5'5" = 5*30.48 cm + 5*2.54 cm = 165.1 cm. Now we can substitute the height (h) and age (a) into the equation: vc = (0.041) h - (0.018) a - 2.69 = (0.041*165.1) - (0.018*20) - 2.69 ≈ 3.97 Liters. Therefore, the predicted vital capacity of this 20-year-old 5'5" female is approximately 3.97 liters.

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Answer:

68%

Step-by-step explanation: