What is the amount of sales tax on a suit priced at $2977 if the sales tax rate is 4%?

Answer: A,B,E

Step-by-step explanation:

I just got done with the assignment and that was the answer

Mary will need 48 minutes to make a full batch of cookies, as determined by setting up a proportion and then converting hours to minutes.

Mary made 1/8 of a batch of cookies in 1/10 of an hour. To find out how long it will take to make a full batch, we set up a proportion based on the information given. Since 1/8 of a batch takes 1/10 of an hour, we want to find out the time for 8/8 (a full batch), which is equivalent to 1.

Setting up the proportion, we can say that 1/8 of a batch is to 1/10 of an hour as 1 full batch (8/8) is to X hours:

1/8 batch : 1/10 hour = 1 batch : X hours

To solve for X, we multiply 1/10 by 8 because there are 8 parts of 1/8 in a full batch:

1/10 hour * 8 = 8/10 hours

Reducing the fraction 8/10, we get:

8/10 = 4/5 hours

To convert 4/5 of an hour to minutes, we multiply by 60:

4/5 hour * 60 minutes/hour = 48 minutes

Therefore, Mary will need 48 minutes to make 1 full batch of cookies.

take the inverse arctan on both sides:

4x-4 = tan(-1)

4x-4 = -0.01745

4x = 3.98255

x = 3.9255 / 4

x = 0.996

Answer: Option (A) is the correct answer.

Explanation:

Kinetic energy is defined as the energy possessed by an object because of it's motion.

Whereas average kinetic energy is the sum of kinetic energy of all the particles of a substance.

Therefore, when water freezes then there will decrease in kinetic energy of particles and thus, particles will gain potential energy.

Hence, we can conclude that when water freezes average kinetic energy of water molecules decreases as the water releases energy to its surroundings.

The average "kinetic-energy" of water molecules decreases as water freezes, because water releases energy to its surroundings, option (a) is correct.

When water freezes, it undergoes a phase transition from a liquid to a solid state. During this process, water molecules lose energy and slow down, causing decrease in their average kinetic energy.

As temperature decreases, water molecules arrange themselves into a more structured pattern due to the formation of hydrogen bonds.

In order for water to freeze, it needs to release energy to its surroundings, in form of heat. This release of energy is necessary to facilitate transformation from a higher-energy liquid state to lower-energy solid state. As a result, average kinetic energy of water molecules decreases as water freezes.

Therefore, the correct option is (a).

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The question is asking us to find out how many players are left-handed from a total of 85 players, given that 80% of the players are left-handed. For this, we perform a simple calculation by finding 80% of 85, which equals 68. So, there are 68 left-handed players in the league.

The subject of this question falls under the category of Mathematics, more specifically, it is about percentage calculations. In order to figure out how many left-handed players there are out of the total 85 players, we need to remember that percent means 'per 100'. So, 80% translates to 80 out of 100. Therefore, to find out how many are left-handed, we need to take 80% of 85.

The calculation is as follows:

Left-handed players = 85 * (80/100)

= 85 * 0.80

= 68

So, there are 68 left-handed players in the local little league.

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The computation of 8C2•5C2 results in 280

The student asked: 'compute the following 8c2•5c2'.

We can solve this using the combinations formula, where nCr = n! / [r!(n-r)!].
 Compute 8C2.-
 8C2
 = 8! / [2!(8-2)!]
 = (8*7) / (2*1) = 28.
 Compute 5C2.
 5C2
= 5! / [2!(5-2)!]
= (5*4) / (2*1) = 10.
  Multiply the results.
  28 * 10 = 280.

Hence, the value of 8C2 • 5C2 is 280.

Option D - The driver earned $9 for each delivery.

Step-by-step explanation:

Given scenario is :

Hourly wage for the driver = $16.50

Total number of hours worked in a day = 6

So, total earning for the day = [tex]16.50\times6=99[/tex] dollars

Now, she made 11 deliveries in $99

So, each delivery cost = [tex]\frac{99}{11}=9[/tex]

Hence, the driver earned $9 for each delivery.

The area of the plane 5x + 4y + z = 20 in the first octant is calculated using a double integral over the xy-plane. The limits are defined by the intersection of x and y with the xy-plane when z=0, and the solution is approximately 66.67 square units.

To solve for the area of the part of the plane that lies in the first octant, we first need to isolate z in our equation. z = 20 - 5x - 4y. The limits for x and y in the first octant are from 0 to positive infinity, but in this case, they will be limited by the plane defined by z = 0 (the xy-plane). x and y will range from 0 to the point where they meet the plane. Therefore, we set z = 0 and solve for both x and y, giving us x = 4 and y = 5.

Now in order to calculate the area, we must interpret this integral on the xyz-plane as a double integral on the xy-plane. Now, we integrate over the region in the xy-plane that x and y range over:

Area = ∫ from 0 to 4 ∫ from 0 to (5 - 1.25x) (20 - 5x - 4y) dy dx

And that is the integral you need to calculate to find the area. Attempting to calculate this integral results in the area ≈ 66.67 square units.

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The new mean age will be less than 14.2 years.

What is mean?

There are several kinds of mean in mathematics, especially in statistics. For a data set, the arithmetic mean, also known as arithmetic average, is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.

According to questions, the mean age of a dance troupe is 14.2 years.

A 7-year-old sibling is invited to join the troupe.

We have to find how does the sibling’s age affect the mean.

There is no possible way to know how much the mean age decreases.

But the new mean age will decrease definitely.

Hence we can conclude that Option C is correct answer.

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To factor out -1/2 - 1/2 from -1/2x + 6, multiply -1/2 by the expression inside the parentheses and distribute. Then, simplify and combine like terms to get the factored form: -3/2x - 6.

To factor out -1/2 - 1/2 from -1/2x + 6, you can rewrite the expression as (-1/2) * (x + 2(6)). Then, distribute to get (-1/2)x - (1/2)(2) * (x + 2(6)). Simplify further to get (-1/2)x - x - 6. Finally, combine like terms to get (-1/2 - 1)(x) - 6. Therefore, the factored form of the expression is -3/2x - 6.

Using the L'Hospital's Rule, we differentiate the numerator and denominator of the given function separately, substitute these derivatives back into the function, and then attempt to evaluate the limit as x approaches 0.

To find the limit of the given function as x approaches 0, we will use the L'Hospital's Rule since the function gets an indeterminate form 0/0 as x approaches 0. L'Hospital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

First, we differentiate the numerator and the denominator separately. For the numerator, the derivative of 2x is 2, and the derivative of sin(2x) is 2cos(2x). So the derivative of the numerator is 2 - 2cos(2x).

For the denominator, the derivative of 2x is 2, and the derivative of tan(2x) is 2sec²(2x), since the derivative of tan(x) is sec²(x) and because of the chain rule, we multiply by 2. So, the derivative of the denominator is 2 - 2sec²(2x).

Now, we substitute these derivatives back into the original function and take the limit as x approaches 0: lim  x→0  (2 - 2cos(2x)) / (2 - 2sec²(2x)).

After further simplifying the above expression, you can evaluate the limit.

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The limit is 0.

We need to find the limit:

lim x→0 (2x − sin(2x)) / (2x − tan(2x))

Both the numerator and the denominator approach 0 as x approaches 0, which means it is in the indeterminate form 0/0. This suggests that we can use L'Hôpital's Rule.

According to L'Hôpital's Rule, we can differentiate the numerator and the denominator and then take the limit of the resulting fraction.

First, let's compute the derivative of the numerator:

Next, let's compute the derivative of the denominator:

Now, we apply L'Hôpital's Rule:

lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x))

As x approaches 0, cos(2x) approaches 1 and sec²(2x) also approaches 1, so:

lim x→0 (2 - 2(1)) / (2 - 2(1)) = 0 / 0

This fraction again gives an indeterminate form. Applying L'Hôpital's Rule a second time will be helpful. We need to differentiate the numerator and the denominator again:

Second derivative of the numerator: d/dx [2 - 2cos(2x)] = 4sin(2x)

Second derivative of the denominator: d/dx [2 - 2sec²(2x)] = -8sec²(2x)tan(2x)

Applying L'Hôpital's Rule once more, we get:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x))

Substitute x = 0:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x)) = 0

Therefore, the limit is 0.

Hello from MrBillDoesMath!

Answer:   Case 1: approximately   429.4, Case 2: 8

Discussion:

Let the unknown be "x". The problem statement could mean either

32 * (435 -x)  = 179     (#1)

or

435 - 32*x = 179             (#2)

It's unclear which one is wanted so we solve both of them.

----------------------------------------------#1

But for case #1

32 * (435 -x)  = 179  

32 * 435 - 32x = 179   or

13920 - 32x = 179

Add 32x to both sides

13920 = 179 + 32x

Subtract 179 from both sides:

13920 - 179 = 32x

Divide both side by x to get

x = (13920 -179)/32 =  13741/32 which is approximately   429.4

For case #2

----------------------------------------------#2

435 - 32x = 179.  Add 32 x to each side

435 -32x + 32x = 179 + 32x. Subtract 170 from each side

435 -179 = 32x or

32x = 256   or x = 8

Regards, MrB

Answer:

Speed of car on the way back = 30 mph

Step-by-step explanation:

Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s

Time taken to cross bridge on the way = 40 seconds

Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m

Time taken to cross bridge on the way back = 30 seconds

Length of bridge = Speed of car on the way back x Time taken on the way back

800 = Speed of car on the way back x 30

Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph

Speed of car on the way back = 30 mph

The arc is every two-point smooth curve. The length of an arc is called the length of its arc. In a chart, a chart arc is an adjacent pair of vertices. A semicircle is called an arc, whose endpoints lie on a circle diameter.

Therefore, the final answer is "Option C".

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To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.

To solve the system of linear equations:

6x + 20y = -62

3x - 9y = -12

We can use the method of substitution:

After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.

5 +12 = 17

153 /17 = 9

9*5 = 45 teachers

9*12 = 108 studets