Find the length of the arc. Use 3.14 for the value of 7. Round your answer to the nearest tent
10 km
90°

The Molar mass = 2. 9 ×10⁻⁷ g/mol

The general ideal gas law is written as;

PV = nRT

such that the parameters of the formula are expressed as;

Now, substitute the values, we have;

0. 005 × 0. 01 = n ×8.314 ×296.25

Multiply the values, we have that;

n = 2.2 ×10⁻⁸mol

Then, we have that;

n = mass/molar

2.2 ×10⁻⁸/0. 075 = molar mass

Divide the values

Molar mass = 2. 9 ×10⁻⁷ g/mol

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

D is 107 and E is 38

Step-by-step explanation:

20x+40=180

20x=140

X=140/20

x=7

M<A=5(7)+3

38

m<a=m<e

15(7)+2

107

m<b=m<d

Answer:

\(\frac{48}{13}\approx 3.7\)

Step-by-step explanation:

Two triangles are similar by AAA ( Angles B and B' are right angles, the two angles in C are congruent because opposite by the vertex, and the third by difference). Corresponding sides are in proportion. In particular \(x:6=8:13 \leftrightarrow 13x=6\cdot8 \rightarrow x = \frac{48}{13} \approx 3.7\)

After change into inches per second, the number is,

= 16.8 inches per second.

We have to given that;

To convert 14 yards per minute to inches per second.

Since, We know that;

1 yards = 36 inches

1 minutes = 60 seconds

Hence, We can change as;

= 14 yards per minute

= 14 x 36 / 30 inches per second.

= 504/ 30 inches per second.

= 16.8 inches per second.

Thus, After change into inches per second, the number is,

= 16.8 inches per second.

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Answer:1024 grid squares

Step-by-step explanation:

Let's call the side length of the original piece of graph paper "x".

Since, side length of the cut out square is then (x-2) because the cut out square has to have an integer number of grid squares, and each side of the square would take up 2 grid squares on the graph paper.

The number of grid squares in the cut out square is then (x-2)^2.

The number of grid squares left on the graph paper is 124, so we have:

x^2 - (x-2)^2 = 124

Expanding the right side:

x^2 - x^2 + 4x - 4 = 124

Simplifying:

4x = 128

therefore:

x = 32

therefore original graph paper contains 32 grids i.e 32^2 = 1024

Answer:

  any of {128, 133, 140, 160, 224, 320, 380, 700, 1024}

  1024 if the original grid was square

Step-by-step explanation:

You want to know how many grid squares are on a piece of graph paper if a square number of grid squares can be cut from it to leave 124 grid squares.

If the graph is square to begin with, a square of x² can be removed from its size (x+a)² to leave 124 squares. That is ...

  (x +a)² -x² = 124

  (a)(2x+a) = 124

The factor pairs of 124 are ...

  124 = 1·124 = 2·62 = 4·31

Of these, only 2 and 62 differ by an even number, so we have a=2 and x=30.

The graph paper could be 32 units square originally, having 1024 grid squares.

There is nothing in the problem statement that requires the original graph paper be square. If it is not necessarily square, there are 13 possible shapes it could be. Those have 9 different possibilities for numbers of grid squares.

The graph paper could have originally had this number of grid squares:

__

Additional comment

You may notice that removing a 24×24 square from a graph that is 25×28 leaves no border on one side.

These values were found using a search script.

<95141404393>

The weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5. The correct option is A.

We know that the formula to calculate the weighted average is: weighted\ average=\frac{w_1x_1+w_2x_2+...+w_nx_n}{w_1+w_2+...+w_n} Where, $x_1,x_2,..x_n$ are the values, and $w_1,w_2,...,w_n$ are the weights. To find the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number, we substitute the values in the above formula as follows.

Weighted\ average=\frac{\frac{2}{3}\times 1+\frac{1}{3}\times 6}{\frac{2}{3}+\frac{1}{3}}\implies weighted\ average=\frac{\frac{2}{3}+2}{1}\implies weighted\ average=\frac{8}{3}\implies weighted\ average=2.67 approx 3.5 Therefore, the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5.

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Answer:

The 8-year-old car could be worth approximately $4500.

Step-by-step explanation:

answer on edge 2020

Answer:

C.the 8 year old car can be worth about 3000 just look at the graph

Step-by-step explanation:

#happycheating

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Take note that Bus 18 is the most reliable in terms of trip times among the line plots shown above. With our understanding of the interquartile range, we can solve this. (IQR)

We must compare the metrics of data variability in order to identify the bus that consistently produces the best accurate results. Range and interquartile range are the metrics of variability that we can utilise in this situation (IQR).

The IQR is the difference between the third quartile (Q3) and the first quartile, whereas the range is the difference between the highest and lowest values in the data set (Q1). Because it is less impacted by extreme values than the range, the IQR provides a more accurate indicator of variability.

Using the given data, we can calculate the range and IQR for each bus:

Bus 47:

Range = 28 - 4 = 24

Q1 = 10, Q3 = 22

IQR = 22 - 10 = 12

Bus 18:

Range = 22 - 6 = 16

Q1 = 9, Q3 = 25

IQR = 25 - 9 = 16

According to these findings, Bus 18 has a narrower range and a higher IQR than Bus 47. The IQR, a more accurate indicator of variability in this situation, reveals that Bus 18's trip times are less variable than those of Bus 47's. Hence, we can say that when it comes to trip times, Bus 18 is the most reliable.

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Answer:

B x = 3 or -12

Step-by-step explanation:

(btw this / is a fraction sign and this ^ is the power of sign)

Let's solve your equation step-by-step.

x^2+9x−36=0

For this equation: a=1, b=9, c=-36

1x^2+9x+−36=0

Step 1: Use quadratic formula with a=1, b=9, c=-36.

x= −b±√b^2−4ac/2a

x= −(9)±√(9)2−4(1)(−36)/2(1)

x= −9±√225/2

= x= 3 or x= -12

Answer:

The square root of 144 will be 12

Answer:

12 is the answer

Step-by-step explanation:

12x12=144

The value of y in the triangle is 10 and option B is the correct answer.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilise the sine function.

The sine function for any right triangle with an angle, let's say ABC, will be:

Sin A = Opposite/hypotenuse

For the given right angled triangle let us consider the trigonometric function sin (60).

Here,

Sin 60 = 5√3 / y

√3/2 = 5√3 / y

y = 2(5√3)/√3

y = 10

Hence, the value of y in the triangle is 10 and option B is the correct answer.

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To find the approximate length of the diameter, d, we need to use the formula for the circumference of a circle, which is C = πd, where C is the circumference and π is approximately 3.14.

First, we need to determine the circumference of the circle. Let's say the circumference is given as 100 centimeters.

Using the formula, we can rewrite it as 100 = 3.14d.

To find the approximate length of the diameter, we need to isolate d. Divide both sides of the equation by 3.14: 100/3.14 = d.

Using a calculator, we get approximately 31.847 centimeters for d.

Rounding to the nearest tenth of a centimeter, the approximate length of the diameter, d, is 31.8 centimeters.

In conclusion, the approximate length of the diameter, d, is 31.8 centimeters.

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1. The multiples of 3 are 30, 60, and 90.

2. The probability is 3/8, as there are 3 multiples of 3 out of 8 total numbers on the spinner.

3.  the expected number of spins showing a multiple of 3 is (3/8) * 80 = 30.

To determine how many spins are expected to show a multiple of 3, we need to follow these steps:

1. Determine which numbers on the spinner are multiples of 3:

The numbers on the spinner are consecutive multiples of 10, beginning with 20. To find the multiples of 3, we need to look for numbers that are divisible by 3. Starting from 20, we have 20, 30, 40, 50, 60, 70, 80, and 90. Out of these numbers, the multiples of 3 are 30, 60, and 90.

2. Determine the probability of a spin showing a multiple of 3:

Since the spinner has 8 equally sized regions, the probability of spinning a multiple of 3 is the number of favorable outcomes (multiples of 3) divided by the total number of possible outcomes. In this case, the probability is 3/8, as there are 3 multiples of 3 out of 8 total numbers on the spinner.

Use the probability to find how many spins out of 80 will result in a multiple of 3:

3. To find the expected number of spins that will result in a multiple of 3, we multiply the probability by the total number of spins. Therefore, the expected number of spins showing a multiple of 3 is (3/8) * 80 = 30.

In conclusion, based on the given information, we can expect around 30 out of the 80 spins to show a multiple of 3 on the spinner.

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Answer:

Try math-way. It gives you the answers for equations, and so much more in algebra.

Step-by-step explanation:

The expression 8(x+4) is a product between 8 and (x+4), which is a number (8) and a sum.

Then, it correspond to Option B: The product of a number and a sum.

The angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.

In given triangles ABC and PQR,

∠ABC ≅ ∠PQR

BC ≅ QR

∠BCA ≅ ∠QRA

so, by ASA Congruence theorem ΔABC ≅ ΔPQR

Therefore, the angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

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Answer:

10x larger

The is like 300 something and Canada is 30 something

The number of sharks found between 76 m depth and 100 m depth is 2.04 shark's population.

The number of sharks found at different depths is calculated as follows;

From the histogram, the population of the fish at depth between 76 m and 100 m can be read off by tracing the depth values towards the frequency axis;

at depth 76 m, the frequency = 1.5

at depth 100 m, the frequency = 0.54

Total number of fish between the depths = 1.5 + 0.54 = 2.04

Thus, this value represents the density of the sharks between 76 m and 100 m.

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The cost of ordering 22 solder-less lugs at the list price less 35% will be $101.20.

Solder-less lugs are priced at $4.25 each, including a 40% discount when purchased in standard packages of 100. To find the original price without the discount, we'll first calculate the price before the 40% discount:

$4.25 / (1 - 0.40) = $4.25 / 0.60 = $7.08 (rounded to 2 decimal places)

Now, if you only need 22 solder-less lugs and are eligible for a 35% discount, we'll calculate the discounted price for each lug:

$7.08 * (1 - 0.35) = $7.08 * 0.65 = $4.60 (rounded to 2 decimal places)

Finally, to find the total cost for 22 solder-less lugs with a 35% discount, we'll multiply the discounted price by the quantity ordered:

$4.60 * 22 = $101.20

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The term "Additional" specifies the additional number of users within the same household that can be included for $3 per month.

A music-streaming service charges $9 per month for a single user. Additional users within the same household can be added for $3 per month. Here, the term "Additional" refers to the extra number of users that can be added with a monthly subscription charge of $3 for the music streaming service. Hence, the term "Additional" specifies the additional number of users within the same household that can be included for $3 per month.

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The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

Karen buys a pack of bottles of water. = 8

Karen sells all 8 bottles of water for rupees =  50p each

=  50p/100 each

= 0.5 rupees

Total rupees for 8 bottles = 8 x 0.5 = 4

The pack costs  = 1.25

Profit % = (Profit / C.P.) × 100

Profit = SP - CP

=  4 - 1.25

= 2.75

then using these values in equation we get :

profit = \(\frac{4 - 1.25}{1.25} * 100\)

profit = (2.75/1.25 )x 100

profit = 2.2 x 100 = 220

profit = 220%

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

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The expression for the product of 2 and the difference of a number and 5 is 2x - 10

An algebraic expression can simply be defined as mathematical expressions that are composed of terms, variables, coefficients, factors and constants

These expressions also known to be made up of various mathematical or arithmetic operations, such as;

From the information given, we have;

The product of 2 and the difference of a number and 5.

Let the number be x

This can be represented thus;

2(x- 5)

expand the bracket, we have;

2x - 10

Hence, the expression is 2x - 10

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Complete question:

Write the expression for

Answer:

Step-by-step explanation:

Givens

m = 1/4

y2 = 4

y1 = 1

x2 = 2

x1 = x

m = (y2 - y1) / (x2 - x1)

Solution

1/4 = (4 - 1) / (2- x)                Simplify

1/4 = 3 / (2 - x)                      Cross multiply

2- x =12                               Subtract 1 from both sides

-x = 12 - 2

-x = 10                                 Multiply by -1

x = -10

Check

1/4 = (4 - 1) / (2 - - 10)

1/4 = 3/(2 + 10)

1/4 = 3 / 12

1/4 = 1/4

Odd as the answer is, it does check.

Answer:

Step-by-step explanation:

Given:

The composite function f · g(x) is:

Restrictions are:

and

Combination of the above gives us the domain:

Correct choice is D

The slope of the line represents the rate of change between the independent variable (number of available staff) and the dependent variable (number of available staff) (wait time).

The slope of the line in this case is -1.62, which means that for every one unit increase in the number of staff available, the wait time decreases by 1.62 units.

In this case, a negative slope indicates that as the number of staff available increases, so does the wait time, indicating a positive relationship between the two variables. In other words, as the number of employees available increases, the wait time decreases.

It is important to remember that the equation models this relationship, and that actual wait times in the real world may not always follow this exact relationship due to other factors that influence wait times.

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Answer:

y= 4.3(4)^x

Step-by-step explanation:

I went to the Desmos Graphing calculator

I then inserted a table and added the two points you gave me to it

I then performed exponential regression to find the rate of change and y-intercept.

I then took the the two values and wrote the equation

A=y-intercept

B=rate

Answer: 45,28,13

Step-by-step explanation:

Firstly let’s call integer 3

‘x’

Following the information given the following equations can be constructed:

integer 3 = x

integer 2 = 2+2x because 2x represents 2 times integer 3 (which is x) and plus two

integer 1 =3((2x+2)-x) what we have written is the difference between integer 2 (which was (2x+2)) and integer 3 which was x and simply multiply the result of that subtraction by 3

next we can treat them like their own variables almost.

integer 1 + integer 2 + integer 3 =86

so now plug in the equations we have constructed for each integer:

(3((2x+2)-x)) + (2x+2) + x = 86

to make it easier to read please see the image attached below to solve for x

After you have gone through the image I have included you should notice x= 13 great we got one integer! (Integer 3)

now plug in 13 into our integer equations :

integer 2: 2(13)+2= 28

Therefore integer 2 is 28

integer 1: 3((2(13)+2)-(13))=
3((28-13)

3(15)

45

Therefore integer 1 is 45.

and integer 3 is x which as we now know is equal to 13