There are 25 students in a class 36 of the students ate hotdogs for lunch now many students ate hot dogs

well, there are 10 years in 1 decade, so 8.7 decades will just be 8.7*10 = 87 years, so

\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &230\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &87\\ \end{cases} \\\\\\ A=230(1 - 0.07)^{87}\implies A=230(0.93)^{87}\implies A\approx 0.42\)

If a sample of 32 runners is taken from a population of 201, the mean is equal to 201.

In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.

In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.

In this context, we can reasonably infer and logically deduce that the mean (μ) could be equal to 201 runners because it represent the average.

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Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

Answer:C

Step-by-step explanation:

I took the test

Answer:

C

Step-by-step explanation:

The types of cars sold in the two months typically get about the same gas mileage.

Answer:

Step-by-step explanation:

The height is 6 units.

The radius is 8 units.

The volume is 128 π cubic units.

If the width of a rectangle with perimeter P is 6 units, its length would be equal to L = P/2 - 6.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + 6)

P = 2L + 12

P - 12 = 2L

L = (P - 12)/2

L = P/2 - 6.

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Answer:

Opal saves more

Step-by-step explanation:

Answer:

she has 16 correct answer

Step-by-step explanation:

Mathematically ,we can translate this word problem into this system of equations :

\(\begin{cases}5x-2y=72&\left( 1\right) \\ x+y=20&\left( 2\right)\end{cases}\)

\(\Longleftrightarrow \begin{cases}5x-2y=72&\left( 1\right) \\ 2x+2y=40&2\times\left( 2\right)\end{cases}\)

\(\Longleftrightarrow \begin{cases}7x=72+40=112&\left( 1\right)+2\times(2) \\ x+y=20&\left( 2\right)\end{cases}\)

\(\Longleftrightarrow \begin{cases}x=\frac{112}{7}=16 \\ y=20-x=20-16=4&\left( 2\right)\end{cases}\)

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:

Step-by-step explanation:

Harry winston dillan paul

By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.

In this triangle we know the length of a side (b = 13) and the measure of two adjacent angles (A = 57°, C = 73°). First, we determine the measure of the missing angle by using triangles properties:

B = 180° - 57° - 73°

B = 50°

Lastly, we determine the missing lengths by the law of the sines:

\(a = 13 \times \frac{\sin 57^{\circ}}{\sin 50^{\circ}}\)

a ≈ 14.232

\(c = 13 \times \frac{\sin 73^{\circ}}{\sin 50^{\circ}}\)

c ≈ 16.229

By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.

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Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Step-by-step explanation:

sutract 5a -3b +2b from a-4b -2c

a-4b-2c-(5a-3b+2b)

a-4b-2c-5a+3b-2b

a-5a-4b+3b-2b-2c

-4a-4b+b-2c

-4a-3b-2c

-(4a+3b+2c)

Answer:

solving a system of equations using graphing is not a useful solution technique because you are plotting on a 2D surface. For example, if you graph the system below, you get the following graph. ... While you can approximate the solution to this system, you cannot say exactly where the intersection point is since it does not fall on integer values on the number lines.

Answer:

\(CE = \boxed{17}\\\\m\angle ECB = \boxed{52}^\circ\)

Step-by-step explanation:

The diagonals of a rectangle bisect each other and are also of equal length

This means in the given rectangle ABCD with AC and BD as diagonals,

the following hold true:
AE = CE = 2x + 1

AC = 2(AE) = 2(2x + 1) = 4x + 2

BD = 3x + 10

Therefore since the diagonals are equal,

AC = BD
→  4x + 2 = 3x + 10
→  4x - 3x = 10 - 2
→  x = 8

CE = 2x + 1 = 2(8) + 1 = 17

BD = 3x + 10 = 3(8) + 10 = 24 + 10 = 34

BE = 1/2 BD= 1/2 (34) = 17

ΔBEC is an isosceles triangle with BE = CE and therefore ∠EBC = ∠ECB

The angles of a rectangle are 90°
We are given m∠EBA = 28°

So m∠EBC = 90 - 28 = 52°

m∠ECB = m∠EBC

m∠ECB  is also 52°

The centre and the radius of the circle is (-7, -1) and 6 units

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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Answer: $ 1302.56

Step-by-step explanation:

First find her income per hour. It says for every hour she earns $12.75 so in 45 hours, she will earn 12.45 time 45.

12.75 * 45 = 573.75  

This means she made $573.75 in 45 hours.

Now we have to find out how much she earns on commission on sales.

To find that multiply 5.75% by the total sales .

5.75% * 12675 = 728.81  

now add $573.75 and $728.81  to find her total income or how much she end that week.

$573.75  +  $728.81   = 1302.56

Answer:

loser you called me a bad word so now I'm taking points

Step-by-step explanation:

(a) We want to find a scalar function \(f(x,y,z)\) such that \(\mathbf F = \nabla f\). This means

\(\dfrac{\partial f}{\partial x} = 2xy + 24\)

\(\dfrac{\partial f}{\partial y} = x^2 + 16\)

Looking at the first equation, integrating both sides with respect to \(x\) gives

\(f(x,y) = x^2y + 24x + g(y)\)

Differentiating both sides of this with respect to \(y\) gives

\(\dfrac{\partial f}{\partial y} = x^2 + 16 = x^2 + \dfrac{dg}{dy} \implies \dfrac{dg}{dy} = 16 \implies g(y) = 16y + C\)

Then the potential function is

\(f(x,y) = \boxed{x^2y + 24x + 16y + C}\)

(b) By the FTCoLI, we have

\(\displaystyle \int_{(1,1)}^{(-1,2)} \mathbf F \cdot d\mathbf r = f(-1,2) - f(1,1) = 10-41 = \boxed{-31}\)

\(\displaystyle \int_{(-1,2)}^{(0,4)} \mathbf F \cdot d\mathbf r = f(0,4) - f(-1,2) = 64 - 41 = \boxed{23}\)

\(\displaystyle \int_{(0,4)}^{(2,3)} \mathbf F \cdot d\mathbf r = f(2,3) - f(0,4) = 108 - 64 = \boxed{44}\)

Answer:

895

Step-by-step explanation:

1 cm = 0.01 m

Just move the decimal 2 times to the right to get your answer. Can I get your Fortnite username? Thanks! It's fine if you don't want to, I like Fortnite, too! XD hope this helps!

8.95 meters = 895 centimeters

Formula: multiply the value in meters by the conversion factor '100'

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Step-by-step explanation:

The candidates are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

6 candidates, which means that \(N = 6\)

2 are the aunt and father, which means that \(k = 2\)

3 are chosen, which means that \(n = 3\)

What is the probability that either your aunt or your father will become a city commissioner?

Probability of at least one of them being chosen, which is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,6,3,2) = \frac{C_{2,0}*C_{4,3}}{C_{6,3}} = 0.2\)

Then

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8\)

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

Answer:

4

Step-by-step explanation:

When x = 5, y = 4, meaning that g(5)=4.

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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