Which point does NOT lie on the circle with center (0, 0) and radius 5?
A. (-3, -4)
B. (-3, 4)
C. (3, -4)
D. (5, 5)

Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x

Refer to the attachments for all solutions!!~

The dimensions of a given rectangle is 33m and 25 m.

Given that, one number is 13 more than another number.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

1) Let the smallest number be x.

Then, the largest number = x+13

So, x+x+13=37

⇒ 2x+13=37

⇒ 2x=24

⇒ x=12

Smallest number =12 and largest number = 25

2) let the unknown number be y

Now, 7-3x=19+3x

⇒ 6x=-12

⇒ x=-2

3) Let the three consecutive integers be x, x+1, x+2

x+x+2=-34

⇒ 2x=-36

⇒ x=-18

4) Let the length of a rectangle be l, then the width of rectangle w=l-8

So, perimeter = 2(l+w)

⇒ 116=2(l+l-8)

⇒ 2l-8=58

⇒ 2l=66

⇒ l=33 m

So, width=33-8=25 m

Therefore, the dimensions of a given rectangle is 33m and 25 m.

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

(a) x<=2

(b) x>-2

(c) x>=10

(d) x<-20

Answer:

B

Step-by-step explanation:

They all follow a sequence such as always add 4 or take 6 away some of them multiply so it is B because it does not follow the sequence

Answer:

42 students would be expected to pick an orange

Answer:

he will have 40 kg

Step-by-step explanation:

10:5=2

20 x 2 = 40

Answer:

A

Step-by-step explanation:

Answer:

\( \boxed{ - \frac{ - 4}{ - h} }\)

Answer:

\((x+1)(x-2)\)

Step-by-step explanation:

You can factor this by grouping.

\(x^2-x-2\)

\(\left(x^2+x\right)+\left(-2x-2\right)\)

\(x\left(x+1\right)-2\left(x+1\right)\)

\(\left(x+1\right)\left(x-2\right)\)

Answer:

0 degrees off center.

Step-by-step explanation:

To determine the degree off center and the overall speed of the ping pong ball, we need to consider the vector addition of the ball's velocity due to smashing and the velocity due to the crosswind. Let's break down the problem step by step:

Calculate the horizontal and vertical components of the ball's velocity due to smashing:

The initial velocity of the ball due to smashing is 60.0 km/h. Since the ball is smashed straight down the center line of the table, the vertical component of the velocity is 0 km/h, and the horizontal component is 60.0 km/h.

Calculate the horizontal and vertical components of the ball's velocity due to the crosswind:

The crosswind velocity is 25.0 km/h, and since it sweeps across the table parallel to the net, it only affects the horizontal component of the ball's velocity. Therefore, the horizontal component of the ball's velocity due to the crosswind is 25.0 km/h.

Determine the resultant horizontal and vertical velocities:

To find the overall horizontal velocity, we need to add the horizontal components of the velocities due to smashing and the crosswind:

Overall horizontal velocity = smashing horizontal velocity + crosswind horizontal velocity

Overall horizontal velocity = 60.0 km/h + 25.0 km/h = 85.0 km/h

Since the vertical component of the velocity due to smashing is 0 km/h and the crosswind does not affect the vertical component, the overall vertical velocity remains 0 km/h.

Calculate the resultant speed and direction:

To find the resultant speed, we can use the Pythagorean theorem:

Resultant speed = √(horizontal velocity^2 + vertical velocity^2)

Resultant speed = √(85.0 km/h)^2 + (0 km/h)^2) = √(7225 km^2/h^2) = 85.0 km/h

The ball ends up with an overall speed of 85.0 km/h.

Since the vertical velocity remains 0 km/h, the ball will not deviate vertically from the center line. Therefore, the ball will end up at the same height as the center line.

To determine the degree off center, we can calculate the angle of the resultant velocity using trigonometry:

Angle off center = arctan(vertical velocity / horizontal velocity)

Angle off center = arctan(0 km/h / 85.0 km/h) = arctan(0) = 0°

The ball will not deviate horizontally from the center line, resulting in 0 degrees off center.

The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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We have that:

then, in this case, we have:

therefore, the velocity of the cart is 0.9 meters per second.

The density of the gold sample is 19.3g/cm³

Let the mass of the gold sample be represented by m

m = 579 g

Let the volume of the gold sample be represented by V

V = 30 cm³

Let the density of the gold sample be represented by ρ

The formula for the density is:

\(Density = \frac{Mass}{Volume}\)

\(\rho = \frac{m}{V} \\\rho = \frac{579}{30} \\\rho = 19.3 g/cm^3\)

The density of the gold sample is 19.3g/cm³

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answer:

3x = y

step-by-step explanation:

૪・ i am inferring you have to create an equation?

・jenny have three times = 3x

・as her fav toys — 3x = y

・new toys = y

・fav toys = x

Answer:

x = 15

Step-by-step explanation:

150+3x-15=180 because of same-side interior angles therorem.

Then, we solve the problem to get 15.

Hope this helped! :)

Answer: 2.91666666667

Answer:

(2 1/3) : (4/5) = 35 /12 = 2 11 /12

1. You convert the mixed number (2 1/3) into an improper fraction which is 7/3.

2.Then you find a new numerator so you multiply the whole number (2) by the denominator (3) which is 6.

3 Add the answer (6) to the starting numerator (1). The new numerator equation: 6+1=7.

4.Write the new numerator (7) over the denominator (3)

Two and one seven third is seven thirds.

5. Then you divide: 7/3 : 4/5 = 7/3 * 5/4 = 7*5/ 3*4

6. Multiply (7 and 5) and (3 and 4) which gives you 35/12.

7.Then you transform it back into a mixed number by dividing 35/12 which gives you 2 11/12.

Answer:

90.24 divided by 6.3

Step-by-step explanation:

For reaching to the answer, we have to test each of the options given

The first option says that the divisor and dividend is 90.24 and dividend is 6.3

Now if we rounded it

So it would be 90 and 6

So, the quotient is

= 90 ÷ 6

= 15

Hence, the first option is correct

i.e. 90.24 divided by 6.3

And, all the other options are wrong

Answer:

4 and 6

Step-by-step explanation:

These are the points in which y=0

The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

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The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

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Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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The variable that is most likely to have a positive correlation with the number of swimsuits purchased is the temperature changing outside.

Correlation measures the relationship between two variables. When there is a positive correlation, it means that the two variables move in the same direction. If one of the variables increases, the other variable increases. If one of the variables decreases, the other variable decreases.

When it is summer, it is expected that the number of swimsuits bought would increase. When it is winter, it is expected that the number of swimsuits bought would decrease.

Here are the options:

A. The number of swimsuit cover-ups the store has in stock

B. The number of sand castles built by store customers

C. The temperature outside changing

D. The number of minutes it takes the store's employees to get to work

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Answer:

36.5x-53=543

Step-by-step explanation:

Answer:

7.5kilometer

Step-by-step explanation:

for 30mins semin runs 5kilometer

then for 1min: (1min×5kilometer)÷30mins,

therefore, for 45mins: (45mins×5kilometer)÷30mins=7.5kilometer

From the given information:

We are being informed that Samin can run for 5 kilometers in 30 minutes;

If Samin can run such a kilometer in 30 minutes;

5 kilometers = 30 minutes

∴

In x kilometers = 45 minutes

By cross multiplying;

(x × 30 minutes) = 5 kilometers × 45 minutes

30x = 225 kilometer/minutes

\(x = \dfrac{225 \ kilometer/minutes}{30 minutes}\)

\(\mathbf{x = 7.5 \ kilometers}\)

Therefore, we can conclude that the Samin can run 7.5 kilometers in 45 minutes.

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Answer:

40 years old

16 years old

Step-by-step explanation:

Son = 8 years old

his father is five times as old.

Father = 5 × 8

= 40 years

How old will the father be when he will be twice as old as his son?

Father = 2 × 8

= 16 years

Father:

Five times as old as son = 40 years old

Twice as old as his son = 16 years old

Answer:

Investment A = 3650

Investment B = 1350

Step-by-step explanation:

Given that:

Total interest earned = 332.50

Total Principal invested = 5000

Investment A:

Rate = 8%

Time = 1 year

Principal = a

Interest earned = 0.08a

Investment B:

Rate = 3%

Time = 1 year

Principal = b

Interest earned = 0.03b

a + b = 5000 ____(1)

0.08a + 0.03b = 332.50 - - - (2)

From (1)

a = 5000 - b

Into (2)

0.08(5000 - b) + 0.03b = 332.50

400 - 0.08b + 0.03b = 332.50

400 - 0.05b = 332.50

-0.05b = - 67.5

b = $1350

a = 5000 - b

a = 5000 - 1350

a = $3650

After solving the differential equation f ''(t) = 2et + 7 sin t to find function t we get f(t) = (1/3)et³ - 7 sin t + (1/3)e(π)³t.

We need to integrate the given second derivative twice with respect to t.

First, we integrate f''(t) with respect to t to obtain f'(t):

f'(t) = ∫(2et + 7 sin t) dt

= et^2 - 7 cos t + C1

where C1 is the constant of integration.

Next, we integrate f'(t) with respect to t to obtain f(t):

f(t) = ∫(et^2 - 7 cos t + C1) dt

= (1/3)et^3 - 7 sin t + C1t + C2

where C2 is the constant of integration.

Using the initial conditions f(0) = 0 and f(π) = 0,

we can solve for C1 and C2:

f(0) = (1/3)e(0)^3 - 7 sin 0 + C1(0) + C2 = 0

Therefore, C2 = 0

f(π) = (1/3)e(π)^3 - 7 sin π + C1(π) + C2 = 0

(1/3)e(π)^3 - C1 = 0

C1 = (1/3)e(π)^3

Therefore, the solution to the differential equation is:

f(t) = (1/3)et³ - 7 sin t + (1/3)e(π)³t.

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Assuming a poisson distribution, the probability of having at most 2 flaws in 450 square feet is approximately 0.062 or 6.2%.

For the probability of at most 2 flaws in 450 square feet, we can use the Poisson distribution.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events occur with a known average rate and independently of the time since the last event.

In this case, we are given that the average number of flaws in 150 square feet is two. Let's denote this average as λ (lambda).

We can calculate λ using the given information:

λ = average number of flaws in 150 square feet = 2

Now, let's find the probability of at most 2 flaws in 450 square feet. Since the area of interest is three times larger (450 square feet), we need to adjust the average accordingly:

Adjusted λ = average number of flaws in 450 square feet = λ * 3 = 2 * 3 = 6

Now we can use the Poisson distribution formula to find the probability. The formula is as follows:

P(X ≤ k) = e^(-λ) * (λ^0 / 0!) + e^(-λ) * (λ^1 / 1!) + e^(-λ) * (λ^2 / 2!) + ... + e^(-λ) * (λ^k / k!)

In this case, we need to calculate P(X ≤ 2), where X represents the number of flaws in 450 square feet and k = 2. Plugging in the values, we get:

P(X ≤ 2) = e^(-6) * (6^0 / 0!) + e^(-6) * (6^1 / 1!) + e^(-6) * (6^2 / 2!)

Calculating each term:

P(X ≤ 2) = e^(-6) * (1 / 1) + e^(-6) * (6 / 1) + e^(-6) * (36 / 2)

Now, let's calculate the exponential term:

e^(-6) ≈ 0.00248 (rounded to five decimal places)

Substituting this value into the equation:

P(X ≤ 2) ≈ 0.00248 * 1 + 0.00248 * 6 + 0.00248 * 18

Calculating each term:

P(X ≤ 2) ≈ 0.00248 + 0.01488 + 0.04464

Adding the terms together:

P(X ≤ 2) ≈ 0.062 (rounded to three decimal places)

Therefore, the probability of having at most 2 flaws in 450 square feet is approximately 0.062 or 6.2%.

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A Linear Equations Digital Escape Puzzle is an engaging activity that incorporates technology and encourages students to use their problem-solving skills to solve linear equations.

What are Linear Equations?

Linear equations are mathematical expressions in which each term is either a constant or a variable raised to the power of 1.

Linear equations are a type of equation that appears in the form of y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope, and b represents the y-intercept.Digital Escape PuzzleA digital escape puzzle is a type of activity in which students use technology to solve puzzles and escape rooms in order to progress through a digital game or learning activity.

Linear Equations Digital Escape PuzzleA linear equations digital escape puzzle is an interactive activity that requires students to solve linear equations in order to progress through a digital escape room or puzzle game. Students must use their problem-solving abilities to determine the slope and y-intercept of various equations, and then use those values to plot points and create graphs.

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The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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