Which one I'll give stars or points

Answer:

Correct!

Step-by-step explanation:

You did it the correct mathematical way, where you divide 4 by 30. Some people get confused and multiply 30 and 4, so good job!

Answer:

Step-by-step explanation: 4÷30=7.5 D = 7.5

The total bill was 520 pesos when the 4 people share the total bill and pay 130 pesos each.

Given data:

Bill paid by each = 130pesos,

Number of people = 4

We have to translate the problem into an equation. Let's assume that the total bill is x. There are a total of 4 people dividing the restaurant bill, Mike and his three friends. Since each of them paid 130 pesos, we need to multiply 130 by the total number of persons involved, we can write the equation as:

x/4 = 130

x = 4 × 130

x = 520

Therefore, the total bill was 520 pesos.

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The value of the rationalization is 5√2

Surds are described as the nth root of a number, say x and a  number r which, when raised to the power n

Given that;

n is a positive integer or  the degree of the root.

It is also seen as an expression that includes a square root, a cube root or other roots.

They are used to write irrational numbers only.

Given the surds;

10/√2 × √2/ √2

Multiply the values

10√2/2

Divide the values

5√2

Hence, the value is 5√2

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The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.

Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.

Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.

The velocity of a particle is modeled by the function;

v(t) = ¹/₁₀(3t - 8)³ + 2

The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.

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Using the area of a rectangle, the total floor area to be tiled = area of the dinning room + area of the lounge floor = 32 m²

The area of rectangle = (length)(width).

Total floor area to be tiled = area of the dinning room + area of the lounge floor

Total floor area to be tiled = (4)(5) + (3)(4)

Total floor area to be tiled = 20 + 12

Total floor area to be tiled = 32 m²

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The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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a) the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

a) To find the probability that a randomly selected Cobalt gets more than 34 MPG, we need to calculate the area under the normal distribution curve to the right of 34 MPG.

Using the z-score formula, we can convert the MPG value to a standard score (z-score) using the formula:

z = (x - μ) / σ,

where x is the given value (34 MPG), μ is the mean (32 MPG), and σ is the standard deviation (3.5 MPG).

Calculating the z-score:

z = (34 - 32) / 3.5 = 0.57

Using a standard normal distribution table or a statistical calculator, we can find the area to the right of the z-score 0.57.

Let's assume the standard normal distribution table gives us a value of 0.2851 for z = 0.57.

Since the total area under the normal curve is 1, the probability of getting more than 34 MPG is:

P(X > 34) = 1 - P(X ≤ 34) = 1 - 0.2851 = 0.7149

Therefore, the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) When selecting a sample of 10 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√10).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √10 ≈ 1.107

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 10 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

We can again convert the value of 34 MPG to a z-score:

z = (34 - 32) / 1.107 ≈ 1.805

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 1.805.

Let's assume the standard normal distribution table gives us a value of 0.035 for z = 1.805.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) When selecting a sample of 20 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√20).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √20 ≈ 0.78

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 20 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

Similarly, we can convert the value of 34 MPG to a z-score:

z = (34 - 32) / 0.78 ≈ 2.564

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 2.564.

Assuming the standard normal distribution table gives us a value of 0.005 for z = 2.564.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

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Answer:

\(y - 3 = - 4(x + 2)\)

true

Step-by-step explanation:

it's at an equal distance

The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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The contrapositive of this statement would be: "If x does not equal -4, then 5x + 7 will not equal to -13."

The contrapositive is defined as the inverse and converse of a conditional statement.

X is equal to 4 we know this is because the sign in between the number means greater than or equal to so 3 x 4 equals 12 which makes the equation on right true and on the left x.

So, the contrapositive of this statement would be:

"If x does not equal -4, then 5x + 7 will not equal to -13."

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Answer:

The Probability of P(X = 3) = 0.333

P(X=3) we need to use the following formula:  

P(X = 3) = f(3)

where f(3) is the probability mass function at 3.

As there are only three values possible, X is a discrete random variable with probability mass function f(x) given by:

f(0) + f(3) + f(9) = 1

Mean(X) = 3f(0)*0 + f(3)*3 + f(9)*9 = 3. ------ equation (1)

Variance(X) = E(X2) - [E(X)]2

Where E(X2) = f(0)*02 + f(3)*32 + f(9)*92 = 6 + 81*f(0) + 81*f(9)  (since X can take only three values)

Substituting given values in the above equation, we get:

6 + 81f(0) + 81f(9) - 32 = 6 ----- equation (2)

Substituting the values of (1) and (2), we get:

f(0) = 4/9 and f(9) = 1/9

Now we can get the value of f(3):

f(0) + f(3) + f(9) = 1.

Using f(0) = 4/9 and f(9) = 1/9, we get f(3) = 4/9 - 1/9 = 1/3

So, P(X = 3) = f(3) = 1/3

Therefore, P(X = 3) = 0.333 (rounded up to 3 decimal places)

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Answer:

GJI = 242.67

Step-by-step explanation:

A circle is 360 degrees

GI + GJI = 360

The arc length is the same as the angle when it is at the center

117.33 + GJI = 360

GJI = 360 - 117.33

GJI = 242.67

Answer:

GJI = 242.67

Step-by-step explanation:

GI + GJI = 360

117.33 + GJI = 360

GJI = 360 - 117.33

GJI = 242.67

Answer:

The correct answer is C: Y = -1/2x - 4.The slope of the given line is -1/2, so any line that is parallel to it will have the same slope. In order to find the equation of a line with the same slope that passes through the point (2, -5), we can use the point-slope form of the equation of a line.The point-slope form of the equation of a line is:y - y1 = m(x - x1)where m is the slope of the line, and (x1, y1) is a point on the line.In this case, we can plug in the values m = -1/2, x1 = 2, and y1 = -5 to get:y + 5 = -1/2(x - 2)Solving for y, we get:y = -1/2x - 4Therefore, the equation of the line that is parallel to the given line and passes through the point (2, -5) is Y = -1/2x - 4.

The magnitude of the acceleration of the speck of clay on the edge of the potter's wheel is approximately 4.85 meters per second squared.

To find the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel, we need to determine the angular velocity of the wheel first.

The angular velocity (ω) can be calculated using the formula:

ω = 2πf

Where f is the frequency of rotation in revolutions per second. In this case, the frequency is 51 rpm, which can be converted to revolutions per second by dividing by 60:

f = 51 rpm / 60 = 0.85 revolutions per second

Now we can calculate the angular velocity:

ω = 2π * 0.85 = 5.36 radians per second

The linear velocity (v) of the speck of clay on the edge of the wheel can be calculated using the formula:

v = ωr

Where r is the radius of the wheel. Since the diameter is given as 34 cm, the radius is half of that:

r = 34 cm / 2 = 17 cm = 0.17 meters

Now we can calculate the linear velocity:

v = 5.36 radians per second * 0.17 meters = 0.91 meters per second

Finally, the magnitude of the acceleration (a) can be calculated using the formula:

a = v^2 / r

Plugging in the values:

a = (0.91 meters per second)^2 / 0.17 meters = 4.85 meters per second squared

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Answer:

D is the correct graph

Step-by-step explanation:

You can plug in points on the graph to check which one works or graph it and compare to those graphs

Answer:

The answer should be D

Hope that helps!

Answer:

110° and 215°

Step-by-step explanation:

the bearing of one point to another is the measure of the clockwise angle from the north line N at the point C to the point D , that is

(a)

bearing of D from C is 110° ( purple shaded angle )

(b)

the bearing of D from C is 215° ( blue shaded angle )

The value of x is 42.

To determine the value of x, we need to analyze the given information regarding the scale factor between Figure A and Figure B.

The scale factor is expressed as the ratio of the corresponding side lengths or dimensions of the two figures.

Let's assume that the length of a side in Figure B is represented by 'x'. According to the given information, Figure A is a scale copy of Figure B with a scale factor of 2/7. This means that the corresponding side length in Figure A is 2/7 times the length of the corresponding side in Figure B.

Applying this scale factor to the length of side x in Figure B, we can express the length of the corresponding side in Figure A as (2/7)x.

Given that the length of side x in Figure B is 12, we can substitute it into the equation:

(2/7)x = 12

To solve for x, we can multiply both sides of the equation by 7/2:

x = (12 * 7) / 2

Simplifying the expression:

x = 84 / 2

x = 42

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There are 12 elements in\($(z \times z) \mid\langle(2, b)\rangle$\)Clearly, \($(0,1)+\langle(2,6)\rangle$\) has order 6 . Thus, group is isomorphic to \($z_2 \times z_6$\) or \($z_{12}$\)

Well, it is not \($\mathbb{Z}$\). What is the order of (the coset)\($[(0,1)]$\) ?

You don't need the fundamental theorem at all. What you need is the following: if \($G, G^{\prime}$\) are groups and \($N \subseteq G, N^{\prime} \subseteq G^{\prime}$\) are normal subgroups then \($N \times N^{\prime}$\) is normal in \($G \times G^{\prime}$\)and

\($$\left(G \times G^{\prime}\right) /\left(N \times N^{\prime}\right) \simeq(G / N) \times\left(G^{\prime} / N^{\prime}\right)$$\)

With that you can easily check that \($\langle(0,3)\rangle=\{0\} \times 3 \mathbb{Z}$\) and so your group is \($\mathbb{Z} \times \mathbb{Z}_3$\).

Thus, there are 12 elements in\($(z \times z) \mid\langle(2, b)\rangle$\)Clearly, \($(0,1)+\langle(2,6)\rangle$\) has order 6 . Thus, group is isomorphic to \($z_2 \times z_6$\) or \($z_{12}$\)

But, no elements have order 12. Thus, group is not cyclic.

Thus, it is isomorphic to \($z_2 \times z_6$\)

\((z \times z) /\langle(2,6)\rangle \cong z_2 \times z_6$$\)

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Answer:

y= 12/5

Step-by-step explanation:

Answer :

C

Explanation :

Answer:

1. 35 pages in 7 days

2. 63 pages in 9 tables

3. 408 student on 8 buses

Step-by-step explanation:

Answer:

If DE// to BC, slope of DE= slope of BC

D=(\(\frac{4+2}{2} ,\frac{6-2}{2}\))

D=(3,2)

E=(\(\frac{4-2}{2} ,\frac{6-4}{2}\))

E=(1,1)

Slope of DE=\(\frac{2-1}{3-1} =\frac{1}{2}\)

Slope of BC=\(\frac{-2-(-4)}{2-(-2)} =\frac{1}{2} =\)Slope of DE

∴DE // to BC.

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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Answer:

Step-by-step explanation:

x^2-9x+20

(x-5)(x-4)

Because -4 and -5 multiplied will make the 20 and added will be -9

Answer:

A

Step-by-step explanation:

I uploaded the of explanation

Answer:

n = 24

Step-by-step explanation:

16+ n/4 =22

Subtract 16 from each side

16-16+ n/4 =22-16

n/4 = 6

Multiply each side by 4

n/4*4 = 6*4

n = 24

Answer:

the answer is 520 I think

Answer:

520

Step-by-step explanation:

Answer;

i=-7

Step-by-step explanation;

TBH we have all we need its given to us in the question, divide both sides by the same amountt

9i=-63

divide by 9 to leave i alone

the one step equation is solved

Answer:

\( \sf \: i = - 7\)

Step-by-step explanation:

Now we have to,

→ find the required value of i.

The equation is,

→ 9i = -63

Then the value of i will be,

→ 9i = -63

→ (9i) ÷ 9 = (-63) ÷ 9

→ (i) = (-7)

→ [ i = -7 ]

Hence, the value of i is -7.

We can write the the area of the trapezoid as 132 square inches.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a trapezoid that has been divided into two right triangles and a rectangle.

We can write the area of the trapezoid as -

A{trapezoid} = 2 x Area{Δ} + Area{Rectangle}

A{trapezoid} = 2 x 1/2 x 3 x 12 + 12 x 8

A{trapezoid} = 36 + 96

A{trapezoid} = 132 square inches

Therefore, we can write the the area of the trapezoid as 132 square inches.

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