Question 1
1 pts
Two bottled waters and three bags of chips cost $4.75, One bottled water and two bags
of chips cost $2.75.How much do the chips cost?
(write answer without dollar sign, ex: $3.25 becomes 3.25)

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

x = 2

Step-by-step explanation:

3x + 4 - x = 8

Combine like terms

2x + 4 = 8

-4 from both sides

2x = 4

Divide by 2

x = 2

Answer:

x=4

Step-by-step explanation:

Add 4 to both sides of the equation

3x=8+4

add 8 and 4

3x=12

Divide each term in 3 x = 12 by 3.

3x/3 = 12/3

Cancel the common factor.

3x/3 = 12/3

Divide x by 1.

x = 12/3

 Divide 12 by 3.

Answer: 7 weeks

Step-by-step explanation:

It would take Kendall and Asa 7 weeks to have the same amount of money.

Let x represent the number of weeks and y represent the total money saved by Kendall. Since she has $50 and save $10 every week, hence:

y = 10x + 50.

Let x represent the number of weeks and z represent the total money saved by Asa. Since she has $15 and save $15 every week, hence:

z = 15x + 15

The number of weeks that it would take Kendall and Asa to have the same amount of money is:

y = z

10x + 50 = 15x + 15

5x = 35

x = 7

Hence it would take Kendall and Asa 7 weeks to have the same amount of money.

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Step-by-step explanation:

remember, the area of a whole circle (360°) is

pi×r²

r being the radius (half is the diameter).

so in circle B the radius is 48/2 = 24 meters.

the shaded area (with the 90° angle or "right angle") represents only a part of the whole circle : 90° out of the total of 360°.

so, the area is

pi×24²×90/360 = pi×576/4 = pi×144 = 452.3893421... m²

≈ 452.4 m²

for the question about circle P and the segment AB I don't have any graphic or so. but the answer is general :

since a whole circle is 360°, then a half-circle (the arc between the endpoints of the diameter) represents 360/2 = 180°.

about the circle A

remember the circumference of a whole circle (360°) is

2×pi×r

so, in our case r = 15 in

and we don't need the length of the full circumference but only of 110° out of the total of 360°.

so,

LG = 2×pi×15×110/360 = 2×pi×110/24 = pi×110/12 =

= pi×55/6 = 28.79793266... in

≈ 28.8 in

for the circle R

the angle J is the angle UJN = 28°.

this is per rule of inscribed angles half the arc angle URN.

so, the angle URN = 2×28 = 56°.

but we need only the angle URL.

the angle URL = angle URN - angle LRN.

the angle LRN is the mirrored version of the angle JRM = 21°.

so, the angle URL = 56 - 21 = 35°.

Answer:

b.3

Step-by-step explanation:

im not 100% sure

Answer:

5y^2(4y^4 - 3y^2 +8

Step-by-step explanation:

20y^6 - 15y^4 + 40y^2

Here are the vectors **t**, **n**, and **b** at the given point:

* **t** = (-3 sin t, 3 cos t, 0)

* **n** = (-3 cos t, -3 sin t, 3 / cos^2 t)

* **b** = (3 cos^2 t, -3 sin^2 t, -3)

The vector **t** is the unit tangent vector, which points in the direction of the curve at the given point. The vector **n** is the unit normal vector, which points in the direction perpendicular to the curve at the given point. The vector **b** is the binormal vector, which points in the direction that is perpendicular to both **t** and **n**.

To find the vectors **t**, **n**, and **b**, we can use the following formulas:

```

t(t) = r'(t) / |r'(t)|

n(t) = (t(t) x r(t)) / |t(t) x r(t)|

b(t) = t(t) x n(t)

```

In this case, we have:

```

r(t) = (3 cos t, 3 sin t, 3 ln cos t)

r'(t) = (-3 sin t, 3 cos t, 3 / cos^2 t)

```

Substituting these into the formulas above, we can find the vectors **t**, **n**, and **b** as shown.

The vectors **t**, **n**, and **b** are all orthogonal to each other at the given point. This is because the curve is a smooth curve, and the vectors are defined in such a way that they are always orthogonal to each other.

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The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.

To find the vectors t, n, and b at the given point, we need to calculate the first derivative, second derivative, and third derivative of the position vector r(t).
Given r(t) = (3 cos t, 3 sin t, 3 ln cos t), we can calculate the derivatives as follows:
First derivative:
r'(t) = (-3 sin t, 3 cos t, -3 sin t / cos t)
Second derivative:
r''(t) = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 sin^2 t / cos t)
       = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 tan^2 t)
Third derivative:
r'''(t) = (3 sin t, -3 cos t, 6 cos t / cos^3 t - 6 sin t / cos t)
        = (3 sin t, -3 cos t, 6 sec^3 t - 6 tan t sec t)
At the given point (3, 0, 0), substitute t = 0 into the derivatives to find the vectors:
r'(0) = (0, 3, 0)
r''(0) = (-3, 0, 3)
r'''(0) = (0, -3, 6)
Therefore, at the given point, the vectors t, n, and b are:
t = r'(0) = (0, 3, 0)
n = r''(0) = (-3, 0, 3)
b = r'''(0) = (0, -3, 6)
These vectors represent the tangent, normal, and binormal vectors, respectively, at the given point.
The tangent vector (t) represents the direction of motion of the curve at that point. The normal vector (n) is perpendicular to the tangent vector and points towards the center of curvature.

The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.
Remember to check your calculations and units when applying this method to different functions.

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The solution to the initial value problem y' - 3y = 10e^(-t+4) sin²(2(t - 4)) - 44(t), with y(0) = 5, is y(t) = e^(3t) + 10e^(-t+4) sin(2(t - 4)) - 44t - 1.

To solve this problem, we'll start by finding the general solution to the homogeneous equation y' - 3y = 0. The characteristic equation is r - 3 = 0, which gives us the solution y₀(t) = Ce^(3t).

To solve the initial value problem y' - 3y = 10e^(-t) + 4sin(2(t - 4)) + 44t with y(0) = 5, we can use an integrating factor and the method of variation of parameters.

Step 1: Homogeneous Solution

First, let's find the homogeneous solution to the equation y' - 3y = 0. This means we solve the equation y' - 3y = 0 without the right-hand side term.

The characteristic equation is given by r - 3 = 0, which yields r = 3. Therefore, the homogeneous solution is y_h = C*e^(3t), where C is a constant.

Step 2: Particular Solution

Next, let's find a particular solution to the non-homogeneous equation y' - 3y = 10e^(-t) + 4sin(2(t - 4)) + 44t. We'll denote this particular solution as y_p.

For the term 10e^(-t), a suitable guess for the particular solution is y_p1 = A*e^(-t), where A is a constant to be determined.

Differentiating y_p1 with respect to t gives y_p1' = -A*e^(-t).

Substituting y_p1 and y_p1' into the differential equation, we have:

(-Ae^(-t)) - 3(Ae^(-t)) = 10e^(-t).

Simplifying, we get -4A*e^(-t) = 10e^(-t).

Comparing the coefficients on both sides, we find A = -10/4 = -5/2.

For the term 4sin(2(t - 4)), a suitable guess for the particular solution is y_p2 = Bsin(2(t - 4)) + Ccos(2(t - 4)), where B and C are constants to be determined.

Differentiating y_p2 with respect to t gives y_p2' = 2Bcos(2(t - 4)) - 2Csin(2(t - 4)).

Substituting y_p2 and y_p2' into the differential equation, we have:

(2Bcos(2(t - 4)) - 2Csin(2(t - 4))) - 3(Bsin(2(t - 4)) + Ccos(2(t - 4))) = 4sin(2(t - 4)).

Simplifying, we get (2B - 3C)cos(2(t - 4)) + (3B + 2C)sin(2(t - 4)) = 4sin(2(t - 4)).

Comparing the coefficients on both sides, we have the following system of equations:

2B - 3C = 0 (1)

3B + 2C = 4 (2)

Solving equations (1) and (2), we find B = 6/13 and C = 4/13.

For the term 44t, a suitable guess for the particular solution is y_p3 = Dt^2 + Et + F, where D, E, and F are constants to be determined.

Differentiating y_p3 with respect to t gives y_p3' = 2Dt + E.

Substituting y_p3 and y_p3' into the differential equation, we have:

(2Dt + E) - 3(Dt^2 + Et + F) = 44t.

Simplifying, we get -3Dt^2 + (2 - 3E)t + (E - 3F) = 44t.

Comparing the coefficients on both sides, we have the following system of equations:

-3D = 0 (3)

2 - 3E = 44 (4)

E - 3F = 0 (5)

Solving equations (3), (4), and (5), we find D = 0, E = -14/3, and F = -14/9.

Therefore, the particular solution is y_p = y_p1 + y_p2 + y_p3, which is:

y_p = (-5/2)e^(-t) + (6/13)sin(2(t - 4)) + (4/13)cos(2(t - 4)) - (14/3)t - (14/9).

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The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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Answer:

In Nelson Mandela's family he was the first to receive a formal education. At that time, very few black kids attained high school education in South Africa.

Answer:

9/25

Step-by-step explanation:

Equatiοns that can be used tο find s, the tοtal distance Kurt swam is as fοllοws:

• s = 2 x 4/8 and

• s = 4/8 + 4/8

Bοth οf these equatiοns can be used tο find s, the tοtal distance Kurt swam.

The equatiοn s = 2 x 4/8 can be used tο find s, the tοtal distance Kurt swam. This equatiοn represents the fact that Kurt swam acrοss the lake and back, which is a tοtal οf twο times the distance acrοss the lake. Since the lake is 4/8 miles acrοss, the equatiοn simplifies tο s = 2 x 4/8, which equals 1 mile.

The equatiοn s = 4/8 + 4/8 can alsο be used tο find s, but it represents the distance Kurt swam in οne directiοn οnly. It adds the distance acrοss the lake and back tοgether, but since Kurt οnly swam in οne directiοn, this equatiοn οnly gives half οf the tοtal distance.

The equatiοn s = 1 is incοrrect because it dοes nοt take intο accοunt the distance acrοss the lake.

The equatiοn s = 2 x 8 is alsο incοrrect because it assumes that the lake is 8 miles acrοss, which is nοt given in the prοblem.

The equatiοn s = 2 + 4+8 is incοrrect because it adds three different distances tοgether, which dοes nοt accurately represent the distance Kurt swam.

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Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Answer:

2nd = 4ft.

1st = 16ft

Step-by-step explanation:

2nd = x

1st = 3x + 4

Piece of rope = 20ft.

(3x + 4) + x = 20

4x + 4 = 20

4x = 16

x = 4 (second piece)

First

3x + 4

3(4) + 4

12 + 4 = 16

Answer: 250

Step-by-step explanation:

20% of 15,000 is 3,000

3,000/12=250

Answer:

$3000 Per Month

Step-by-step explanation:

Hi there,

How I like to solve these is first take the total number (15,000) and divide it by 100 to then find how much 1% of 15,000 is.

So :

15,000 / 100

=

150

Now we know :

1% = $150

We need to find 20% now so all we do is multiply.

150 x 20

($150 x 20%)

= $3,000 Per Month

I hope this helps!

If you have any questions or concerns be sure to comment or message me ! :)

EDIT : The other person is most likely right. I am 17 and dont have insurance yet Lol

Answer:

  -3 < x < 1

Step-by-step explanation:

In general, an absolute value function is a piecewise-defined function, with each piece having its own applicable domain. However, the absolute value inequality |a| < b is fully equivalent to the compound inequality -b < a < b. This can be used to solve the given inequality.

We can isolate the absolute value expression by undoing the operations done to it.

  3|x +1| -2 < 4 . . . . . given

  3|x +1| < 6 . . . . . . . add 2

  |x +1| < 2 . . . . . . . . divide by 3

The absolute value inequality is now in the form described above, so can be "unfolded" to a compound inequality:

  -2 < x +1 < 2

Subtracting 1 finds the solution for x:

  -3 < x < 1

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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Answer:

3

Step-by-step explanation:

3 is not a factor of 16.

Is that a valid answer? lol

Hi there!

First of all, let's determine the factors of 16.

Remember, a factor is a number that a number can be evenly divided by.

Example: 5 is a factor of 10, because 10 can be evenly divided by 5.

So, the factors of 16 are:

1, 2, 4, 8, and 16.

Now, there's an infinite amount of numbers that are not factors of 16. Here are some of them:

3, 5,7,9, 10,11, 12, 13, 14, 15...

Hope it helps.

Feel free to ask if you have any doubts.

\(\bf{-MistySparkles^**^*\)

Answer:

Step 2 explains why Colton's solution is incorrect because he subtracted 13 on both sides instead of adding it on both sides.

Hope it helps!

Answer:

'Cause he didn't use the inverse operation! ^^

Step-by-step explanation:

Heres the correct way to solve it:

x-13=26

x=26+13

x=39

The correct way is to add 13 to both sides and not subtract.

--

Hope that this helped! Best wishes.

--

The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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Answer & Step-by-step explanation:

Read the Example Below....

Answer:

.50 = equally likely as unlikely

1 = certain

.25 = unlikely

0 = impossible

.75 = likely

Step-by-step explanation:

Think of these as percentages, it'll help you figure out.

.50 is 50%

1 is 100%

.25 = 25%

0 is 0%

.75 = 75%

Answer: all points are a solution except for (4, 2) (and (2, 0) i think)

Step-by-step explanation:

Answer:

Step-by-step explanation:

All the step of construction is explained below. The required regular hexagon is given below.

Construct a regular hexagon inscribed in a circle using the construction tool. Insert a screenshot of the construction here.

In the first step, make a circle with a radius, and connect the center and circumference.

In the second step, make an angle which is calculated by the formula.

⇒ 360 / n

Where n is the number of sides of the polygon. Then we have

⇒ 360 / 6 = 60

In the third step, take protector or arc length of the circumference and cut the another arc.

In the fourth step, connect all the point.

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\( - 6x - 42 = - 10x + 62\)

Add sides 42

\( - 6x - 42 + 42 = - 10x + 62 + 42 \\ \)

\( - 6x = - 10x + 104\)

Add sides 10x

\( 10x - 6x =10x - 10x + 104 \)

\(4x = 104\)

Divided sides by 4

\( \frac{4}{4}x = \frac{104}{4} \\ \)

\(x = 26\)

_________________________________

Done ♥️♥️♥️♥️♥️

Answer:

yaaaa

Step-by-step explanation: