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The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.

The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.

This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.

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The  times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:

[tex]4e^{(-3t)[/tex] sin(2πt) = 0

Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:

4[tex]e^{(-3t)[/tex] = 0

This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.

sin(2πt) = 0

The sine function is zero at integer multiples of π.

So, we can set 2πt equal to integer multiples of π:

2πt = 0, π, 2π, 3π, ...

Solving for t in each case, we get:

t = 0, 1/2, 1, 3/2, ...

Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

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The function g(x) in the form a(x-h)^2 + k is: [tex]g(x) = (x + 2)^2 - 4[/tex]

Starting with[tex]f(x) = x^2[/tex], the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting[tex]f(x) = x^2:[/tex]

[tex]g(x) = (x + 2)^2 - 4[/tex]

Expanding the square:

[tex]g(x) = x^2 + 4x + 4 - 4[/tex]

Simplifying:

[tex]g(x) = x^2 + 4x[/tex]

Now we need to rewrite this expression in the form [tex]a(x-h)^2 + k.[/tex] To do this, we will complete the square:

[tex]g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4[/tex]

Therefore, the function g(x) in the form a(x-h)^2 + k is:

[tex]g(x) = (x + 2)^2 - 4[/tex]

Where a = 1, h = -2, and k = -4.

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Answer:

10 millimeters

Step-by-step explanation:

The diameter of the button is twice the radius. Therefore, the diameter of Jasmine's pants button is 10 millimeters.

Answer:no idea

Step-by-step explanation:

The coordinates of the vertices after a dilation of the scale factor would be:

To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.

Given the vertices:

W = (5, 10)

V = (0, -10)

U = (5, -10)

After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:

W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)

V' = (0 * 1/2, -10 x 1/2) = (0, -5)

U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)

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1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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The value of x will be 10.

Given a triangle we need to set a proportion to solve for the value of x,

Therefore, according to the definition of the similar triangles,

x / 5 = 15+5 / x

x² = 5 × 20

x² = 100

x = 10

Hence the value of x will be 10.

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Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.

Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:

Order: Zocor 40 mg po qd for 60 days

= 60 tabs since it is once per day (qd)

Total mg = 2,400 mg (40 mg x 60 tabs)

On hand: 20 mg tabs

Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs

Total mg = 2,400 mg (20 mg x 120 tabs)

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We can use the formula for the volume of a pentagonal pyramid to solve this problem:

Volume = (1/3) × Base Area × Height

We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:

48 = (1/3) × 12 × Height

Multiplying both sides by 3 gives:

144 = 12 × Height

Dividing both sides by 12 gives:

Height = 12

Therefore, the height of the pentagonal pyramid is 12 centimeters.

The point (4, - 1) will not be a solution to the system of linear inequalities shown.

The solution of the  linear inequalities is calculated by simplifying the  linear inequalities as follows;

The given linear inequalities;

y ≥ -x/4  + 7

y > 4x + 4

Solve the linear inequalities as follows;

4x + 4 ≥ -x/4 + 7

Collect similar terms together;

4x + x/4 ≥ 7 - 4

4x + x/4 ≥ 3

Multiply through by 4;

16x + x ≥ 12

17x ≥ 12

divide through by 17;

x ≥ 12/17

x ≥ 0.7

The value of y is calculated as;

y ≥ -x/4  + 7

y ≥ - (0.25 x 0.7) + 7

y ≥ 6.8

Since y is greater than or equal to 6.8, the point (4, - 1) will not be a solution to the system of linear inequalities shown.

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Okay, here are the steps to solve this problem:

1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48

2) We want to find the time (t) when the rocket hits the ground (h = 0)

3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0

4) Factor the left side: - 3(t2 - 0t) + 48 = 0

5) Solve for t2 - 0t: t2 - 0t = 16

6) Add 0t to both sides: t2 = 16 + 0t

7) Take the square root of both sides: t = 4

Therefore, the time for the rocket to hit the ground is 4 seconds.

So in this case, t = 4

Let me know if you have any other questions!

Answer:

4 seconds.

Step-by-step explanation:

When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]

Now set this equal to 0

[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.

[tex]-48 = -3t^2[/tex]

[tex]16 = t^2[/tex]

From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.

Hope this helps

The equation that represents the amount of money in Sara's piggy bank is y = 0.6x + 1 and the equation that represents the amount of money in Kim's piggy bank is y = 0.2x + 2.2.

The equation that represents the amount of money in Sara's piggy bank over time can be written as

Y = 0.6x + 1

Where Y represents the total amount of money in Sara's piggy bank and x represents the number of weeks.

Similarly, the equation that represents the amount of money in Kim's piggy bank over time can be written as

Y = 0.2x + 2.2

Where Y represents the total amount of money in Kim's piggy bank and x represents the number of weeks.

To visualize these equations, we can create a graph where the x-axis represents the number of weeks and the y-axis represents the amount of money in the piggy bank. We can plot the points for each week and draw a line connecting them. The resulting graph will show the trend of the amount of money in each piggy bank over time.

Here is a graph that represents the scenario

In the graph, the red line represents the amount of money in Sara's piggy bank and the blue line represents the amount of money in Kim's piggy bank. As we can see, Sara's piggy bank grows faster than Kim's piggy bank due to the higher allowance she receives for doing her chores.

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A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay

Auto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).

The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.

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Answer:

(- 2, 0 ) , (1, - 3 )

Step-by-step explanation:

the solutions to the system of equations are at the points of intersection with the curve and the straight line.

points of intersection are at (- 2, 0 ) and (1, - 3 ) , then

solutions are (- 2, 0 ) , (1, - 3 )

Segment BF is 36 will be the accurate statement.

A triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.

From the given triangle, the following expression is true:

EC/FC = AC/BF+FC

Substitute the given parameters into the formula to have:

20/30 = 24+20/BF+30

20/30 = 44/BF+30

2/3 = 44/BF + 30

2(BF+30) = 132

2BF + 60 = 132

2BF = 132 - 60

2BF = 72

BF = 36

Hence the correct statement will be that segment BF is 36

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Answer:

A. 4ab² + 2x

Step-by-step explanation:

If you want to get rid of those pesky parentheses, you have to use the superpower of distributive property. It lets you multiply everything inside the parentheses by the number outside. For example:

4(ab²+1/₂c + x) = 4ab² + 2c + 4x

Boom! No more parentheses!

To combine like terms, you have to add or subtract the numbers in front of the terms that have the same variable and exponent. For example:

2x - 4x = -2x

Bam! Only one x left!

Here are the steps to simplify the expression:

4(ab²+1/₂c + x) - 2(c+x)

= 4ab² + 2c + 4x - 2c - 2x (use superpower)

= 4ab² + 4x - 2x (combine like terms)

= 4ab² + 2x (simplify)

So, the answer is A. 4ab² + 2x.

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

R500

Step-by-step explanation:

20 books x R25 each = R500.

The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.

P(B) = 1/4

P(A and B) = 3/25

The conditional probability is used to find the P(A|B):

P(A|B) = P(A and B) / P(B)

Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.

By substituting the given values in the given probability, we get:

P(A|B) = (3/25) / (1/4)

Divide the fraction and multiply it with its reciprocal:

P(A|B) = (3/25) * (4/1)

P(A|B) = 12/25

Therefore, we can conclude that the missing probability is P(A|B) is 12/25.

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The complete question is:

Find the missing probability.

P(B)=1/4P

(AandB)=3/25P

P(A|B)=?

Answer:

-7

Step-by-step explanation:

divide by 7 on both sides and you get i = -7

Given statement solution is :- Outputs and values g(2/3) = 2/3.

To summarize:

g(0) = 0

g(-1) = undefined

g(2) = undefined

g(2/3) = 2/3

To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:

g(0):

Substitute x = 0 into the function:

g(0) = 0 / √([tex]1 - 0^2[/tex])

= 0 / √(1 - 0)

= 0 / √1

= 0

Therefore, g(0) = 0.

g(-1):

Substitute x = -1 into the function:

g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])

= (-1) / √(1 - 1)

= (-1) / √0

Since the square root of 0 is undefined, g(-1) is undefined.

g(2):

Substitute x = 2 into the function:

g(2) = 2 / √([tex]1 - 2^2[/tex])

= 2 / √(1 - 4)

= 2 / √(-3)

Since the square root of a negative number is undefined in the real number system, g(2) is undefined.

g(2/3):

Substitute x = 2/3 into the function:

g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])

= (2/3) / √(1 - 4/9)

= (2/3) / √(5/9)

= (2/3) / (√5/√9)

= (2/3) / (√5/3)

= (2/3) * (3/√5)

= 2√5 / 3√5

= 2/3

Therefore, outputs and values g(2/3) = 2/3.

To summarize:

g(0) = 0

g(-1) = undefined

g(2) = undefined

g(2/3) = 2/3

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Answer:

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Step-by-step explanation:

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The length of fencing needed around her triangular garden is 41 feet.

A given shape which has three sides and three measures of internal angles which add up to 180^o is said to be a triangle.

For Mary to build a fence around her triangular garden, the amount of fencing needed can be determined by adding the length of each side of the garden.

So that;

A + B + C = 180^o

A + 49 + 40 = 180

A = 180 - 89

   = 91

A = 91^o

Applying the sine rule, we have;

a/Sin A = b/Sin B = c/Sin C

a/Sin A = b/Sin B

a/Sin 91 = 13/ Sin 49

aSin 49 = 13*Sin 91

             = 12.998

a = 12.998/ 0.7547

  = 17.22

a = 17 ft

Also,

b/Sin B = c/Sin C

13/Sin 49 = c/ Sin 40

cSin 49 = 13*Sin 40

             = 8.3562

c = 8.3562/ 0.7547

  = 11.0722

c = 11 feet

Thus the amount of fencing required = 13 + 17 + 11

                                                    = 41

The fencing required is 41 feet length.

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The outside border of the garden would have walked around approximately  58%.

Without more information about the shape and dimensions of the garden, it's impossible to give an exact answer. However, if we assume that the garden is a rectangle, we can use the formula for the perimeter of a rectangle to estimate the percentage of the garden's border that would be walked around.

Let's say that the length of the garden is L and the width of the garden is W. The perimeter of the rectangle is then:

P = 2L + 2W

If the person walks from point A to point B along the outside of the garden, they are essentially walking along two sides of the rectangle. Let's call these sides S1 and S2. Depending on the location of A and B, S1 and S2 may be two adjacent sides, two opposite sides, or one side and one diagonal.

To estimate the percentage of the garden's border that the person would walk around, we can calculate the length of S1 and S2 and divide by the total perimeter of the rectangle:

Percentage walked = (S1 + S2) / P * 100%

Again, without more information about the shape and dimensions of the garden, we can't give an exact answer. However, if we assume that the person walks along two adjacent sides of the rectangle, the percentage of the garden's border that they would walk around would be:

Percentage walked = (2L + W) / (2L + 2W) * 100%

Simplifying this expression, we get:

Percentage walked = (2L + W) / (2(L + W)) * 100%

Assuming that L and W are measured in the same units (e.g. meters), we can simplify further:

Percentage walked = (2 + W/L) / (2 + 2W/L) * 100%

For example, if the length of the garden is 10 meters and the width of the garden is 5 meters, then the percentage of the garden's border that the person would walk around if they walked along two adjacent sides would be:

Percentage walked = (2 + 5/10) / (2 + 2*5/10) * 100%

= 7/12 * 100%

= 58.3%

So the outside border of the garden would have walked around approximately  58%.

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The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

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