Mann Park is the shape of a triangle.
On a map, it has borders that measure 5 inches inches, 7 inches
and 9 inches. If the shortest border of Mann Park is
1000 meters long, how long in meters, is its longest
border?

Answer:

Step 1: Construct a circle through three points not on a line.

a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by

drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and

name the point of intersection of the perpendicular bisectors O. How do you know that point O

is the center of the circle that passes through the three points?

Answer:

Step-by-step explanation:

To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.

This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:

OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2

Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.

Answer: 6.38

.................

The solution is the area of the figure is 53.17.

The area of a trapezoid is found using the formula, A = ½ (a + b) h,

where 'a' and 'b' are the bases (parallel sides) and 'h' is the height .

here, we have,

from the given figure we get,

a = 10,

b = 6

h = 8

so, A = 64

again, the cut triangle is a equilateral triangle with side = 5

then, area of triangle = √3/4 * 5^2

                                   = 10.82

so, required area = 53.17

Hence, The solution is the area of the figure is 53.17.

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The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Regarding the pattern, we have that:

Regarding subtraction by even numbers, we have that:

Hence the pattern cannot be subtract 4, as the sequence would be composed either by all even numbers or all odd numbers.

Regarding subtraction by odd numbers, we have that:

We can see that the results alternate, hence the pattern can be subtract 5.

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Answer:

Alright, so we want to know how much that can be earned in one year. So that's going to be 3000. And this is simple interest. So this is one plus 0.011, which equals $3,033. And that's the solution to this exercise.

Answer:

$3,036

Step-by-step explanation:

The new customer can open a money market account. The bank will deposit $3,000 into the account.

The bank will pay 1.2% (0.012) in interest every year. This interest will increase the original amount to $3,036.

Equivalence means to be same, whether it be value, temperature, size, etc.

Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.

To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.

Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.

The correct answers are given below:

(a) 1 to 55

(b) 40%

Since Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.

To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)

Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.

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Answer:

First side: 40in

Second side: 20in

Third side: 36in

Step-by-step explanation:

Let's call the triangle's first, second, and third sides a, b, and c respectively.

The perimeter of the triangle is 96in: a+b+c=96

The length of the first side is twice the second: a=2b

The third side is 16in more than the second: c=b+16

Now, consider the equation a+b+c=96 again, but sub '2b' in for a, and 'b+16' for c, in order to find the value of b:

a+b+c=96

2b+b+b+16=96

4b=80

b=20

Use this value for b to find a and c:

a=2b=2(20)=40

c=b+16=20+16=36

Answer:

Step-by-step explanation:

Let's call the length of the second side "x". Then, the length of the first side is 2x and the length of the third side is x + 16.

The perimeter of the triangle is the sum of the lengths of its sides, so we can set up an equation to solve for x:

x + 2x + (x + 16) = 96

Expanding the equation and solving for x, we get:

4x + 16 = 96

4x = 80

x = 20

So, the length of the second side is 20 inches, the length of the first side is 2 * 20 = 40 inches, and the length of the third side is 20 + 16 = 36 inches.

Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.

The equation for the vertical movement of an object will be:

H(t) = -16*t^2 + v0*t + h0

Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height,  55ft.

Then the height equation is:

H(t) = -16*t^2 + 85*t + 55

The object will hit the ground when the height is equal to zero, then we need to solve:

-16*t^2 + 85*t + 55 = 0

Using the quadratic formula we will get:

[tex]t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}[/tex]

We only care for the positive solution, which is:

t = (-85 - 103.7)/-32 = 5.9

So it will take 5.9 seconds for the object to hit the ground.

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The values of f(-1) , f(0) and f(2) are 0, 8 , 16 .

What is a function ?

Function can be defined in which it relates an input to output.

Given function ,

f ( x ) =  4x + 4 when x < 0

= 4x + 8 when x >= 0

f(-1) = 4x + 4

= 4 ( -1 ) + 4

= 0

f(0) = 4x + 8

= 4*0 + 8

= 8

f(2) = 4x + 8

= 4*2 + 8

= 8 + 8

= 16

Therefore, The value of f(-1) , f(0) and f(2) are 0, 8 , 16 .

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When x changes from 2 to 5, the average velocity (or average rate of change of y with respect to x) is 9.33 m/s. When x changes from 2 to 2 + h, the average velocity is 2 + hm/s.

Average speed is determined by dividing the total distance you travelled by the total time, whereas average velocity is determined by dividing your displacement (a vector Throughout the entire period, position to your finish position).

(A) The following formula is used to get the average velocity when x changes from 2 to 5:

value of y at x = 2

= 2²+2 = 6 m

value of y at x = 5

= 5²+5 = 30 m

displacement equals 30 – 6 = 24 m.

Time is 5 - 2 = 3 seconds.

average velocity

= displacement /Time duration

= 24/3 = m/s

B) Value of y at x = 2 = 5 for x changing from x to x plus ie for minimal change in x.

Displacement during a little change in x will be 0 because the value of y will once again be 5.

C )  

y(x) = x² + x

dy / dx = 2x + 1

dy / dx  represents instantaneous  velocity

so when x = 2

instantaneous velocity = 2 x 2 +1

= 5 m /s

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The value of x for the given expression will be 22/3.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is triple x less by 10 is at least 12. The mathematical form of the expression can be written as below:-

3x - 10 = 12

3x = 10 + 12

3x = 22

x = 22 / 3

Hence, the value of x for the expression 3x - 10 = 12 is x = 22 / 3.

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Step-by-step explanation:

we need to remember 2 things for right-angled triangles (which we need to use to find the sides of the rectangle, so that we then can calculate the area) :

1. Pythagoras

a² + b² = c²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

2. geometric mean theorem

height = sqrt(p×q)

with p and q being the segments of the baseline the height is splitting it into. in our case MA and AL.

so, to get the length of the rectangle (PL) we use Pythagoras :

PL² = 6² + 8² = 36 + 64 = 100

PL = 10 units

to get PM we first need to get ML. and for that we need to get MA.

6 = sqrt(MA × 8)

36 = MA × 8

MA = 36/8 = 4.5 units

that means ML = 8 + 4.5 = 12.5 units

and again Pythagoras

ML² = PL² + PM²

12.5² = 10² + PM²

156.25 = 100 + PM²

56.25 = PM²

PM = 7.5 = 7.5 units

so, the area of the rectangle is

10 × 7.5 = 75 = 75.00 units²

to "round" to the nearest hundredth.

Answer:B

Step-by-step explanation:

Answers

9x+6x=2600

15x=2600

x=520/3

9x=9×520/3=1560

6x=6×520/3=1040

Answer:

75a%

or

3/4a

or

0.75a

Step-by-step explanation:

I answer for what I understand, a number a is reduced by 50% and the result increased by 50%

a - 50% = 50% or 1/2 or 0.5

    2. increase

50 + 50% = 75% or 3/4 or 0.75

The solution to the equation 16^{2x - 3} · 4^{-2x} = 4^2 include the following: C. x = 4.

In Mathematics, laws of indices can be defined as the standard principles or rules that are used for simplifying an equation or expression that involves powers (exponents) of the same base.

By rewriting the mathematical expression and applying the multiplication law of indices, we have the following:

16^{2x - 3} · 4^{-2x} = 4^2

4^2{2x - 3} · 4^{-2x} = 4^2

2{2x - 3} + {-2x} = 2

4x - 6 - 2x = 2

2x = 2 + 6

2x = 8

x = 8/2

x = 4.

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Refer to the attached images.

**Should be arctan(tanx)=x on the last page**

The required, Ask each regular customer which flavor they would like to see in his shop, would be the best method. Option C is correct.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Asking each regular customer which flavor they would like to see in the shop would be the best method because the customers are the ones who will be buying and consuming the ice cream, so their preferences are the most important. By directly asking the customers for their opinions, the owner can get a better understanding of what flavors people are interested in, and it can also help to build a relationship with the customers by showing that their input is valued.

Option A, determining the current best-selling flavor, would only provide information about the current sales and not necessarily reflect customers' interests in new flavors. Option B, visiting other ice cream shops, could provide some ideas, but it would not necessarily reflect the local market and the preferences of the shop's specific customer base. Option D, randomly generating customers to survey, may not be representative of the actual customer base and may not provide a reliable indication of which new flavor to sell.

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Answer:

64 is not divisible by 6 because although it is divisible by 2, it is not divisible by 3 so it is not divisible by 6.

Step-by-step explanation:

Yes, the given statement is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that;

The statement is about the decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

Now, A fraction is terminating decimal as if the denominator of the fraction contains terms in the form of 2ᵃ, 5ᵇ or 2ᵃ x 5ᵇ.

Then, It is said that, there is a digit in thousandth place.

Hence, the statement given is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

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a) The value of z-score is -0.299.

c) The IQR value is measure of spread of data,  IQR = 4.25.

d) There is outliers since observations are not less than 30.375 and greater than 47.375.

The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.

Given:

Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3

(a) The value of z-score is calculated as follows,

μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88

σ = 3.61

So, z = X - μ / σ  

 = 37.8 - 38.88/3.61

 = −  0.299

(b) Quartile:

Q₁ = ( n+1/4)th value

= (24+1/4)th

= 6.25th

=  36.2 + 0.25 x ( 37.3 −  36.2 )  

= 36.47

and, M = ( n+1/2)th value

= (24+1/2)th

= (24+1/4)th

=  12.5 t h

= 38.4 + 38.5/2

= 38.45

Q₃ = 3( n+1/4)th

= 3(24+1/4)th

= 18.75 t h  

= 40.6 + 0.75 x ( 41.4  −  40.6 )  

= 41.2

(c) Interquartile​ range

=  Q ₃ −  Q ₁  

= 41.2  −  36.47  

= 4.25

(d) Lower fences =  Q₁− 1.5 ( I Q R )  

                           =  36.75 −  1.5  ( 4.25 )  

                           =   30.375  

Upper fences = Q ₃+1.5

                      =  41 + 1.5( 4.25 )  

                      = 47.375

Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.

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Answer:

Step-by-step explanation:

To find the percent of the people who attended the Baybridge Middle School Winter Formal who are not students at Baybridge, we can use the following steps:

Find the fraction of non-student attendees: 18 attendees out of 90 total attendees can be represented as 18/90.

Convert the fraction to a decimal: 18/90 = 0.20, which can be rounded to 0.2.

Convert the decimal to a percentage: 0.2 * 100 = 20%.

So, 20% of the people who attended the Baybridge Middle School Winter Formal are not students at Baybridge.

Answer:

              Based on the measures of the following triangle's angles, the triangle can be classified as an obtuse triangle.

Step-by-step explanation:

              In order to decide which type of triangle this is, first we must understand what an acute, right, and obtuse triangle are. Acute triangles are triangles with all three of its angles less than 90°, right triangles are triangles with one angle that is exactly 90°, and obtuse triangles are triangles with one angle that is greater than 90°. Overall, we can determine the type of this triangle by looking at its angles.

             The given triangle has the angles 25°, 136°, and 19°. Now we can compare it to the rules above and see whether this triangle is acute, right, or obtuse. As the given triangle has an angle that is greater than 90°, we can conclude that the following triangle is an obtuse triangle.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

0.392 < p < 0.508

Step-by-step explanation:

[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.45\pm 1.645\sqrt{\frac{0.45(1-0.45)}{200}}\\\\CI_{90\%}\approx0.45\pm0.058\\\\CI_{90\%}=\{0.392,0.508\}[/tex]

Thus, we are 90% confident that the true population proportion [tex]\hat{p}[/tex] is between 0.392 and 0.508, assuming conditions are met.

The linear equation that passes through the two given points is:

y = (5/8)*x + 19/8

We want to find the equation of a line that passes through (1, 3) and (9, 8).

Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:

slope = (y₂ - y₁)/(x₂ - x₁)

Here we know the two points (1, 3) and (9, 8).

Then the slope is:

slope = (8 - 3)/(9 - 1) = 5/8

We can write the line as:

y = (5/8)*x + b

To  find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:

3 = (5/8)*1 + b

3 = 5/8 + b

3 - 5/8 = b

24/8 - 5/8 = b

19/8 = b

The linear equation is:

y = (5/8)*x + 19/8

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Answer:

Step-by-step explanation:

The tide over a 24-hour period can be modeled by a sinusoidal function of the form:

f(x) = A * sin(Bx) + C

where A is the amplitude, B is the frequency, and C is the vertical shift.

To determine the values of A, B, and C, we need three points. Let's use the following points:

(0, 5): This is the value of the tide at midnight, 5 ft.

(12, 9.5): This is the value of the tide at its high, 9.5 ft.

(6, 0.5): This is the value of the tide at its low, 0.5 ft.

Using the first point (0, 5), we can calculate the vertical shift, C:

C = 5

Using the second point (12, 9.5), we can calculate the amplitude, A:

A = (9.5 - 5) / 2 = 2.25

Using the third point (6, 0.5), we can calculate the frequency, B:

0.5 = 2.25 * sin(B * 6) + 5

4.5 = 2.25 * sin(B * 6)

2 = sin(B * 6)

B * 6 = sin^-1(2)

B * 6 = pi / 2

B = pi / (2 * 6) = pi / 12

So, the final equation is:

f(x) = 2.25 * sin(pi * x / 12) + 5

This represents one period of the sinusoidal function that models the tide over a 24-hour period, with time x measured in hours since midnight.

Answer: 2: 56 degrees

4: 56 degrees

(Number 6 is not in the image)

Step-by-step explanation:

So for #2 we know the whole angle is 90 degrees, so all we have to do is 90-34 = 56

And for #4, we know the angle is 180 so all we have to do is 180-124=56