The distance a person falls on a bungee chord in
metres, h may be mod- elled with time, t in seconds according to: h
= 2 * (t - 5) ^ 2 - 50
a) What is the height of a person after 4 seconds?

The overall chances of winning the games before playing were 52%, and after playing and winning once but losing twice, the overall chances of winning are 17.33%. This shows that the new information has changed your belief about the probability of winning, and you now suspect that your chances of winning are lower than before.

Before playing the games, the expected value of winning is calculated by multiplying the probability of winning with the corresponding probabilities and adding them together. This is shown below:

E(win) = (0)(0) + (0.1)(0.01) + (0.2)(0.02) + (0.3)(0.04) + (0.4)(0.1) + (0.5)(0.15) + (0.6)(0.2) + (0.7)(0.25) + (0.8)(0.16) + (0.9)(0.04) + (1)(0) = 0.52

After playing the games and winning once but losing twice, the expected value of winning is calculated by multiplying the probability of winning with the corresponding probabilities, and adding them together. However, the probabilities are adjusted based on the new information. The new probabilities are shown below:

P(win) = (0)(0) + (0.1)(0.01)(1/3) + (0.2)(0.02)(1/3) + (0.3)(0.04)(1/3) + (0.4)(0.1)(1/3) + (0.5)(0.15)(1/3) + (0.6)(0.2)(1/3) + (0.7)(0.25)(1/3) + (0.8)(0.16)(1/3) + (0.9)(0.04)(1/3) + (1)(0)(1/3) = 0.17333

Therefore, the overall chances of winning the games before playing were 52%, and after playing and winning once but losing twice, the overall chances of winning are 17.33%. This shows that the new information has changed your belief about the probability of winning, and you now suspect that your chances of winning are lower than before.

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Answer: A maximum height corresponds to:

B. h(t) = 26,200 - 16t^2

A minimum height corresponds to:

C. h(t) = 6 for 7 ≤ t ≤ 8

Height staying the same corresponds to:

D. h(t) = 12 for 2 ≤ t ≤ 3

Starting height corresponds to:

A. h(0) = 7

Using the provided data, we can find the function values that correspond to the given times:

h(1.5) = 26,200 - 16(1.5)^2 = 26,157

h(4) = 16

Therefore, the statement that corresponds to "6-7" is missing from the given options.

Step-by-step explanation:

The value of x in the triangle given the midsegment points and sections is 1.35 units

The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.

The midsegments of triangle UWY are VR, VZ, ZR

To find the value of x, we use a theorem called the mid segment theorem which states that:

"The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle."

The third side of triangle UWY is WY and it measures 2.7.

Therefore, x will be 2.7 divided by 2 2.7/2 which will give us the value 1.35 i.e. x = 1.35

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Answer:

Step-by-step explanation:

The question is illustrated with the attached image.

Angle of elevation is the angle between a line of sight and the horizontal surface.

Let h be the height of the tower

First, calculate distance BC (x).

This is calculated using the following tan ratio,

tan52=h/x

h=xtan52

From the attached image:,

CD=47+x

tan31=h/x+47

h=(x+47)tan31

xtan52=(x+47)tan31,

solving for x we get, x=41.156m

h=xtan52=41.156 * tan52=53.2m

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.8\% of 25}}{\left( \cfrac{3.8}{100} \right)25}\implies \text{\LARGE 0.95}[/tex]

Answer:

To find 3.8% of 25, we can convert the percentage to a decimal and then multiply it by 25:

3.8% = 0.038 (converting percentage to decimal)

0.038 x 25 = 0.95

Therefore, 3.8% of 25 is 0.95.

Answer:

there is no chart or questions

Step-by-step explanation:

They will have to change the plugs, rotate the tyre, and replace the brake pads all at once for the first time​ after 30,000 km.

LCM is the abbreviated form for Least Common Multiple. LCM of two or more numbers is the lowest of all the common multiples of them.

Given,

Plugs are changed every 30,000 km

Rotate the tyres every 10,000 km

Replace the break pads blades every 15,000 km

All the three will be done together for the first time when all the multiples of the three distances intersect for the first time.

It is enough to find the LCM of 30000, 10000 and 15000 to find the least distance travelled when all the things are done together.

Multiples of 30,000 = 30000, 60000, 90000, ...........

Multiples of 10,000 = 10000, 20000, 30000, .......

Multiples of 15,000 = 15000, 30000, 45000, ........

The common multiple for the first time is 30,000.

Hence all the changes will be made to the car together for the first time after 30,000 km.

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The regular pentagon's perimeter is therefore sqrt(101) units when its adjacent edges are at A(-3, 5) and B(7, 6).

The perimeter of a two-dimensional object is the space surrounding it. It represents the total length of the shape's edges. Typically, the perimeter is calculated using measures like centimetres, metres, or feet.

given

We can use the calculation for the distance between the two provided vertices to determine the length of one side:

sqrt[(7 - (-3))2 Plus (6 - 5)2] yields AB. = sqrt[10^2 + 1^2] = sqrt(101) (101)

Since the five sides of a normal pentagon are all the same length, one side's length is:

sqrt(101) / 5

s = AB / 5

Now, utilising the method for the regular pentagon's perimeter, we have:

Circumference = 5s = 5 sqrt(101) / 5 = sqrt (101)

The regular pentagon's perimeter is therefore sqrt(101) units when its adjacent edges are at A(-3, 5) and B(7, 6).

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Answer:

x= 27.4

Step-by-step explanation:

a triangle's angles always equal 180 so

34.6+118+x=180

add 34.6 and 118 to get

152.6+x=180

subtract both sides by 152.6 to get

x=27.4

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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We can conclude that the Ratio of arc = scale factor of dilation.

An arc in mathematics is a section of a circle's or curve's perimeter. An open curve is another name for it.

The circumference of a circle, sometimes referred to as its perimeter, serves as its boundary. The distance between any two locations traced along the circle of an arc is hence its length.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Now, we know that arc of a circle can be found by using formula:

= Ф × π/180° × r

Arc of Circle A=  90 × π/180 × 3

                       = 3π/2

Arc of Circle B = 90 × π/180 × 9

                        = 9π/2

So, Ratio of arc = Arc of Circle B/Arc of Circle A

                         = 9π/2 ÷ 3π/2 = 3.

Hence, we can see that Ratio of arc = scale factor of dilation.

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Answer:

28cm

Step-by-step explanation:

[tex] \frac{44}{22} \times 14 = 28[/tex]

Answer:

(4[tex]x^{2}[/tex]+2)([tex]x^{2}[/tex]-3)

Step-by-step explanation:

 4x    +2

  x       -3

ABCD is the square base and A is the apex. As you can see, the apex is not directly above the center of the base, which makes this an oblique square pyramid.

An oblique square pyramid is a type of three-dimensional geometry that has a square base and four triangular faces that meet at a point, called the apex, but the apex is not directly above the center of the base. In other words, the pyramid is "tilted" or "leaning" to one side.

The key difference between an oblique square pyramid and a regular square pyramid is the location of the apex. In a regular square pyramid, the apex is directly above the center of the base, while in an oblique square pyramid, the apex is off-center.

Here is a diagram of an oblique square pyramid:

In this diagram, ABCD is the square base and A is the apex. As you can see, the apex is not directly above the center of the base, which makes this an oblique square pyramid.

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The factors of the form (x - c) are (x - 2) and (x² + 49).

To factor the polynomial f(x) = x³ - 2x² + 49x - 98 into factors of the form (x - c), we can use synthetic division with the given zero of 2.

2 | 1 -2 49 -98
  |     2  0  98
    1  0 49   0

The result of the synthetic division gives us the quotient (x² + 49) and a remainder of 0, confirming that 2 is indeed a zero of the polynomial.

Now we can write the polynomial as the product of (x - 2) and the quotient (x² + 49):

f(x) = (x - 2)(x² + 49)

Since the quadratic factor (x² + 49) cannot be factored further using real numbers, the final factorization of the polynomial is:

f(x) = (x - 2)(x² + 49)

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The approximate area of the school is 22857 kilometer square.

The approximate area of the school can be found by multiplying the fraction of space covered by the STEM Innovation Academy building by the total area of the space.

In this case, the fraction of space covered is (4)/(7) and the total area of the space is 40,000 square kilometres.

To find the approximate area of the school, we can multiply these two values together:

(4)/(7) * 40,000 = 22,857.14

Therefore, the approximate area of the STEM Innovation Academy building is 22,857.14 square kilometres.

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Answer:

y = 3x + 10

Step-by-step explanation:

y represents total he pays

x represents items he buys

total he pays = $3 for each item + $10 movie

y = 3x + 10

The vertex of the parabola is (5, 4). The solution has been obtained by using quadratic formula.

What is quadratic formula?

The quadratic formula is used to determine an equation's roots. This formula assists in evaluating the solutions of the quadratic equations instead of the factorization approach.

We are given equation as  y = -x² + 10x - 21.

Using quadratic formula, we know that x = -b/2a

So,

x = -10/-2

x = 5

On substituting this in the equation, we get

y = -5² + 10(5) - 21

y = -25 + 50 - 21

y = 4

Hence, the vertex of the parabola is (5, 4).

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If a rectangular prism has dimensions of 1.5 feet by 3.5 feet by 2 feet, its volume, expressed in cubic feet, is 10.5 cubic feet.

The rectangular prism's measurements are —

3.5 feet in length

1.5 feet wide in Size

Height is two feet.

The volume of the rectangular prism is calculated by multiplying these dimensions collectively.

Volume equals length, width, and height, or 3.5 feet, 1.5 feet, and 2 feet.

= 10.5 cubic feet of volume

Hence, the rectangular prism has a volume of 10.5 cubic feet.

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The answer is f(-x) = x^4 + 6x + 2 and the function is neither even nor odd.

To find f(-x), we simply substitute -x for x in the original function:

f(-x) = (-x)^4 - 6(-x) + 2 = x^4 + 6x + 2

Now, to determine if f is even, odd, or neither, we compare f(x) and f(-x). If f(x) = f(-x), then the function is even. If f(x) = -f(-x), then the function is odd. If neither of these conditions are met, then the function is neither even nor odd.

In this case, f(x) = x^4 - 6x + 2 and f(-x) = x^4 + 6x + 2. These are not equal, so the function is not even. However, if we multiply f(-x) by -1, we get:

-f(-x) = -x^4 - 6x - 2

This is also not equal to f(x), so the function is not odd either. Therefore, the function is neither even nor odd.

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To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations.

Kathleen's prediction is flawed because she assumed that the average number of pets per household would remain the same for all households in the state, which may not necessarily be true. The sample size of 200 households may not be representative of the entire population of households in the state, and there may be variations in the number of pets per household across different regions or socioeconomic groups.

To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations. Alternatively, she could use data from existing sources, such as census data, to estimate the number of pets per household in different regions of the state and adjust her prediction accordingly. It's also worth noting that factors such as pet ownership trends, cultural attitudes towards pets, and population growth may also impact the accuracy of Kathleen's prediction and should be taken into account.

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The sum of number is 270, after adding 5 to each number , sum of numbers is 320 and mean is 32.

The mathematical average of a group of two or more numbers is arithmetic mean, add the numbers in a set together and divide by the total number of numbers in the set.

Here the mean of 10 number is 27. We know that ,

[tex]mean=\frac{sum of numbers}{total numbers}\\[/tex]

[tex]27= \frac{sum of numbers}{10}[/tex]

=sum of numbers = 27*10=270.

Now 5 added to each number, we need to add 5 in 10 times( because 10 total number), Then 5*10=50.

Sum of numbers after adding 5 to each number [tex]270+50=320[/tex]

Now, [tex]mean=\frac{320}{10}=32[/tex]

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The following functions can be simplify as follows:

(a) f+g=x²+3x+8

(b) f-g=x²-13x-8

(c) fg=x³+3x²-40x-40

(d) f/g= (x-5)/(x+8) domain is x≠-8.

(a) To find f+g, we simply add the two functions together:

f+g=x^{2}-5x+x+8= x^{2}+3x+8

(b) To find f-g, we subtract g from f:

f-g=x^{2}-5x-(x+8)= x^{2}-6x-8= x^{2}-13x-8

(c) To find fg, we multiply the two functions together

:fg=(x^{2}-5x)(x+8)= x^{3}+3x^{2}-40x-40

(d) To find f/g, we divide f by g:

f/g= (x^{2}-5x)/(x+8)= (x-5)/(x+8)

The domain of this function is all real numbers except for -8, since dividing by zero is undefined. So the domain is x≠-8.

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Answer: Point B is (-2,0) and Point C is (0,3)

Step-by-step explanation:

We know x-intercept is when y=0 and y-intercept is when x=0

Let's first find the x-intercept by replacing y with 0.

6x-4(0)=-12

now let's solve for x

6x-0=-12

x=-2

so Point B is (-2,0)

Now let's find the y-intercept by replacing x with 0

6(0)-4y=-12

now solve for y

-4y=-12

y=3

So point C is (0,3)

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

To determine the value of the car after 2 years, we need to plug in x=2 into the exponential function y=20000*(13000/20000)^x.

y=20000*(13000/20000)^2

y=20000*(0.65)^2

y=20000*0.4225

y=8450

Therefore, the value of the car after 2 years is $8450.

To round to the nearest dollar, we can look at the decimal part of the number. Since the decimal part is less than 0.5, we can round down to the nearest whole number.

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

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The magnitude of the vector ū is approximately 5.10, and the angle is approximately 281.31°.

The magnitude of a vector is the length of the vector, and is calculated using the Pythagorean Theorem. The angle of a vector is the direction in which the vector points, measured counterclockwise from the positive x-axis.

To find the magnitude of the vector ū = (-1,5), we can use the formula:

magnitude = √(x^2 + y^2)

where x and y are the components of the vector.

Plugging in the values of x and y from the vector ū, we get:

magnitude = √((-1)^2 + (5)^2)

Simplifying the expression, we get:

magnitude = √(1 + 25)

magnitude = √(26)

magnitude ≈ 5.10

To find the angle of the vector, we can use the formula:

angle = tan^-1(y/x)

Plugging in the values of x and y from the vector ū, we get:

angle = tan^-1(5/-1)

angle = tan^-1(-5)

angle ≈ -78.69°

Since the angle is measured counterclockwise from the positive x-axis, we need to add 360° to get the angle in the correct quadrant:

angle = -78.69° + 360°

angle = 281.31°

Therefore, the magnitude of the vector ū is approximately 5.10, and the angle is approximately 281.31°.

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About 5,000 more fans attended the third round finals than the third round time trials.

From the question, we are to find the approximate difference between the attendance of the third round finals and the third round time trials.

From the given data, we have:

Attendance Time             Trials                      Finals

1st round                           12,645                    17,352

2nd round                         16,234                    21,896

3rd round                          18,817                     23,773

Third round finals attendance = 23,773

Third round time trials attendance = 18,817

The difference between these two numbers is:

23,773 - 18,817 = 4,956

Rounding this to the nearest thousand gives:

4,956 ≈ 5,000

Hence, The number of fans that attended the third round finals than the third round time trials is about 5,000

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The order of the decimal number from least to greatest is

4.08< 4.7<4.76<4.9.

Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.

Here the given decimal numbers are,

=>  4.76, 4.9, 4.08,4.7

Now ordering the number from smallest to largest

=>4.08< 4.7<4.76<4.9.

Hence the order of the decimal number from least to greatest is 4.08< 4.7<4.76<4.9.

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