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Final answer:

Time's accuracy is crucial in sports, and a high school track coach's new stopwatch with an uncertainty of ±0.05 s may not be suitable for distinguishing very close race outcomes, such as those within a few hundredths of a second apart.

Explanation:

Time is a fundamental measurement in athletic competitions, particularly in track and swimming events, where even hundredths of a second can determine the outcome. The precision of time measurements has become increasingly important with the advancement of athletes' abilities, pushing the limits of human performance. In recent history, various advanced instruments have been developed to ensure the accuracy of timing in these competitions.

For instance, a high school track coach who has recently acquired a new stopwatch might find it incredibly useful or not depending on its precision. If the manual states the stopwatch has an uncertainty of ±0.05 s, this could affect the outcome of close races. Given that the top runners on the coach's team regularly clock 100-m sprints with times that may only differ by a few hundredths of a second, this level of uncertainty could be problematic in accurately distinguishing winning times.

Considering a scenario where the first-place sprinter came in at 12.04 s and the second-place sprinter at 12.07 s, the new stopwatch’s uncertainty range may not clearly differentiate between the two, since the difference in their times is within the margin of error of the stopwatch. This is relevant when comparing a sprinter's 100-meter sprint time of 12.04 seconds one week and 11.96 seconds the next week; due to the uncertainty of the stopwatch, we cannot conclusively say that this week's time was faster.faster.

Answer:

In the next two levels the tree we have 8 branches

Step-by-step explanation:

In mathematics, the Fibonacci numbers, commonly denoted Fₙ, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones.

The Fibonacci numbers are given as 1,2, 3,5,8,13........n

The Second level according to the Fibonacci sequence indicates that the tree will have 8 branches

Answer:

21,34

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

Root is the opposite of a power of 2.

Find 7 to the power of 2 to find the number inside:

7^2 = 7 * 7 = 49

49 is your answer, or B)

~

Answer:

49

Step-by-step explanation:

I believe that the answer is (A)

It is a locus of points that is equidistant from a fixed point called the center. Which is the correct answer would be an option (A)

Hyperbola is defined as a conic section, a two-branched open curve, produced by the intersection of a circular cone.

(x-h)²/b² - (y-k)²/a² = 1

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

The variable h represents the x-offset from the origin,

and k represents the y-offset from the origin.

Here it is a locus of points that are all equal distance from the center, a constant point.

Therefore, it is a locus of points that is equidistant from a fixed point called the center.

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Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 4)² + (y - 1)² = 34 ← is in standard form

with centre = (4, 1 ) and r² = 34 ⇒ r = [tex]\sqrt{34}[/tex] → A

Final answer:

The equation represents a circle with the center at (4,1) and a radius of 5.83 units.

Explanation:

The center of the circle is at (4,1) and the radius is 5.83 units.

To find the center of the circle, you simply take the opposite of the numbers inside the parentheses of (x - 4) and (y - 1), giving you the center (4, 1). The radius is the square root of the number on the right side of the equation, which is √34 = 5.83 units.

Answer:2

Step-by-step explanation:

In relation to the independent variable, one graph represents a linear relationship, as shown by the linear equation examples provided. The remaining graphs depict quadratic, inverse, and exponential relationships.

The question asks, 'When compared with the independent variable, how many of the graphs represent a linear relationship?' In the given examples, 'y = 6x + 8', '4y = 8', and 'y + 7 = 3x' are all linear equations. This means they represent a linear relationship between two variables, often plotted on horizontal and vertical axes of a graph. In such graphs, the independent variable is usually plotted on the horizontal (x) axis and the dependent variable on the vertical (y) axis.

If we look at the information regarding different types of relationships, the examples show a linear, quadratic, inverse, and exponential relationship graph. As the linear graph is the only one representing a linear relationship, the answer is that 1 out of 4 graphs, when compared with the independent variable, represents a linear relationship.

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Answer:its 3 (7)(4) 4(7)(3) 12(7) i just did it

Answer:

C,D,E

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

Answer:

X = 12 - Angle EFG = 48

Answer:

[tex]\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54[/tex]

The degrees of freedom are:

[tex] df=n-1=10-1=9[/tex]

Now we can calculate the p value using the alternative hypothesis:

[tex]p_v =2*P(\chi^2 >13.54)=0.279[/tex]

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Step-by-step explanation:

Assuming the following data:"12.14 12.05 12.27 11.89 12.06

12.14 12.05 12.38 11.92 12.14"

We can calculate the sample deviation with this formula:

[tex]s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]n=10[/tex] represent the sample size

[tex]\alpha=0.05[/tex] represent the confidence level  

[tex]s^2 =0.0217 [/tex] represent the sample variance

[tex]\sigma^2_0 =0.12^2= 0.0144[/tex] represent the value to verify

Null and alternative hypothesis

We want to determine whether the standard deviation differs from 0.12 ounce, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma^2 = 0.0144[/tex]

Alternative hypothesis: [tex]\sigma^2 \neq 0.0144[/tex]

The statistic can be calculated like this;

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

[tex]\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54[/tex]

The degrees of freedom are:

[tex] df=n-1=10-1=9[/tex]

Now we can calculate the p value using the alternative hypothesis:

[tex]p_v =2*P(\chi^2 >13.54)=0.279[/tex]

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Answer:

B and c.

Step-by-step explanation:

Area is: L x W.

8 x 3 = 24

6 x 4 = 24

Feel free to let me know if you need more help. :)

Answer:

b. and c.

Step-by-step explanation:

Area of a rectangle is wl

8 x 3 = 24

6 x 4 = 24

Answer:

-35-42j

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the value of each variable.

We can see that angle b corresponds to diameter of circle. We know that the measure of an angle that is inscribed to the diameter of a circle is 90 degrees . Therefore, the value of b will be 90.

we can see that angle is an inscribed angle of arc 99 degrees. We know that measure of an inscribed angle is half the measure of inscribed arc.

[tex]a=\frac{1}{2}\cdot 99[/tex]

[tex]a=49.5[/tex]

Therefore, the value of a is 49.5 units.

We know that measure of all angles of a triangle is 180 degrees. The measure of 3rd angle will be half the measure of c, so we can set an equation as:

[tex]a+b+\frac{1}{2}c=180[/tex]

[tex]49.5+90+\frac{1}{2}c=180[/tex]

[tex]139.5+\frac{1}{2}c=180[/tex]

[tex]139.5-139.5+\frac{1}{2}c=180-139.5[/tex]

[tex]\frac{1}{2}c=40.5[/tex]

[tex]\frac{1}{2}c\cdot 2=40.5\cdot 2[/tex]

[tex]c=81[/tex]

Therefore, the value of c is 81.

To calculate the amount after 2 years, use the formula for continuous compound interest. To find how long it will take for the amount to be $10,000, rearrange the formula and solve for t.

To calculate the amount after 2 years, we can use the formula for continuous compound interest: A = P * e^(rt), where A is the amount, P is the principal, e is Euler's number approximately equal to 2.71828, r is the interest rate, and t is the time in years.

Using the given values, we have A = 5900 * e^(0.06 * 2).

Using a calculator, we can find that A is approximately $6488.85.

To find how long it will take for the amount to be $10,000, we can rearrange the formula and solve for t. In this case, we have 10000 = 5900 * e^(0.06t).

Dividing both sides by 5900 and taking the natural logarithm of both sides, we get ln(10000/5900) = 0.06t.

Using a calculator, we find that t is approximately 3.41 years.

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Answer:

B. 2.3

Step-by-step explanation:

Answer:

If the distance is 4.6 centimeters, then the actual distance has to be 2.3 kilometers.

Step-by-step explanation:

[tex]\frac{2 cm}{1 km}[/tex]

[tex]\frac{2}{1} * \frac{4.6}{?}[/tex]

[tex]\frac{4.6}{2}[/tex]

2.3 km

So, you answer is letter choice 2.3 kilometers.

Answer:

5

Step-by-step explanation:

That's all I could come up with

The solutions to the quadratic equation [tex]$x^2 = 25$[/tex] are x = 5 and x = -5. Thus, the correct options are 5 and -5.

To solve the quadratic equation [tex]\(x^2 = 25\)[/tex] by finding square roots, we take the square root of both sides.

Taking the square root of 25, we get [tex]\(x = \pm 5\)[/tex].

So, the solutions are [tex]\(x = \pm 5\)[/tex].

Therefore, the correct options are:

5

-5

Answer:

bull-market

Step-by-step explanation:

Answer:

Step-by-step explanation:

volume V1=4/3 π(r1)³=4/3 π×7³

V2=4/3 π(r2)³=4/3 π×4³

V1-V2=4/3 π(7³-4³)=4/3π(343-64)

=4/3×π×279

=4π×93

=372π mm³

Answer: There is 15

Step-by-step explanation: 3a-2b

                                             21-6=15

Answer:

54

Step-by-step explanation:

this is wrong don't mind it

Answer:

I got 16.7%

Step-by-step explanation:

Question:

1. The females worked less than the males, and the female median is close to Q1.

2. There is a high data value that causes the data set to be asymmetrical for the males.

3. There are significant outliers at the high ends of both the males and the females.

4. Both graphs have the required quartiles.

Answer:

The correct option is;

1. The females worked less than  the males, and the female median is close to Q1

Step-by-step explanation:

Based on the given data, we have;

For males

Minimum = 0

Q1 = 1

Median or Q2 = 20

Q3 = 25

Maximum = 50

For females;

Minimum = 0

Q1 = 5

Median or Q2 = 6

Q3 = 10

Maximum = 18

Therefore, the values of data that affect the statistical measures of spread and center are that

The females worked less than the males as such the statistical data for the females have less variability than the males in terms of interquartile range

Also the female median is very close to Q1, therefore it affects the definition of a measure of center.

Answer:

the answer is the second one

Step-by-step explanation:

Answer:

1 unit

Step-by-step explanation:

We have the following formula to find  the length of an arc that subtends an angle of radians is:

S = rΘ where:

Given the information in this question, we have:

=> the length of an arc in this question is:

1*1 = 1 unit

Hope it will find you well

Final answer:

The length of an arc in a circle with radius 1 that subtends an angle of a radians is a units.

Explanation:

The student's question asks for the length of an arc in a circle with a radius of 1 that subtends an angle of a radians. The formula to calculate the arc length (s) is derived from the fact that the circumference of a circle (S) with radius r is S = 2πr. A full revolution around a circle results in an angular rotation of θ = 2π radians.

The arc length for an angle a radians in a circle with radius r is therefore s = r × a. Since the radius of the circle in this question is 1, the arc length is simply equal to the angle a in radians. Thus, the length of the arc is a units.

Answer:

40 2-point questions and 14 5-point questions

On a 150 point exam with 54 questions, consisting of 2 point and 5 point questions, there are 40 two-point questions and 14 five-point questions.

To determine how many 2 point and 5 point questions are on a 150 point exam with 54 questions, we need to set up a system of equations and solve it. Let x represent the number of 2 point questions and y represent the number of 5 point questions. We have two equations based on the information given:

Solving these equations simultaneously, we multiply the first equation by 2, which gives us 2x + 2y = 108. Subtracting this from the second equation cancels out x, yielding 3y = 42. Dividing both sides by 3 gives us y = 14. Substituting the value of y back into the first equation, we have x + 14 = 54, which gives us x = 40.

Therefore, there are 40 two-point questions and 14 five-point questions on the exam.

Answer:

18

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume = πr²h

= 3.14 * 5 * 5 * 10

= 785 in³

Answer:

Option C is the correct answer

Step-by-step explanation:

Brian’s and Geoff’s cars started the same distance from the sensor.

From the given data we get,

time      1s       3s     5s    8s

Brian     34      38     42    48

Kelsey   27      31     35    41

Geoff     27      33     39    48

From the above table we can conclude that Brian’s and Geoff’s cars started the same distance from the sensor.

So the answer is option C

Answer:

i would like to say the answer is 17

Step-by-step explanation:

Answer:

300 cm

Step-by-step explanation:

1 meter is 100 centimetres, so 3 meters would result in 3 x 100, which equals 300.

The area of a regular decagon whose apothem is 14 mm is 560 square milli meter

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain

We have to find the area of a regular decagon whose apothem is 14 mm and side length of 8m

Area of decagon = 1/2×Apothem×perimeter

Perimeter =Number of sides ×side length

=10×8

=80

Area of decagon = 1/2×14×80

=7×80

= 560 square mm

Hence, the area of a regular decagon whose apothem is 14 mm is 560 square milli meter

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The area of a regular decagon is approximately 605.5 mm².

Area of a regular decagon :

Area = (1/2) × Perimeter × Apothem

If we denote the side length by 's,' we can find it using the relationship between the number of sides, the side length, and the apothem:

The number of sides (n) is 10 because it is a decagon.

The formula for the side length of a regular polygon given its apothem (a) is:

[tex]s = 2a \times tan(\pi/n).[/tex]

Substitute n = 10 and a = 14 mm into the formula:

s = [tex]2 * 4 mm \times tan(\pi/10)[/tex]

   ≈ 8.65 mm.

Then, the perimeter (P) of the decagon is:

[tex]P = n \times s[/tex]

 = 10 *8.65 mm

≈ 86.5 mm.

Now, use the area formula:

Area = (1/2) × P × a

           = (1/2) × 86.5 mm × 14 mm

            ≈ 605.5 mm².

So, the area of the regular decagon is approximately 605.5 mm².