Four pencils are held together with a band.
Each of the pencils diameter 10mm.
Find the length of the band in this position
Give your answer in terms of π.

Answer:

17/52

Step-by-step explanation:

there are 13 diamonds in a standard deck of 52 cards.

the probability of getting a diamond will therefore be 13/52 = 1/4

there are 4 aces in a standard deck of 52 cards.

the probability of getting an ace will therefore be 4/52 = 1/13

the probability of getting a diamond or an ace will be 1/4 + 1/13

= 17/52

Answer:

Step-by-step explanation:

The independent variable is time (t), determining the distance covered.

The point (12, 4) means Noah walks for 12 hours, covering 4 miles.

To find time for 7[tex]\frac{1}{2}[/tex] miles,  [tex]\frac{1}{3}d = t \),[/tex] Substitute 7.5 for d, yielding [tex]\( \frac{1}{3} 7.5 = t \) = 2.5 hour[/tex]. So, (2.5, 7.5) represents Noah taking 2.5 hours to walk 7[tex]\frac{1}{2}[/tex] miles.

1. **Identify the independent variable**:

In the equation [tex]\( \frac{1}{3}d = t \),[/tex] the independent variable is time (t). The independent variable is the one that stands alone and is not dependent on other variables. In this case, time (t) is independent as it determines the distance covered (d).

2. **What does the point (12, 4) represent in this situation**:

  The point (12, 4) represents a specific instance in the relationship between time and distance. In this case, it means that when Noah walks for 12 hours, he covers a distance of 4 miles. This point is a solution to the equation  [tex]\( \frac{1}{3}d = t \),[/tex] where 12 hours corresponds to the time (t) and 4 miles corresponds to the distance (d).

3. **What point would represent the time it took to walk 7 1/2 miles**:

  To find the point representing the time it takes to walk 7 1/2 miles, we substitute 7.5 miles into the equation and solve for time (t). First, we rewrite the equation without fractions to make the calculation simpler:

[tex]\[ \frac{1}{3}d = t \][/tex]

[tex]\[ \frac{1}{3} \times d = t \][/tex]

[tex]\[ \frac{1}{3} \times 7.5 = t \][/tex]

 Now, we simply multiply 1/3 by 7.5:

[tex]\[ t = \frac{1}{3} \times 7.5 \][/tex]

[tex]\[ t = 2.5 \][/tex]

  So, the time it takes to walk 7[tex]\frac{1}{2}[/tex] miles is 2.5 hours. Therefore, the point representing this situation is (2.5, 7.5), indicating Noah takes 2.5 hours to walk 7.5 miles. This point satisfies the equation [tex]\( \frac{1}{3}d = t \)[/tex], where 2.5 hours corresponds to the time (t) and 7.5 miles corresponds to the distance (d).

In summary, the independent variable in this situation is time (t), the point (12, 4) represents Noah walking for 12 hours and covering 4 miles, and the point (2.5, 7.5) represents Noah taking 2.5 hours to walk 7[tex]\frac{1}{2}[/tex] miles.

Answer:

0.1574 = 15.74% of the​ player's serves are expected to be between 116 mph and 146 ​mph

Step-by-step explanation:

Problems of normally distributed(bell-shaped) samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 101, \sigma = 15[/tex]

What proportion of the​ player's serves are expected to be between 116 mph and 146 ​mph?

This is the pvalue of Z when X = 146 subtracted by the pvalue of Z when X = 116. So

X = 146

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{146 - 101}{15}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a pvalue of 0.9987

X = 116

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{116 - 101}{15}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.9987 - 0.8413 = 0.1574

0.1574 = 15.74% of the​ player's serves are expected to be between 116 mph and 146 ​mph

To find the proportion of the player's serves between 116 mph and 146 mph, calculate the z-scores and use a z-table.

To find the proportion of the player's serves between 116 mph and 146 mph, we need to calculate the z-scores for these values and then use a z-table.

The formula for calculating the z-score is z = (x - mean) / standard deviation. So, for 116 mph: z = (116 - 101) / 15 = 1; and for 146 mph: z = (146 - 101) / 15 = 3.

The z-score of 1 corresponds to a cumulative proportion of 0.8413 and the z-score of 3 corresponds to a cumulative proportion of 0.9987. So, the proportion of serves between 116 mph and 146 mph is 0.9987 - 0.8413 = 0.1574, rounded to four decimal places.

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Answer:5,7

Step-by-step explanation:

Answer:

x^2+8x+16

(x+4)^2

Step-by-step explanation:

x^2 +8x

Take the coefficient of the x term

8

Divide by 2

8/2 =4

Square it

4^2 =16

x^2+8x+16

We can factor it into

(x+8/2) ^2

(x+4)^2

Final answer:

Completing the square for the expression x² + 8x involves adding and subtracting 16 to form the perfect square trinomial (x + 4)² and then subtracting 16. The factored form of the resulting trinomial is (x + 4)² - 16.

Explanation:

To complete the square for the expression x² + 8x, we need to find a number that, when added to 8x, will make the expression a perfect square trinomial. The number we're looking for is ²⁄8², which is 16. So, we add and subtract 16 within the expression to maintain equality.

The expression becomes x² + 8x + 16 - 16. Now the first three terms form a perfect square trinomial (x + 4)², and we still have -16. The expression is (x + 4)² - 16.

To factor the trinomial, we write it as the square of a binomial: (x + 4)². Hence, the expression x² + 8x can be written as (x + 4)² - 16, which is the factored form of the trinomial resulting from the completion of the square.

Answer:

So the decay percentage rate is of 70.8%

Step-by-step explanation:

An exponentil function has the following format:

[tex]y = ca^{x}[/tex]

In which c is a constant.

If a>1, we have that a = 1 + r and r is the growth rate.

If a<1, we have that a = 1 - r and r is the decay rate.

In this problem:

a = 0.292

A is lesser than 1, so r is the decay rate.

1 - r = 0.292

r = 1 - 0.292

r = 0.708

So the decay percentage rate is of 70.8%

Answer:

[tex] Y =\frac{16.5}{1.5}= 11[/tex]

[tex] X = 18-11=7[/tex]

And then we conclude that for the first job he works 7 hours and for the second job 11 hours

Step-by-step explanation:

We can define the following notation:

[tex]X[/tex] represent the number of hours worked for one job

[tex]Y[/tex] represent the number of hours worked for the other job

[tex]p_x = 9[/tex] represent the hourly payment for the first job

[tex]p_y = 7.50[/tex] represent the hourly payment for the other job

And we can define the following equations:

[tex] X+ Y= 18[/tex]   (1) represent the toal number of hours worked

[tex] 9X +7.5 Y = 145.50[/tex]  (2) represent the total amount earned

From equation (1) if we solve for X we got:

[tex] X = 18-Y[/tex] (3)

Replacing equation (3) into equation (2) we got:

[tex] 9(18-Y) +7.5 Y =145.50[/tex]

And after solve the equation we can find the value of Y:

[tex] 162 -9Y +7.5 Y =145.50[/tex]

[tex]16.5 = 1.5 Y[/tex]

[tex] Y =\frac{16.5}{1.5}= 11[/tex]

And solving for X from equation (3) we got:

[tex] X = 18-11=7[/tex]

And then we conclude that for the first job he works 7 hours and for the second job 11 hours

Answer:

1

Step-by-step explanation:

because one pizza is cut into 8 so

1 piece would be even

=1

The amount of pizza received by each person is 0.125.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The number of pizza is 1.

And, the total number of people is 8.

Now, the share of each people can be obtained as follows,

Consider that each people get the equal share.

The arithmetic operation used in this case is division.

Then, the problem can be solved by dividing 1 by 8 as follows,

⇒ 1 ÷ 8 = 1/8 = 0.125

The result of the division is a decimal number which shows that the amount of pizza for each people is the smallest part less than the whole.

Hence, the share of pizza received by each person is 0.125.

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To enclose a circular garden with a radius of 14m, you would need 88 meters of fencing.

To find the amount of fencing required to enclose a circular garden, you need to calculate the circumference of the garden. The formula for circumference is given by C = 2πr, where r is the radius of the garden.

Given that the radius is 14m, you can use the value of π as 22/7. So, the circumference is C = 2 * (22/7) * 14 = 88m.

Therefore, you would need 88 meters of fencing to enclose the circular garden.

Answer:

2/3

Step-by-step explanation:

To find the slope take the difference of the y's over the difference of the x's

(8-6)/ (12-9)

2/3

Answer: a) The graph opens up.

Step-by-step explanation:

The vertex is the minimum/maximum of a parabola.

We know that the vertex is in the second quadrant (so it is in the quadrant of positive y values and negative x values)

We also know that it has no real roots, so the graph never touches the x-axis, and knowing that the vertex is above the x-axis, then the graph must open upwards.

Then the correct option is:

a) The graph opens up.

When the vertex of the graph of a quadratic function is in the second quadrant and has no real solutions, this means that the graph opens down. The other statements provided are not necessarily true in this specific context.

In the context of this problem related to quadratic functions, if the vertex of the graph is in the second quadrant and there are no real solutions, the correct statement is (b) the graph opens down. Quadratic functions in the second quadrant that have no real solutions indeed point downwards. This is due to the fact that the function cannot touch or cross the x-axis (indicating that there are no real solutions).

As for option (c), the y-intercept could be any real number, so it does not have to be 0. Concerning option (d), the axis of symmetry can't be x = 0 as the vertex is in the second quadrant and x = 0 is the y-axis. Lastly, option (a) is false because if the graph opened up it would pass through the x-axis, providing real solutions, contrary to what is given in the problem.

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Answer:

help me and I will help you

Answer:

v = 3

Step-by-step explanation:

7(v - 3) + 7v = 21

distribute the 7 into the parentheses

7v -21 +7v = 21

combine like terms

14v - 21 = 21

add 21 on both sides

14v + 21 - 21 = 21 + 21 which equals 14v = 42

divide both sides by 14 to isolate v

14v/14 = 42/14

v = 3

hope this helps :)

Answer:

(a) 0.3144

(b) 0.1497

(c) 0.654

(d) [tex]1.125\times 10^{-5}[/tex]

Step-by-step explanation:

It is given that in a survey 68% of callers complain about the service.

So the probability that a caller complaint about the service = 0.68

Therefore probability that caller does not complain for the service = 1-0.68 = 0.32

(a) Probability of next three caller complain about service [tex]=0.68\times 0.68\times 0.68=0.3144[/tex]

(b) Probability that next two caller complain but not third  

[tex]=0.68\times 0.68\times 0.32=0.1497[/tex]

(c) Two out of three calls produce a complaint

[tex]=^3C_20.68^2\times 0.32=0.654[/tex]

(d) None of the 10 calls produce a complaint

[tex]=0.32^{10}=1.125\times 10^{-5}[/tex]

The probability of individual and consecutive complaints from a call center are calculated using the given percentage of complaints. These calculations are based on the assumption of a consistent 68% complaint rate and that each complaint is an independent event.

The subject of this question is probability, a concept in mathematics. To answer your question, we need to make some assumptions. We must assume that each caller's complaint is an independent event - that is, whether one caller complains does not affect whether the next caller will complain. We also need to assume that the 68% complaint rate is consistent, meaning it does not vary with time or for any other reason.

(a) The probability of three consecutive callers complaining would be (0.68)^3 = 0.314432.
(b) The probability of the next two callers complaining, but not the third would be (0.68)^2* (1-0.68) = 0.147456.
(c) Two out of the next three calls producing a complaint could occur in three ways (CCN, CNC, NCC where C is a complaining caller and N is a non-complainer). So, it would be 3*(0.68)^2* (1-0.68) = 0.442368.
(d) The probability of none of the next 10 calls producing a complaint would be (1 - 0.68)^10 = 0.0000040859.

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Answer:

  (x, y, z, w) = (3, 7, 6, 8)

Step-by-step explanation:

Your list equation seems to resolve to 6 equations:

The first equation tells you ...

  0 = x -3 . . . . . subtract x

  3 = x . . . . . . . add 3

We can check this in the third equation:

  2(3) -1 = 5 . . . true

The fifth equation tells you ...

  8 = w . . . . . . . subtract 1

We can check the value of y in the last equation:

  9(7) = 8(7) +7 . . . true

The variable values are ...

  (x, y, z, w) = (3, 7, 6, 8)

Answer:

You would create another equations that have same form as given equation.

For example, given y = (2/3)x - 5

=> Other one could be y = 2[(1/3)x - 5/2]

...

Hope this helps!

:)

Answer:

Sample Response/Explanation: To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.

Step-by-step explanation:

Answer:

v= 205.3

Step-by-step explanation:

The formula to solve a pyramid is v=(l*h*w)/3.

11*7*8=616

616/3=205.333.... (repeating 3)

about 205.3

~sorry I couldn't draw it out~

Answer:

6

Step-by-step explanation:

If there was one man, he would have taken 15×4= 60 hours

To complete the job in 10 hours, 60÷10 = 6 men will be needed

To paint the room in 10 hours instead of 15, the calculation shows that 6 men would be needed. This is determined through the concept of work rate and inverse proportions, calculating the total man-hours and then dividing by the desired hours.

The question involves determining the number of men needed to paint a room in 10 hours, given it takes 15 hours for 4 men to paint the same room. This problem can be solved using the concept of work rate and inverse proportions, which is a common method in Mathematics to deal with time and work problems. First, we calculate the work rate of the 4 men together and then find how many men would be needed to complete the job in 10 hours at a proportional rate.

Calculation steps:

Therefore, 6 men would be needed to paint the room in 10 hours.

Answer:

Domain: all real values

Step-by-step explanation:

f(x)=(x+1)^2

The domain is the values for x

We can use any value for x in the equation

Domain: all real values

Answer:

All real values of x

Step-by-step explanation:

f(x) = (x + 1)² is defined for all x

Hence the domain includes all real values of x

Answer:

B and C

Step-by-step explanation:

Answer:

parabola and quadratic

Step-by-step explanation:

just answered it

Answer: 3 pages per minute

Step-by-step explanation:

61x=183

x= the amount of pages

183/61= 3 pages

You can check this by multiplying 3 by 61 which = 183.

Answer:

3

Step-by-step explanation:

183             x

-----   =      -----

61                1

Cross Multiply

183= 61x

Divide

3=x

Answer:

The original number was 18.1.

Step-by-step explanation:

This question can be solved using a simple rule of three.

When a number is decreased by 17% the result is 15.

So 15 is 100-17 = 83%. The original number is 100%. Then

15 - 0.83

x - 1

[tex]0.83x = 15[/tex]

[tex]x = \frac{15}{0.83}[/tex]

[tex]x = 18.1[/tex]

The original number was 18.1.

Answer:

20

Step-by-step explanation:

Mean is the average of the numbers. You get the average by adding all the numbers and then dividing by the amount of numbers there are.

Example: 17+24+26+13=80 divided by 4 is 20

Answer: 2/3

Step-by-step explanation:

N is the total number of students

M is the number of students thta like math

S is the number of students that like science.

We know that half of the elements in M also are elements from S

And a third of the elements of S also are elements of M

And because those elements are common elements for both sets, we should have that:

M/2 = S/3

then we have that:

M = (2/3)*S

The ratio is 2/3

this means that the number of students that like math is 2/3 times the number of students that like science.

The ratio of the number of students who like math to the number of students who like science is 2/3

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

For the given case, we can assume the real quantities by variables.

Let we have:

By given information, we have:

Since the statement "M/2 students like science too" and "S/3 students like maths too" are same thing, so they're taking about same students who like math and science both, thus:

[tex]\dfrac{M}{2} = \dfrac{S}{3}\\\\\text{Multiplying both the sides by 2/S}\\\\\dfrac{M}{S} = \dfrac{2}{3}[/tex]

Thus, the ratio needed (ratio of number of students liking math to the number of students liking science) is M/N = 2/3

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Answer:

x=[tex]\frac{5}{2}[/tex]

Step-by-step explanation:

First, subtract 5 on both sides since when you subtract 5 from 5, it will give you 0.

Basically we are trying to get rid of the +5.

2x+5-5=10-5

2x=5

Divide by 2 to get rid of the 2 that is combined with the x.

2x/2=5/2

x=[tex]\frac{5}{2}[/tex]

Answer:x=5/2

Step-by-step explanation:

2x+5=10

Subtract 5 from both sides

2x+5-5=10-5

2x=5

Divide both sides by 2

2x/2=5/2

x=5/2

Answer:

D

Step-by-step explanation:

8^2+x^2=16^2

With 97% confidence, we estimate that the true standard deviation of the firm's employees' work hours lies within the range of approximately 5.832 to 7.950 hours per week.

To construct a 97% confidence interval for the standard deviation [tex](\(\sigma\))[/tex], we use the chi-square distribution. The formula for the confidence interval is given by:

[tex]\[ \left( \sqrt{\frac{(n-1)s^2}{\chi_{\alpha/2}^2}}, \sqrt{\frac{(n-1)s^2}{\chi_{1-\alpha/2}^2}} \right) \][/tex]

where [tex]\(n\)[/tex] is the sample size, [tex]\(s\)[/tex]  is the sample standard deviation, [tex]\(\alpha\)[/tex]is the significance level, and [tex]\(\chi_{\alpha/2}^2\)[/tex]  and [tex]\(\chi_{1-\alpha/2}^2\)[/tex]  are the chi-square critical values.

Given that [tex]\(n = 50\)[/tex] , [tex]\(s = 7.2\)[/tex] , and [tex]\(\alpha = 0.03\)[/tex]  (97% confidence level corresponds to [tex]\(\alpha/2 = 0.015\))[/tex] , we look up the critical values from the chi-square distribution table. For 49 degrees of freedom (50-1), the critical values are approximately 31.449 and 71.420.

Substitute these values into the formula:

[tex]\[ \left( \sqrt{\frac{49 \times 7.2^2}{31.449}}, \sqrt{\frac{49 \times 7.2^2}{71.420}} \right) \][/tex]

The formula for the confidence interval is:

[tex]\[ \left( \sqrt{\frac{(n-1)s^2}{\chi_{\alpha/2}^2}}, \sqrt{\frac{(n-1)s^2}{\chi_{1-\alpha/2}^2}} \right) \][/tex]

Given:

[tex]\[ n = 50, \ s = 7.2, \ \alpha = 0.03 \][/tex]

For 49 degrees of freedom (50-1), the chi-square critical values are approximately 31.449 [tex](\(\chi_{\alpha/2}^2\))[/tex]  and 71.420 [tex](\(\chi_{1-\alpha/2}^2\))[/tex] .

Now, substitute these values into the formula:

[tex]\[ \left( \sqrt{\frac{49 \times 7.2^2}{31.449}}, \sqrt{\frac{49 \times 7.2^2}{71.420}} \right) \][/tex]

Calculating this yields approximately (5.832, 7.950).

Therefore, the 97% confidence interval for the standard deviation of the weekly work hours is approximately (5.832, 7.950).

In summary, with 97% confidence, we estimate that the true standard deviation of the firm's employees' work hours lies within the range of approximately 5.832 to 7.950 hours per week.

Answer:

the answer is 7.5. hope this helps

Answer:

7.5

Step-by-step explanation:

Answer:

b,c

Step-by-step explanation:

We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.

The null hypothesis (H0) is that the mean NAEP math score for young men nationwide is 275. The alternative hypothesis (Ha) is that the mean score is less than 275. The level of significance is 5%.

The t-test statistic is -0.86 and the p-value is 0.20. Since the p-value is greater than the significance level (0.20 > 0.05), we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.

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