Assume that the volume of air in an average adult’s lung follows a transformed sine function, as function of time t in seconds,
V (t) = A + B sin(ωt)
Below is a table of measurements of the volume. Identify constants A, B, and ω so that the function above fits these measurements. After 12 seconds, the measurements will repeat.
t - 0 3 6 9 12
V(t) - 7 9 7 5 7

answer is POSITIVE 26,

Step-by-step explanation:

because when you add positive 11 to get zero, you just need to add positive 15 to get POSITIVE 15

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:

[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:

The correct answer would be C (-3, 7)

Step-by-step explanation:

The first coordinate is the x (-3) and the second is the y (+7); therefore, the coordinate of the fourth vertex on the plane is (-3, 7).

Answer:

your answer should be C (-3, 7)

Step-by-step explanation:

brainliest pls

Have a nice day

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:

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:

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:

the answer is 7.5. hope this helps

Answer:

7.5

Step-by-step explanation:

Answer:5,7

Step-by-step explanation:

Answer:

b,c

Step-by-step explanation:

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:

search on google

Step-by-step explanation:

Answer:

$1,958.23

Step-by-step explanation:

Annual income = $67,525

Total FCIA = 15.3% of salary

Since my annual income is $67,525 the FCIA contribution = 15.3%.

But 12.4% is for Social Security.

The remaining 2.9%(15.3% - 12.4%) will be for Medicare taxes.

The total deduction for I and my employer for medicare taxes will be:

2.9% * $67,525

= $1,958.225

The total deduction for medicare would be: $1,958.23

Note: Assuming we were asked to calculate only employee's medicare, the deduction would be 50% of $1,958.23.

Answer:

1958

Step-by-step explanation:

Answer:

You have to make them equal first. Start with that.

1/8  --> 3/24

1/6 ---> 4/24

1/3  --> 8/24

Now, order them.

1/8, 1/6. 1,3

Answer:

(a) 99% confidence interval for the percentage of girls born is [0.804 , 0.896].

(b) Yes​, the proportion of girls is significantly different from 0.50.

Step-by-step explanation:

We are given that a clinical trial tests a method designed to increase the probability of conceiving a girl.

In the study 400 babies were​ born, and 340 of them were girls.

(a) Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                    P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of girls born = [tex]\frac{340}{400}[/tex] = 0.85

             n = sample of babies = 400

             p = population percentage of girls born

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                    of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [[tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

= [ [tex]0.85-2.58 \times {\sqrt{\frac{0.85(1-0.85)}{400} } }[/tex] , [tex]0.85+2.58 \times {\sqrt{\frac{0.85(1-0.85)}{400} } }[/tex] ]

 = [0.804 , 0.896]

Therefore, 99% confidence interval for the percentage of girls born is [0.804 , 0.896].

(b) Let p = population proportion of girls born.

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.50      {means that the proportion of girls is equal to 0.50}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.50      {means that the proportion of girls is significantly different from 0.50}

The test statistics that will be used here is One-sample z proportion test statistics;

                               T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of girls born = [tex]\frac{340}{400}[/tex] = 0.85

             n = sample of babies = 400

So, the test statistics  =  [tex]\frac{0.85-0.50}{\sqrt{\frac{0.85(1-0.85)}{400} } }[/tex]

                                     =  19.604

Now, at 0.01 significance level, the z table gives critical value of 2.3263 for right tailed test. Since our test statistics is way more than the critical value of z as 19.604 > 2.3263, so we have sufficient evidence to reject our null hypothesis due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of girls is significantly different from 0.50.

To construct a 99% confidence interval for the percentage of girls born, calculate the sample proportion and use it to construct the confidence interval. The method appears to be effective.

To construct a 99% confidence interval for the percentage of girls born, we first need to calculate the sample proportion. In this case, the sample proportion of girls is 340/400 = 0.85. Using this proportion, we can construct the confidence interval using the formula.

Confidence Interval = sample proportion ± z x √((sample proportion x (1 - sample proportion)) / sample size). Calculating the confidence interval, we find that it is 0.808 to 0.892. Since this interval does not include the value of 0.5, the method appears to be effective.

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Answer:

B and C

Step-by-step explanation:

Answer:

parabola and quadratic

Step-by-step explanation:

just answered it

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:

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

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:

  80/99

Step-by-step explanation:

When the repeat starts at the decimal point, put the digits over an equal number of 9s.

  [tex]0.\overline{80}=\boxed{\dfrac{80}{99}}[/tex]

This fraction cannot be reduced.

Final answer:

To convert the repeating decimal 0.80 (with 80 repeating) to a fraction, set up an equation where x equals the repeating decimal, then multiply by 10 and subtract the original equation to eliminate the repeating part, and solve for x to get 8/9.

Explanation:

The number 0.80 with 80 repeating is often represented as 0.8 with a line over the 8, indicating that the 8 is repeating indefinitely. To convert 0.80 repeating to a fraction, we can use the following method:

Let x equal the repeating decimal: x = 0.888...

Multiply both sides by a power of 10 to move the decimal point to the right of the repeating digits. Here, we multiply by 10: 10x = 8.888...

Subtract the original equation from this new equation to get rid of the repeating decimal: 10x - x = 8 (9x = 8).

Now solve for x: x = 8/9.

Thus, 0.80 with 80 repeating as a fraction is 8/9.

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:

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: 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

Learn more about ratios here:

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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:

  (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:

The correct answer to the following question will be "32 servings".

Step-by-step explanation:

The given values are,

A bag of chips = 24 ounces

Serving size = 3/4 ounces

Servings = ?

Now,

On dividing "24 ounces" by "3/4 ounce", we get

⇒  [tex]\frac{24}{\frac{3}{4}}[/tex]

⇒  [tex]24\times \frac{4}{3}[/tex]

⇒  [tex]8\times 4[/tex]

⇒  [tex]32[/tex]

Thus, the bag of chips contains "32" servings.

Final answer:

To determine the number of servings in a 24-ounce bag of chips with a serving size of 3/4 ounce, divide the total weight by the serving size, resulting in 32 servings.

Explanation:

The student has asked a question about how to calculate the number of servings in a bag of chips given its total weight and the size of each serving. This is a mathematics problem involving division.

To find out the number of servings in a 24-ounce bag of chips where each serving is 3/4 ounce, you divide the total weight of the bag by the weight of a single serving:

Number of servings = Total weight of the bag / Weight of one serving

Number of servings = 24 oz / (3/4 oz)

To divide the fractions, you multiply by the reciprocal of the serving size, which is:

Number of servings = 24 oz × (4/3)

Number of servings = 32

Therefore, there are 32 servings in the 24-ounce bag of chips.

Answer:

A =42.9866 in^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

The radius is 3.7

A = pi (3.7)^2

Approximating pi by 3.14

A = 3.14 (3.7)^2

A =42.9866

Answer:

The area, in square inches, of the circle is 43.01.

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:

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:

694 cubic inches

Step-by-step explanation:

Dimension of prism

Length = 15.5 inches

width =  8 inches

height =  7 inches

Volume of regular prism is given  by area of base * height

area of base  = length * width ( as bin is rectangular)

area of base  = 15.5 * 8 square inches = 124 square inches

Volume of regular prism = area of base * height

      = 124 * 7 cubic inches = 868 cubic inches

_________________________________________________

868 cubic inches is the full capacity of the recycling bin

it is given that recycling bins need to be emptied when it is 80% full

so we need to find the 80% capacity of recycling bin

80% capacity of recycling bin = 80/100 *  full capacity of the recycling bin

                  = 0.8 * 868 cubic inches = 694.4 cubic inches

694.4 cubic inches is the amount needed before the recycle bin is ready to empty .

But question says answer should in nearest cubic inch

hence answer is 694 cubic inches