how to make the fraction bar??

The rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

The formula for the area of a circle is shown as  :

A = πr^2

where A = area

π = 3.142

r = radius

We will differentiate with respect to time, :

dA/dt = 2πrn xdr/dt

we have that dA/dt = 3 ft²/s

3 = 2π(25) x dr/dt

we calculate for  dr/dt,

dr/dt = 3/(50π) =  0.019 ft/s

In conclusion, if a person is making an ice rink by pouring water out of a hose. If water is spreading in a circular shape and the area covered by water grows with the rate of 3 ft?/sec, the rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

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The rate of change is obviously that term that describe the change over a certain period. In this problem, we are given with the condition that LaToya is able to burn 20 calories per minute. Therefore, the rate of change is 20 calories per minute.

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Answer:B

Step-by-step explanation:20 calories per minute

Answer:

$4,680

Step-by-step explanation:

Rate : 10 dollars a week

You will have saved up $4,680 in 9 years.

Function: The function itself represents the relationship between the input and output variables. It gives the values of the dependent variable (usually denoted as y) for different values of the independent variable (usually denoted as x).

First derivative: The first derivative of a function measures the rate of change of the function at a given point. It tells us where the function is increasing or decreasing, as it indicates the slope of the function at each point. A positive first derivative indicates an increasing function, while a negative first derivative indicates a decreasing function.

Second derivative: The second derivative of a function measures the rate of change of the first derivative. It tells us where the function is concave up or concave down, as it indicates the curvature of the function at each point. A positive second derivative indicates a concave up function, while a negative second derivative indicates a concave down function. The second derivative also provides information about the inflection points of the function.

In summary, the function itself represents the relationship between variables, the first derivative tells us about the function's increasing or decreasing behavior, and the second derivative tells us about the function's concavity or curvature.

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a) Rounding this to the nearest whole number, we get an expected number of runs scored in a season of 10,935.

b)  We can assume that the expected number of runs scored in a season of 500 is not achievable with any reasonable batting average.

a. To find the expected number of runs scored in a season for a team with a batting average of 0.235, we substitute 0.235 for x in the regression equation:

y = 9,760 + 5,000x

y = 9,760 + 5,000(0.235)

y = 9,760 + 1,175

y ≈ 10,935

Rounding this to the nearest whole number, we get an expected number of runs scored in a season of 10,935.

b. To find the assumed team's batting average given an expected number of runs scored in a season of 500, we rearrange the regression equation and solve for x:

y = 9,760 + 5,000x

500 = 9,760 + 5,000x

5,000x = -9,260

x = -1.852

This negative value for x doesn't make sense in the context of batting average, so we can assume that the expected number of runs scored in a season of 500 is not achievable with any reasonable batting average.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:

2.24units

Step-by-step explanation:

Let the coordinate be A(3, -5) and A'(2, -3)

Using the formula for calculating the distance between two points

D = √(x2-x1)²+(y2-y1)²

AA' = √(2-3)²+(-3-(-5))²

AA' = √(-1)²+(-3+5))²

AA' = √1+2²

AA' =√5

AA' = 2.24 units

Note that the coordinate points are assumed

Answer:

It’s C

Step-by-step explanation:

Just did the quiz

Answer:

36 days.

Step-by-step explanation:

60 + 15 = 75 soldiers.

By proportion the number of days that the provisions will last

=  45 * (60/75)

=  45 * 4/5

= 36 days.

The specific value that the mean reading speed of a random sample of second-grade students will exceed cannot be determined solely based on the given information.

The statement mentions a "chance" but does not provide any specific information about the distribution or standard deviation of the reading speeds. Without knowing the variability of the data, it is not possible to determine a precise value that the mean reading speed will exceed.

To estimate the value, we would need additional information such as the standard deviation or a confidence interval. With this information, statistical techniques such as hypothesis testing or confidence intervals could be used to determine the likelihood of the mean reading speed exceeding a particular value.

Therefore, without more information, we cannot determine the exact value that the mean reading speed of a random sample of second-grade students will exceed. The statement implies that there is a possibility, but without additional data or assumptions, it is not possible to provide a specific value.

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Answer:

|x+3|>8

Step-by-step explanation:

x is positive, so remove the absolute value signs. Adding a number greater than 5 to 3 will result in a number greater than 8.

Answer:

1

Step-by-step explanation:

1+1=2

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1 = False (6x6 = 36)

2 = True ( 6 + 5 = 11)

3 = True ( 6/2 = 3)

4 = True (17 - 6 = 11)

Answer:

false

true

true

true

Step-by-step explanation:

The value of the standard error of the mean in each of the following cases:

a. The population size is infinite = 1.4142

b. The population size is N = 50,000 = 1.4135

c. The population size is N = 5000 = 1.4073

d. The population size is N = 500 = 1.343

The standard error is a statistical technique used to measure variability. SE is the abbreviation. A statistic's or parameter estimate's standard error is the standard deviation of its sample distribution. It can be defined as an approximation of that standard deviation.

Standard error calculation:

σ = 10

n = 50

A) when size is infinite, the standard deviation of the sample mean is given by the formula;

σ_x' = σ/√n

Thus,

σ_x' = 10/√50

σ_x' = 1.4142

B) size is given, thus, the standard deviation of the sample mean is given by the formula;

σ_x' = (σ/√n)√((N - n)/(N - 1))

Thus, with size of N = 50,000, we have;

σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))

σ_x' = 1.4142 x 0.9995

σ_x' = 1.4135

C) at N = 5000;

σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))

σ_x' = 1.4073

D) at N = 500;

σ_x' = 1.4142 x √((500 - 50)/(500 - 1))

σ_x' = 1.343

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Option C. No, because the 100 adults were selected without replacement, the selections are dependent.

The binomial probability formula assumes that the trials are independent, meaning that the probability of success or failure for each trial remains the same regardless of the outcomes of previous trials. However, in this case, the 100 adults were selected without replacement, so the probability of being left-handed for each selection depends on the outcomes of previous selections. Therefore, the binomial probability formula cannot be used to find the probability in this situation. Instead, the hypergeometric distribution can be used to account for the dependence between selections.

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Complete question:

It is assumed that approximately 15% of adults in the U.S. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not?

A. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.

B. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.

C. No, because the 100 adults were selected without replacement, the selections are dependent.

D. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.

By using the concept of confidence interval, it can be inferred that

If many random samples of size 50 are selected from all students at this school, approximately 95% of the intervals would capture the true proportion of students who use the community's public library.

Second option is correct

What is confidence interval?

Suppose there is an unknown parameter. Confidence interval gives the range of estimate of that unknown parameter.

Suppose the parameter to be estimated is \(\theta\)

A confidence interval for the parameter \(\theta\), with  level of confidence 1 - a, is an interval  (u, v) with the property:

P(u < \(\theta\) < v) = 1 - a, a is the level of significance

Here confidence interval is 95%

The 95% confidence interval for the true proportion of all students who use the

community's public library is 0.25 to 0.34

Sample size = 50

Since confidence interval of 95% is given, so a concept of sample size will be used here

So the correct interpretation will be

If many random samples of size 50 are selected from all students at this school, approximately 95% of the intervals would capture the true proportion of students who use the community's public library.

Second option is correct

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The capital letter H has 2 reflectional symmetry and 2 rotational symmetry.

A figure has reflectional symmetry if it can be reflected across a line and still look the same. For the capital letter H, there is two lines of symmetry, which is the vertical line and horizontal line that divides the letter into two equal halves. Reflecting the letter across this line produces the same letter. So, the H has only 2 reflectional symmetries.

A figure has rotational symmetry if it can be rotated by some angle and still look the same. For the capital letter H, if we rotate it 180 degrees and 360 degrees about the center point of the letter, it will look the same. There is no other angle of rotation that produces the same letter. Therefore, the H has only 2 rotational symmetries.

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--The question is incomplete, answering to the question below--

"How many reflectional symmetries does this figure have?

Enter your answer

___ reflectional symmetries

How many rotational symmetries does this figure have?

Enter your answer

___ rotational symmetries"

Answer:

x=0

Step-by-step explanation:

add 4 to -1 that gives you 3 and then slide 3 to the other side which gives you 3-3 and that equals 0.

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

Answer:

a=(69)/(16)

Step-by-step explanation:

Answer:  A. $970

Step-by-step explanation:

An individual earning $60,000 would pay 10% on the first $9,700 they earned then pay for remaining amount earned depending on which tax brackets the amount falls within.

The probability that a randomly selected adult has an IQ between 94 and 116 is approximately 0.4176, or 41.76%. This implies that there is a relatively high chance of encountering individuals within this IQ range in the adult population.

To find the probability that a randomly selected adult has an IQ between 94 and 116, we need to standardize the values using the mean and standard deviation provided. We can then use the standard normal distribution table or a calculator to find the area under the curve between the z-scores corresponding to these values.

First, we calculate the z-scores for the IQ values:

z1 = (94 - 105) / 20 = -0.55

z2 = (116 - 105) / 20 = 0.55

Using the standard normal distribution table or a calculator, we find the corresponding probabilities for these z-scores.

P(-0.55 < Z < 0.55) ≈ P(Z < 0.55) - P(Z < -0.55)

Consulting the standard normal distribution table, we find that P(Z < 0.55) is approximately 0.7088, and P(Z < -0.55) is approximately 0.2912.

P(-0.55 < Z < 0.55) ≈ 0.7088 - 0.2912 ≈ 0.4176

Therefore, the probability that a randomly selected adult has an IQ between 94 and 116 is approximately 0.4176, or 41.76%.

Conclusion: Based on the given mean and standard deviation for the normal distribution of IQ scores, we calculated the probability that a randomly selected adult has an IQ between 94 and 116 to be approximately 0.4176, or 41.76%. This implies that there is a relatively high chance of encountering individuals within this IQ range in the adult population.

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

The measure of the smaller angle of the complementary angles is: 36 degrees.

If the sum of two angles equals 90 degrees, then they are complementary angles.

Given that the ratio of two complementary angles is 3:2, therefor:

3x + 2x = 90

5x = 90

5x/5 = 90/5

x = 18

The smaller angle = 2x = 2(18) = 36 degrees.

The larger angle = 3x = 3(18) = 54 degrees.

Therefore, the measure of the smaller angle of the complementary angles is: 36 degrees.

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Suppose we want to compute x≡ab(mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. True statements are:

According to the Chinese remainder theorem, if one knows the remainders of the Euclidean division of an integer n by multiple numbers, one may uniquely calculate the remainder of the division of n by the product of these integers, provided that the divisors are pairwise coprime (no two divisors share a common factor other than 1).

Fermat's little theorem is identical to the assertion that ap 1 1 is an integer multiple of p if an is not divisible by p, that is, if an is coprime to p. If a = 2 and p = 7, for example, 26 = 64, then 64 1 = 63 = 7 9 is therefore a multiple of 7.

x≡ab(mod pq)

Thus, (x1 - x2) divided by m1

Since, m1, m2,........mk are relatively prime

This follows system of congruence in CRT at most one solution.

Fermat's Little Theorem allows us to conclude that a^p−1 ≡1(modp) for any integer a and any prime p,

assume 0≤a≤p-1. This is result of modular arithmetic. So, results hols trivially.

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To find the price at which the designer will sell the maximum number of shirts, we need to determine the vertex of the quadratic function representing the number of shirts sold.

The equation for the number of shirts sold is given by:

S = -4x^2 + 80x - 76

This is a quadratic function in the form of:

S = ax^2 + bx + c

To find the price at which the maximum number of shirts is sold, we need to locate the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -4 and b = 80. Plugging in these values, we can calculate the x-coordinate:

x = -80 / (2*(-4))

x = -80 / (-8)

x = 10

Therefore, the designer will sell the maximum number of shirts at a price of $10. Hence, the correct option is c) $10.

Answer:

x = 1.28t^2 > 5.5

Answer:

\(t\le \:7.04\)

Step-by-step explanation:

\(1.28\ge \cfrac{t}{5.5}\:(\bold{Switch \: sides})\)

\(\cfrac{t}{5.5}\le \:1.28\)

\(\cfrac{5.5t}{5.5}\le \:1.28\cdot \:5.5\:(\bold{ Multiply\: both\:sides\:by\: 5.5})\)

\(t\le \:7.04\)

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