Match each function with the correct type. av a. polynomial of degree 2 b. linear = f(t) 5+2 + 2t + c - 5+3 – 2t - 1 - valt) -t + 5 g(t) 128t1.7 - vl(n) = 178(3.9)" C. power d. exponential e. ration

Answer: 30 meters

Step-by-step explanation:

50/12=4.1666

4.1666x7=29.162 round it to 30

Answer:

29.19

Step-by-step explanation:

50/12=4.17

4.17= how far she ran in 1 second

4.17*7=29.19

Answer:

29/40

Step-by-step explanation:

Answer:

29/40

Step-by-step explanation:

Hope it helps

Answer:

\(x - 2x - 15 \: divided \: by \: x - 3\)

Thus, the total number of clients that got haircuts have blond hair is 9.

A prospective outcome of an experimentation or trial is described to as an outcome in probability theory. Only one result will materialise on each trial of an experiment since each possible outcome is distinct and numerous results are mutually exclusive.

Given number of hair colours:

Total colours = 12

Probability = favourable event / total outcome

Probability(blond hair) = 3/12 = 1/4

Total customers = 36

Number of clients have blond hair = 1/4 *36 = 9

Thus, the total number of clients that got haircuts have blond hair is 9.

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The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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The normal vector, f, to the surface of the inner conductor is a unit vector in the radial direction, pointing away from the conductor.

a. The normal vector, f, to the surface of the inner conductor is a unit vector in the radial direction, pointing away from the conductor.

b. The boundary condition at the surface of the conductor (medium 2) is that the normal component of the electric field is equal to the surface charge density.

c. The boundary condition in the dielectric (medium 1) is that the tangential component of the electric field is equal to zero.

d. The surface charge density, Ps, at the surface of the conducting cylinder is P.

The complete question is:

An infinitely long conducting cylinder of radius a (medium 2) has a surface charge density P. The cylinder is surrounded by a dielectric (Er = 4, medium 1) that contains no free charges (that is to say p = 0 inside the dielectric). Defining 2 as the axis of the conducting cylinder, the electric field, E, inside the dielectric medium (whenra) is found as: E = Er*sin(θ)/r.

a. What is the normal vector, f, to the surface of the inner conductor?

b. What is the boundary condition at the surface of the conductor (medium 2)?

c. What is the boundary condition in the dielectric (medium 1)?

d. What is the surface charge density, Ps, at the surface of the conducting cylinder?

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Step-by-step explanation:

To create a frequency table for Sarita's data, we need to first count the number of times each value appears in the data set. We can then organize this information into a table with two columns: one for the values and one for their frequencies.

Here is the frequency table for Sarita's data:

Value Frequency

0 2

3 2

4 2

5 2

6 1

7 2

8 2

10 1

11 1

12 2

13 1

15 1

17 1

To create this table, we first counted the number of times each value appears in the data set. For example, the value 0 appears twice, so its frequency is 2. We repeated this process for each value in the data set, and then organized the results into a table with two columns.

The first step in simplifying the expression 2(x+3)+5 = 2x+2(3)+5.

Given expression in 'x' is 2(x+3)+5.

In order to simplify this expression, we need to expand it by opening the parenthesis. That is, we need to distribute 2 over (x+3) first. For this we multiply 2 into (x+3) and then only we can add 5 to it.

So, 2(x+3) +5 = 2x + 2(3) +5

                     = 2x +6 +5

                     = 2x+11

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Answer:

B

Step-by-step explanation:

B. Wendy leaves school to go home. She walks 60 yards north and then 80 yards west. She is 10 yards from the school.

got it right on edge

Answer:

37.3275

Step-by-step explanation:

I just put it on the calculator :)))))

The value of L4 for f(x) = 68cos(x/3) over [3π/4, 3π/2] is 0.

To find the value of L4, we first need to calculate the Fourier coefficients of the function f(x). Using the formula for the Fourier coefficients, we get:       an = (2/π) ∫[3π/4,3π/2] 68cos(x/3)cos(nx) dx = (2/π) [68/3 sin((3π/2)n) - 68/3 sin((3π/4)n)]

bn = (2/π) ∫[3π/4,3π/2] 68cos(x/3)sin(nx) dx  = 0  Since the function f(x) is even, all the bn coefficients are 0. Therefore, we only need to consider the an coefficients. Using the formula for L4, we get: L4 = (a0/2) + Σ[n=1 to ∞] (an cos(nπ/2))

Since a0 is 0 and all the bn coefficients are 0, the sum simplifies to: L4 = Σ[n=1 to ∞] (an cos(nπ/2))  = (2/π) [68/3 cos(3π/8) - 68/3 cos(3π/4) + 68/3 cos(5π/8)] = 0

Therefore, the value of L4 for f(x) = 68cos(x/3) over [3π/4, 3π/2] is 0.

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To solve this problem, let's represent the number as "x."

According to the given information, we can set up the following equation:

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 800

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 8007x = 800

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 8007x = 800Dividing both sides by 7:

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 8007x = 800Dividing both sides by 7:x = 800 / 7

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 8007x = 800Dividing both sides by 7:x = 800 / 7Calculating the value:

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 8007x = 800Dividing both sides by 7:x = 800 / 7Calculating the value:x ≈ 114.29

According to the given information, we can set up the following equation:(3/5) * x = (1/4) * x + 40To simplify the equation, let's get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators, which is 20:20 * (3/5) * x = 20 * (1/4) * x + 20 * 40Simplifying further:12x = 5x + 800Now, let's isolate the variable x by subtracting 5x from both sides:12x - 5x = 8007x = 800Dividing both sides by 7:x = 800 / 7Calculating the value:x ≈ 114.29Therefore, the number is approximately

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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Answer:

man it’s one in the morning and your picture is blurry a f

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

AC = 25 units is the length of AD.

The Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.

Length of BC = 10 units

Length of DC = 4 units

We will use geometric mean theorem in the given right triangle to get the length of side AC.

\(hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25\)

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The probability that the sampling distribution of sample proportions is less than 91% is very low, approximately 0.0000025.

The sample size is n = 81 and the population proportion is p = 0.95. The mean of the sampling distribution of sample proportions is equal to the population proportion, which is 0.95. The standard deviation of the sampling distribution of sample proportions is given by the formula sqrt(p*(1-p)/n), which is approximately 0.03. Thus, the z-score corresponding to a sample proportion of 0.91 is (0.91 - 0.95)/0.03 = -1.33. The probability that the sampling distribution of sample proportions is less than 91% is the same as the probability that a standard normal variable is less than -1.33, which is approximately 0.0000025 (using a standard normal distribution table or calculator). This indicates that it is very unlikely to obtain a sample proportion less than 91% if the true population proportion is 95%.

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The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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Grid Square is another name for the coordinate plane. It can be inferred therefore that the equation [y=-1/5x-2] is to be graphed.

To graph the above equation, we need to find the (x, y) pairs that satisfy the equation, then draw a line for the points.

Note that we can find this by simply substituting random values into x to find the y pair.

For example,

Where y = -(1/5)x - 2

If x = 1, then

y = (-(1/5) * 1) -2

y = -2.2

Where x = 2 then,

y = -2.4

Where x = 3

y = -2.6

Where x = 4

y = -2.8

Where x = 5

y = -3

Thus, the (x,y) pairs are as follows:

(1, -2.2)

(2, -2.4)

(3, -2.6)

(4, -2.8)

(5, -3)

Plotted on a graph, we would get the result attached.

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Answer:

b=3.464 a=2.121

Step-by-step explanation:

Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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a) the calculated t-value (2.344) is greater than the critical t-value (1.984), we reject the null hypothesis. b) The p-value associated with a t-value of 2.344 is approximately 0.010 (two-tailed test).

(a) To determine if the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, we can conduct a two-sample t-test.

Let's define our null hypothesis (H0) as "there is no significant difference in average yearly reading growth between Program A and Program B" and the alternative hypothesis (H1) as "Program A leads to higher average yearly reading growth than Program B."

We have the following information:

For Program A:

Sample size (na) = 64

Sample mean (xA) = 1.2

Sample standard deviation (sA) = 0.26

For Program B:

Sample size (nb) = 100

Sample mean (xB) = 1.0

Sample standard deviation (sB) = 0.28

To calculate the test statistic, we use the formula:

t = (xA - xB) / sqrt((sA^2 / na) + (sB^2 / nb))

Substituting the values, we have:

t = (1.2 - 1.0) / sqrt((0.26^2 / 64) + (0.28^2 / 100))

t ≈ 2.344

Next, we determine the critical t-value corresponding to a 5% significance level and degrees of freedom (df) equal to the smaller sample size minus 1 (df = min(na-1, nb-1)). Using a t-table or statistical software, we find the critical t-value for a two-tailed test to be approximately ±1.984.

(b) To calculate the p-value, we compare the calculated t-value to the t-distribution. The p-value is the probability of observing a t-value as extreme as the one calculated, assuming the null hypothesis is true.

From the t-distribution with df = min(na-1, nb-1), we find the probability corresponding to a t-value of 2.344. This probability corresponds to the p-value.

(c) Based on the results of the hypothesis test, where we rejected the null hypothesis, we can conclude that there is evidence to suggest that Program A leads to higher average yearly reading growth compared to Program B.

(d) To calculate the probability of a Type II error (β), we need additional information such as the significance level (α) and the effect size. The effect size is defined as the difference in means divided by the standard deviation. In this case, the effect size is (xA - xB) / sqrt((sA^2 + sB^2) / 2).

Let's assume α = 0.05 and the effect size (xA - xB) / sqrt((sA^2 + sB^2) / 2) = 0.1. Using statistical software or a power calculator, we can calculate the probability of a Type II error (β) given these values.

Without the specific values of α and the effect size, we cannot provide an exact calculation for the probability of a Type II error. However, by increasing the sample size, we can generally reduce the probability of a Type II error.

In summary, the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, suggesting that Program A leads to higher average yearly reading growth. The p-value of the test results is approximately 0.010. Based on these findings, it may be recommended to adopt Program A over Program B. The probability of a Type II error (β) cannot be calculated without specific values of α and the effect size.

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The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

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Answer:

Yes.

Step-by-step explanation:

Every X value corresponds with a DIFFERENT Y value.

That is the definition of a function.

Answer:

98 units.

Step-by-step explanation:

Circumference = 2 * pi * radius

615.44 = 2 * 3.14 * r

r = 615.44 / (2 * 3.14)

 =2 * 3.14

 = 98 units.

The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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To lower the salt concentration to 0.01 lb/gal of water in under one hour, water should be poured into the tank at a rate of 500 gallons per minute.

To find the rate at which pure water should be poured into the tank, we can use the concept of salt balance. Let's denote the rate at which water is poured into the tank as 'R' (in gal/min).

The initial volume of the tank is 500 gallons, and the salt concentration is 0.05 lb/gal. The amount of salt initially in the tank is given by 500 gal * 0.05 lb/gal = 25 lb.

We want to lower the salt concentration to 0.01 lb/gal in under one hour, which is 60 minutes.

To do this, we need to remove 25 lb - (0.01 lb/gal * 500 gal) = 20 lb of salt.

Since the volume of the solution in the tank is kept constant, the rate at which salt is removed is equal to the rate at which water is poured in, multiplied by the difference in salt concentration. Therefore, we have:

R * (0.05 lb/gal - 0.01 lb/gal) = 20 lb

Simplifying, we get:

R * 0.04 lb/gal = 20 lb

Dividing both sides by 0.04 lb/gal, we find:

R = 20 lb / 0.04 lb/gal

R = 500 gal/min

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Answer:

x = 30

Step-by-step explanation:

To get the left side of the triangle, take the square root of the left squares area, 576, to get the two sides a nd b of 24 and 18. Use the Pythagorean theorem (a^2 + b^2 = c^2) to get x = 30

Good luck with your homework :)