Find the distance of d, of ab

Answer:

Step-by-step explanation:

Given line ;

\(y = \frac{5}{4} x -3\\\\m = slope\\m = \frac{5}{4}\)

1. Perpendicular and passes through (4,-6)

\(m_1 = \frac{5}{4} \\\\m_2 = \frac{-1}{m_1} \\\\m_2 = \frac{-1}{\frac{5}{4} } \\\\m_2 = -\frac{4}{5} \\\\(4,-6)=(x ,y)\\\)

Substitute the values above into slope intercept form ; y=mx+b and solve for b.

\(y =mx+b\\\\-6 = -\frac{4}{5} (4) + b\\\\-6 = -\frac{16}{5} + b\\\\-6 + \frac{16}{5} = b\\\\-\frac{14}{5} = b\\\\b = -\frac{14}{5}\\\\m = - \frac{4}{5}\)

Substitute new values into ; y =mx+b.

\(y = -\frac{4}{5} (x)- (\frac{14}{5} )\\\\y = -\frac{4}{5} x - \frac{14}{5}\)

2.Parallel and passes through (4,-6)

\(m = \frac{5}{4} \\\\(4,-6)=(x_1,y_1)\)

Substitute values into point slope  form and simplify

\(y-y_1=m(x-x_1)\\\\y - (-6) = \frac{5}{4} (x -4)\\\\y+6 = \frac{5}{4} x -5\\\\y = \frac{5}{4} x -5-6\\\\y = \frac{5}{4} x -11\)

In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

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Answer:

52.2% or A

Step-by-step explanation:

55+50 = 105

105/200 = 0.525

0.525 x 100 (to get the percent) = 52.5%

Answer:

52.5%

Step-by-step explanation:

Add together the number of papers delivered on Saturday and Sunday. Then divide that by the total number of papers delivered.

55+50 = 105

105/200=52.5%

The value of x in the given digram using trigonometry to the nearest tenth is 7.15.

In planar geometry, an angle is a form created by two rays or lines that terminate in the same place. The name "angle" comes from the Latin "angulus," which means "corner". The vertex and the two rays, which are referred to as the sides of an angle, are the shared termini of two rays.

Given an angle and the length of the adjacent side, we are to determine the value of the hypotenuse using cos.

Cos = adjacent / hypotenuse

cos 33 = 6 /x

x = 6 / cos 33

x = 6 / 0.83867

x = 7.15

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The 30 unit tone is the stimulus intensity at which Demetri detects the tone in 50% of the trials. This indicates that it is the level at which the auditory stimulus is perceptually just above the threshold of his hearing.  The correct answer is: 30 unit tone.

In an auditory detection study using the method of constant stimuli, the threshold for hearing is typically defined as the stimulus intensity at which a participant detects the stimulus on a certain percentage of trials. In this case, Demetri's threshold for hearing tones would be determined based on the detection rates for different stimulus intensities.

Given the information provided:

- Demetri never detects the 10 unit tone.

- He detects the 20 unit tone 25% of the trials.

- He detects the 30 unit tone 50% of the trials.

- He detects the 40 unit tone 80% of the trials.

- He detects the 50 unit tone 95% of the trials.

Based on this data, we can observe that Demetri's detection performance improves as the stimulus intensity increases. The threshold for hearing is typically defined as the stimulus intensity at which the participant detects the stimulus on 50% of the trials. In this case, Demetri detects the 30 unit tone on 50% of the trials, indicating that it corresponds to his threshold for hearing.

Therefore, the correct answer is: 30 unit tone.

The 30 unit tone is the stimulus intensity at which Demetri detects the tone in 50% of the trials. This indicates that it is the level at which the auditory stimulus is perceptually just above the threshold of his hearing. Stimulus intensities below 30 units (such as the 10 unit and 20 unit tones) fall below his threshold and are not detected reliably. On the other hand, stimulus intensities above 30 units (such as the 40 unit and 50 unit tones) are detected with higher percentages, indicating that they are clearly audible to him.

By determining the threshold for hearing, researchers can understand the sensitivity of an individual's auditory system and make comparisons across participants or study conditions. In this case, Demetri's threshold is identified as the 30 unit tone, indicating the minimum stimulus intensity he can reliably detect.

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Answer:

Step-by-step explanation:

for the triangle:

1.9x8/2= 7.6mi (this is area)

perimeter=17mi

for the trapezoid:

area= 18.36+13.6=31.96yd

perimeter=24.1yd

Answer:

the answer to your question is 61

Step-by-step explanation:

54+7=61

Answer:

47

Step-by-step explanation:

54-7=47

I'm assuming we are trying to find Rita's score. We know that the total is 54. "The sum" refers to addition, so we must reverse the problem to find her score

54- 7= 47

Total - 7 = her score

Based on the given data, the probability of rolling a 4 on the next roll of this die is 0.3 or 30%.

It is used to predict and estimate the likelihood of future events and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of rolling next is a 4:

The total number of times the die was rolled is:

⇒ 8 + 4 + 3 + 9 + 2 + 4 = 30

The number of times the die landed on 4 is 9.

Then, the probability of rolling next a 4 is:

⇒ 9/30 = 3/10

⇒ 9/30 = 0.3

Therefore, based on the given data, the probability of rolling a 4 on the next roll of this die is 0.3 or 30%.

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The first step is to assign variables to the unknowns in the problem. Let's use "l" to represent the length of the rectangle and "w" to represent the width.

Next, we can translate the given information into equations. We are told that the area of the rectangle is 55 square yards, so we have the equation lw = 55.

We are also told that the length is 4 yards less than 3 times the width. Using the variables we assigned earlier, we can write this as l = 3w - 4.

To find the dimensions of the rectangle, we can substitute the second equation into the first equation.

(3w - 4)w = 55

Expanding and simplifying this equation gives us

3w^2 - 4w - 55 = 0

We can solve this quadratic equation to find the possible values for w. Once we find the values of w, we can substitute them back into the second equation to find the corresponding values of l.

The process to find the dimensions of the rectangle is to set up and solve the equation for area and then substitute the solution into the equation for length.

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Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

m∠RSP = 130°

Step-by-step explanation:

In parallelogram,opposite angles are equal.

m∠RSP = m∠PQR

m∠RSP = 130°

Answer:

∠RSP=130

Step-by-step explanation:

It is given that ∠PQR = 130°

∴∠RSP = 130° (vertically opposite angles are equal in a parallelogram)

The equation is x = 25 for 12 less than one-fifth of a number is -7. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

The number will be x.

(1/5)x can be used to represent "one-fifth of a number."

Consequently, "12 less than one-fifth of a number" may be expressed as:

(1/5)x - 12

We may put up the equation because the problem statement states that this expression equals -7:

(1/5)x - 12 = -7

We may first add 12 to both sides of the equation to find x:

(1/5)x = 5

Next, multiply each side by 5:

x = 25

Consequently, the following equation represents the problem statement:

(1/5)x - 12 = -7

Moreover, x = 25 is the answer.

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Answer:

The second set or second one.

Step-by-step explanation:

(-1,1)

(-3,-1)

(-2,-4)

(2,-2)

The negative numbers becomes positive

The positive numbers becomes negative, if you compare the coordinates, before & after.

Hope this helps!

Answer: To solve the inequality, we start by isolating the variable n:

-6(n-1) < 3

-6n + 6 < 3

-6n < -3

n > 1/2

And for the other inequality:

2(n+1) > 0

2n + 2 > 0

2n > -2

n > -1

Now, we can plot these solutions on a number line:

[-----1/2-----][-------------n > 1/2----------------]

[-----n > -1-----][-------------]

So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).

Step-by-step explanation:

The coordinates of the point q on the segment with endpoints a (2, −1) and c (4, 2) which partitions the segment in a 4:1 ratio. are (2, 7/5).

We can solve this question by using the section formula, which states that if we have a line segment with endpoints (x1, y1) and (x2, y2) and we want to find a point on the segment that divides it in the ratio of m:n, then the coordinates of the point can be found using the following formula:

q(x,y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

In our case,

m=4, n=1

x1=2, x2=4

y1=-1 ,y2=2

By using the given values in the formula mentioned above, we get the coordinates of q as:

q(x,y)=( [4*4+1*2]/5 ,[4*2+1*-1]/5 )

q(x,y)=( 18/5), (7/5)

So the x coordinate of q is: 18/5

the y coordinate of q is: 7/5

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Answer:

k+i =290

Step-by-step explanation:

The three angles added together form a circle, which is 360 degrees

k+i + 70 = 360

We want to find the sum of k+i, so we subtract 70 from each side

k+i + 70-70 = 360-70

k+i =290

Answer:

20X=200 because an equation contains LHS and RHS

The number of the seats within the 25th row is 227.

According to the statement

We have to seek out that the quantity of seats are within the twenty-fifth row of the left section.

So, For this purpose, we all know that the

According to the information:

The number of seats within the first row of the left section of the Ming-Sun Theater is 9.

As with the middle section, the amount of seats in each succeeding row is 2 over the row ahead of it.

From this information, the equation become to search out the seats is:

Number of seats within the given row(x) = 9x+2

And the number of seats is: Number of seats within the 25th row(25) = 9(25)+2

Number of seats within the 25th row(25) = 225+2

Number of seats within the 25th row(25) = 227.

So, The amount of the seats within the 25th row is 227.

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Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

On solving the provided question we can say that - positive integers 32 and 125 are prefect powers

positive numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. Positive integers can be natural or counted numbers. These numbers can also be expressed as Z+. Integers that are positive are to the right of 0 on the number line. Z+. Positive integers are numbers like 1, 2, 3, and so forth. Natural numbers or countable numbers are other names for them. Any figure higher than zero is a positive number.

here we have,

\(a^b\)

where

a and b are positive integer

and, \(b \geq 2\)

so, positive integers 32 and 125 are prefect powers

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Answer:

Answer is as follows

Step-by-step explanation:

a. The probability of choosing a blue marble can be found by dividing the number of blue marbles by the total number of marbles in the jar. So the probability of choosing a blue marble is:

P(blue) = 4/18 = 2/9

b. Similarly, the probability of choosing a green marble is:

P(green) = 4/18 = 2/9

c. There are no black marbles in the jar, so the probability of choosing a black marble is 0.

Answer:

Blue marbles: \(\frac{2}{9}\)

Green marble: \(\frac{2}{9}\)

Black marble: \(0\)

Step-by-step explanation:

It is given that a jar contains 4 blue, 4 green, 7 yellow, and 3 red marbles, for a total of 18 marbles in all. To solve for probability, you will put the part of what you are solving for (in this case, a certain color marble) over the whole (which includes all colors of the marble together).

a. What is the probability of choosing a blue marble?

It is given to us that there are 4 blue marbles total in the given jar. Therefore, the fraction of blue marbles/all marbles will be 4/18.

You may be asked to simplify. Simplify fractions by dividing common factors. The common factor in this case will be 2:

\(\frac{(\frac{4}{18})}{\frac{2}{2}} = {\frac{2}{9}\)

\(\frac{2}{9}\) is your probability for blue marbles.

b. What is the probability of choosing a green marble?

It is given to us that there are 4 green marbles total in the given jar. Therefore, the process will be the same as blue, meaning that your answer is 2/9 simplified:

\(\frac{\frac{4}{18}}{\frac{2}{2}} = \frac{2}{9}\)

\(\frac{2}{9}\) is your answer.

c. What is the probability of choosing a black marble?

There are no black marbles in the given set (the colors being blue, green, yellow, and red). Therefore, within the given set, there will be no chance of obtaining a black marble.

\(0\) is your answer.

~

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Answer:

y = 8

x = 8√5

z = 4√5

Step-by-step explanation:

Using the formula (which is a geometric mean):

a        y

---- = -----

x        a

Where a is the altitude (y), x is a projection (16), and y is the other projection (4):

y        4

---- = -----

16       y

Cross multiply:

y² = 16 (4)

y² = 64

√y² = √64

y = 8

To find x and z, use the Pythagorean Theorem:

16² + y² = x²

256 + 8² = x²

256 + 64 = x²

320 = x²

√320 = √x²

√64√5 = √x²

8√5 = x

x = 8√5

4² + y² = z²

16 + 64 = z²

80 = z²

√80 = √z²

√16√5 = √z²

4√5 = z

z = 4√5

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Domain would be the farthest x value to left and the farthest x value to right

Range would be lowest y value to highest y value

The give statement "Parametric tests such as f and t tests are more powerful than their nonparametric counterparts, when the sampled populations are normally distributed." is true.

Parametric tests such as F and t tests make use of assumptions about the distribution of the data being tested, such as that it is normally distributed. This is known as the “null hypothesis” and it is assumed to be true until proven otherwise. In a normal distribution, the data points tend to form a bell-shaped curve. For these types of data distributions, the parametric tests are more powerful than nonparametric tests because they are better equipped to make precise inferences about the population. A nonparametric test, on the other hand, does not make any assumptions about the data and is therefore less powerful. For example, F and t tests rely on the assumption that the data is normally distributed while the Wilcoxon Rank-Sum test does not. As such, the F and t tests are more powerful when the sampled populations are normally distributed.

Therefore, the given statement is true.

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If 66 sixth graders are randomly selected, the probability that the sample mean would be greater than 92.25 wpm is approximately 0.2142 or 21.42%.

If the sample size is sufficient, we can apply the theorem of central limitation to determine the pattern of distribution of sample means. Since n = 66 is a big enough number in this situation, we may use a normal distribution to roughly comparable the distribution of the sample means.

The general population's mean, which is 89 wpm, is the same as the mean value of the sample means. The following formula can be used to identify the average deviation of the sample means, commonly referred to as the standard deviation or error of the mean:

Standard error is equal to standard deviation squared.(sample size) Standard deviation: 16 squared(66) standard deviation: 1.969 Using the following formula, we can now standardise the sample mean: The formula for z is (sample mean - population mean) / standard error. z = (92.25 - 89) / 1.969 z = 1.732

We may determine the probability when a standard normal random variable is greater than 1.732 using the standard normal distribution table or calculator. This likelihood is roughly 0.0429, or 4.29%. we must remember that rather than just looking for any random variable, we are seeking for the probability that a sample mean is higher than 92.25 wpm. As a result, we must use the sample mean distribution, which we roughly categorized as a normal distribution.

The z-score must then be converted using the following formula to its original units of measurement: Sample mean equals population mean plus z times the standard error. 89 + 1.732 * 1.969 is the sample mean.

92.25 is the sample mean.

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The surface is sufficiently large so that the effects of edge conditions can be neglected. The properties of the fluid are constant. Radiation heat transfer is neglected. The flow is natural (free) convection. The Prandtl number is constant.

Heat transfer rate due to free convection from a vertical surface of 1.2 m high and 0.45 m wide to quiescent air that is 47°C colder than the surface can be calculated by using the following formula :Q = h × A × ΔTWhere Q is the rate of heat transfer, h is the convective heat transfer coefficient, A is the surface area, and ΔT is the temperature difference between the surface and the surrounding quiescent air.

The convective heat transfer coefficient can be calculated by using the following formula :h = Nu × k / LWhere Nu is the Nusselt number, k is the thermal conductivity, and L is the characteristic length. In this case, the characteristic length is the height of the surface. The Nusselt number can be calculated by using the following formula :

Nu =\(0.68 + (0.67 × Gr × Pr / (1 + (0.492 / Pr)^(9/16))^4/9 )^(1/4) × (1 + (0.492 / Pr)^(9/16))^2/9 × (Gr × Pr / (1 + (0.492 / Pr)^(9/16))^4/9)^(1/4) × (1 + (0.492 / Pr)^(9/16))^2/9\)

Where Gr is the Grashof number, Pr is the Prandtl number, and L is the characteristic length. The Grashof number can be calculated by using the following formula :

Gr = gβΔT L³ / v²

Where g is the acceleration due to gravity, β is the coefficient of thermal expansion, ΔT is the temperature difference, L is the characteristic length, and v is the kinematic viscosity. The coefficient of thermal expansion can be calculated by using the following formula :

β = 1 / T_avg

Where T_avg is the average temperature of the surface and the surrounding quiescent air.

The kinematic viscosity can be calculated by using the following formula :

v = μ / ρ

Where μ is the dynamic viscosity and ρ is the density. The dynamic viscosity can be obtained from the given data. The density can be calculated by using the ideal gas law :

ρ = P / R T

Where P is the pressure, R is the gas constant, and T is the temperature. The pressure can be assumed to be constant. The gas constant can be obtained from the given data. State applicable assumptions : The surface is vertical. The flow is steady and laminar.

The surface is sufficiently large so that the effects of edge conditions can be neglected. The properties of the fluid are constant. Radiation heat transfer is neglected. The flow is natural (free) convection. The Prandtl number is constant.

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The area of the region between the curves y=sinx and y=cosx that contains the point (0,0) is 4π.

The area of the region between the curves y=sinx and y=cosx that contains the point (0,0) is the integral of the absolute value of the difference between the two functions. This is expressed mathematically as:

∫|sinx-cosx|dx

Using integration by parts, we can break this integral into two parts:

∫sinx dx - ∫cosx dx

Integrating each of these parts separately and substituting in the limits of integration from 0 to 2π, we get the following:

2π - 0 - (-2π)

Simplifying, this gives us the area of the region as 4π.

Therefore, the area of the region between the curves y=sinx and y=cosx that contains the point (0,0) is 4π.

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