a researcher is told that the average age of respondents in a survey is 49 years. she is interested in finding out if most respondents are close to the average age. the measure that would most accurately answer this question is the

Answer:

Step-by-step explanation:

The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with six sides, so we will let n = 6. The sum of the interior angles in this polygon would be 180(6 – 2) = 180(4) = 720. The angle on the bottom left is a right angle because of the square indicator. We know that this is 90 degrees. If we take the sum of the angles that we know we get 593. 720 - 593 = 127. x = 127.

Answer:

x=127

Step-by-step explanation:

take 180(n-2) where n=6, and you get 180(6-2) which simplified is 180(4) = 720. The sum of all the other angles is 593. subtract 593 from 720 (720-593=127). 127 is the angle of x.

all the steps laid out:

1. 180(n-2)

2. n=6

3. 180(6-2)

4. 180(4) = 720

5. 126 + 112 + 155 + 110 + 90 = 593

6. 720 - 593 = 127

7. x=127

The speed of the plane after it encounters the wind is C.285mph

Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j

= (320 × 0)i + (320 × -1)j

= 0i - 320j

= - 320j mph

Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph

So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'

= -320j mph + 35j mph

= -285j mph

So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph

= 285 mph

So, the speed of the plane after it encounters the wind is C.285mph

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Answer:

\(0.926\)

Step-by-step explanation:

\(1-7.4/100\)

\(1-0.074\)

\(=0.926\)

(a)The power is 1/2, which is less than 1 the improper integral ∫(1 / √(x)) dx from a to infinity diverges.

b)The value of the integral of ∫(1 / √(x)) dx from 1 to infinity is ln(√2 + 1).

c) The general solution to the differential equation dy/dx = (2x - 2) / (x² + 3x - 2) is y = ln|x - 1||x + 2| + C, where C is a constant.

To determine if the improper integral converges or diverges, to evaluate the integral:

∫(1 / √(x)) dx from a to infinity

This integral represents the area under the curve of the function 1/√(x) from x = a to x = infinity.

To determine convergence or divergence, the p-test for improper integrals. For the p-test, the power of x in the denominator, which is 1/2.

If the power is greater than 1, the integral converges. If the power is less than or equal to 1, the integral diverges.

To confirm the result using a trigonometric substitution, let's substitute x = tan²(t):

√(x) = √(tan²(t)) = tan(t)

dx = 2tan(t)sec²(t) dt

substitute these values into the integral:

∫(1 / √(x)) dx = ∫(1 / tan(t))(2tan(t)sec²(t)) dt

= ∫2sec(t) dt

To determine the limits of integration. Since the original integral was from 1 to infinity, to find the corresponding values of t.

When x = 1, tan²(t) = 1, which implies tan(t) = ±1. the positive value because dealing with positive values of x.

tan(t) = 1 when t = π/4

The integral with the appropriate limits:

∫(1 / √(x)) dx = ∫2sec(t) dt from t = 0 to t = π/4

Evaluating the integral:

∫2sec(t) dt = 2ln|sec(t) + tan(t)| from t = 0 to t = π/4

Plugging in the limits:

2ln|sec(π/4) + tan(π/4)| - 2ln|sec(0) + tan(0)|

ln(√2 + 1) - ln(1)

ln(√2 + 1)

The given differential equation is:

dy/dx = (2x - 2) / (x^2 + 3x - 2)

To find the general solution,  by factoring the denominator:

dy/dx = (2x - 2) / [(x - 1)(x + 2)]

decompose the fraction into partial fractions:

dy/dx = A/(x - 1) + B/(x + 2)

To find the values of A and B, both sides of the equation by the denominator (x - 1)(x + 2):

2x - 2 = A(x + 2) + B(x - 1)

Expanding the right side and collecting like terms:

2x - 2 = Ax + 2A + Bx - B

Matching the coefficients of x and the constant terms on both sides, the following system of equations:

A + B = 2 (coefficient of x)

2A - B = -2 (constant term)

Solving this system of equations,  A = 1 and B = 1.

Substituting these values back into the partial fraction decomposition:

dy/dx = 1/(x - 1) + 1/(x + 2)

integrate both sides with respect to x:

∫ dy = ∫ (1/(x - 1) + 1/(x + 2)) dx

Integrating each term separately:

y = ln|x - 1| + ln|x + 2| + C

Combining the logarithmic terms using properties of logarithms:

y = ln|x - 1||x + 2| + C

This is the general solution to the given differential equation.

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a) To discover the relocation of the molecule, we got to coordinate the speed work v(t) over the time interim [0, 3]. The result of this integration will be the alteration in position, or relocation, of the molecule over that interim. ∫v(t) dt = ∫(3t - 5) dt = (3/2)t\(^{2}\) - 5t + C

where C is the constant of integration. To discover the esteem of C, we are able to utilize the beginning condition that the particle's position at t = is zero. This gives us:

(3/2)(0)2 - 5(0) + C

C = So the antiderivative of v(t) with regard to t is:

(3/2)t2 - 5t

Able to presently utilize this antiderivative to discover the uprooting of the molecule over the interim [0, 3]:

Uprooting = [(3/2)(3)2 - 5(3)] - [(3/2)(0)2 - 5(0)]

= (27/2) - 15

= 3/2

the uprooting of the molecule over the interim [0, 3] is 3/2 meters.

b) To discover the separate traveled by the molecule over the interim [0, 3], we got to consider the absolute value of the speed work since remove may be a scalar amount and we are not concerned with the heading of movement. So we have:

|v(t)| = |3t - 5| = 3t - 5, since 3t - 5 is positive for t > 5/3.

For ≤ t < 5/3, the integrand 5 - 3t is negative, so we have:

∫|v(t)| dt = ∫(5 - 3t) dt = 5t - (3/2)t2 + C1

For 5/3 ≤ t ≤ 3, the integrand 3t - 5 is positive, so we have:

∫|v(t)| dt = ∫(3t - 5) dt = (3/2)t2 - 5t + C2

5(0) - (3/2)(0)2 + C1 =  (3/2)(5/3)2 - 5(5/3) + C2

C2 = (25/6) + (25/3) = (50/3)

So the antiderivative of |v(t)| with regard to t is:

∫|v(t)| dt = { 5t - (3/2)t2, for ≤ t < 5/3

{ (3/2)t2 - 5t + (50/3), for 5/3 

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

Answer:

11 times N= 33

Step-by-step explanation:

If you do 33 divided by 11 you get 3 so N would be 3

11 times 3=33

9514 1404 393

Answer:

  a = -10

Step-by-step explanation:

Subtract 5x from the given equation and compare to the desired equation.

  -5x +y = -6

  ax +2y = 6

For the lines to have the same slope, the ratio of x and y coefficients must be the same.

  -5/1 = a/2

  -10 = a . . . . . multiply by 2

Answer:

4/25

Step-by-step explanation:

i am pretty sure this is correct:)

Answer:

4/25

I think it's the correct answer

Answer:

1/2

Step-by-step explanation:

Conditioning is much more likely when the CS and the US are presented together on every trial. The answer is option (2).

Classical conditioning is a type of learning that occurs through association. In classical conditioning, a neutral stimulus (NS) is repeatedly paired with an unconditioned stimulus (US) to elicit a conditioned response (CR). The most effective way to establish this association is by presenting the NS and the US together on every trial. In contrast, if the US occurs without the CS, or if the US is not presented after the CS in some trials, the association between the NS and the US is weakened, making conditioning less likely to occur.

Hence, option (2) is the correct answer.

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The answer is:

Work/explanation:

The difference is the result of subtracting one number from another one.

So the difference of twice a number and 9 means we subtract twice a number (let n be that number) and 9: 2n - 9

Next, 5 times that difference is 5(2n - 9)

Finally, this equals 7 : 5(2n - 9) = 7

__________________________________________________________

Use the distributive property

\(\sf{5(2n-9)=7}\)

\(\sf{10n-45=7}\)

Add 45 on each side

\(\sf{10n=7+45}\)

\(\sf{10n=52}\)

Divide each side by 10

\(\sf{n=\dfrac{52}{10}}\\\\\\\sf{n=\dfrac{26}{5}}\)

The answer of the given question based on the population is , the correct option is B) a parameter.

In statistics, a population is a group or set of individuals, objects, events, or measurements that share at least one common characteristic. This characteristic is usually a variable or a set of variables that the researcher is interested in studying or measuring. For example, the population might be all the adults living in a particular city, or all the trees in a particular forest.

B) a parameter.

A parameter is  value that describes  characteristic of  entire population. It is typically computed from the information obtained from sample of  population, but it is used to describe  entire population. For example, mean income of all households in city is a parameter.

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Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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The length of the red line segment on this number line is: C. 2 1/2.

A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare or determine the difference (distance) between two numbers plotted on it. Additionally, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Note: Each interval on this number line represents 1/4 and the total intervals between the red dots is 10.

From the number line shown above, we have:

Distance = 10 ×  (1/4)

Distance = 10/4

Distance = 5/2

Distance = 2 1/2.

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a) With V=0 at infinity, what is the electric potential at corner A  is -5.07 μC and corner B is = +2.48 μC.

b) The amount of work is required to move a charge from B to A along a diagonal of the rectangle is -2.59 μC.

c) Yes, this work increase the electric potential energy of the three-charge system inside the rectangle but not on a diagonal and outside the rectangle.

The electric potential at a point in a rectangle can be calculated using the electric potential equation. In the given figure, we have a rectangle with sides of length 4.34 cm and 18.5 cm, with charges q1 = -5.07 μC and q2 = +2.48 μC.

=> -5.07 + 2.48 = -2.59

To find the electric potential at corner A and corner B, we must first calculate the electric field from the two charges.

If V=0 at infinity, then the electric potential at corner A and corner B can be calculated using the electric potential equation given by V = ∫E⋅dr.

The amount of work required to move the same charge q3 from point B to point A along a path that is inside the rectangle but not on a diagonal and outside the rectangle will be different.

This is because the path of the charge will determine the electric field and electric potential at each point.

If the path is longer and passes through areas of higher electric potential, then more work will be required to move the charge

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Answer:

Step-by-step explanation:

4 8

The exponential function is given by y = 0.9(1.082)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the fish weights at x inches.

Using point (4, 1.24):

1.24 = ab⁴   (1)

Using point (10, 1.99):

1.99 = ab¹⁰  (2)

From equation 1 and 2:

b = 1.082, a = 0.9

The exponential function is given by y = 0.9(1.082)ˣ

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To spend twice as much time in the air, the juggler must toss the balls to a height of 4.4 yards.

The time it takes for an object to fall to the ground is given by the equation:

t = sqrt(2h/g)

where h is the height of the object and g is the acceleration due to gravity (9.8 m/s²).

If the juggler wants the balls to spend twice as much time in the air, they need to toss them to a height that is four times higher. So, the new height must be:

h = 4 * 2.2 = 4.4 yards

Therefore, the juggler must toss the balls to a height of 4.4 yards if they want them to spend twice as much time in the air.

Here are some other things to consider:

The juggler's technique may also affect how long the balls stay in the air. For example, if they throw the balls with a lot of force, they will stay in the air for longer.

The air resistance may also affect how long the balls stay in the air. For example, if the air is very humid, the balls will slow down more quickly and will not stay in the air for as long.

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To spend twice as much time in the air, the juggler must toss the balls to a height of 4.4 yards.

The time it takes for an object to fall to the ground is given by the equation:

t = sqrt(2h/g)

where h is the height of the object and g is the acceleration due to gravity (9.8 m/s²).

If the juggler wants the balls to spend twice as much time in the air, they need to toss them to a height that is four times higher. So, the new height must be:

h = 4 * 2.2 = 4.4 yards

Therefore, the juggler must toss the balls to a height of 4.4 yards if they want them to spend twice as much time in the air.

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The lateral surface area of the cylinders {W} and {Y} are same.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given are the dimensions of the cylinder as shown in the image.

The lateral surface area of the cylinder is -

L.S.A = 2πrh

{ 1 } -

L.S.A {W} = 2π x 3 x 9 = 54π

{ 2 } -

L.S.A {X} = 2π x 4 x 2 = 16π

{ 3 } -

L.S.A {Y} = 2π x 4.5 x 6 = 54π

Therefore, the lateral surface area of the cylinders {W} and {Y} are same.

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Answer:

Slope: 1/5

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

since both are square it is 12

Answer:
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate

Answer: The answer to number 13 is true because when you graph it, it is a straight line and the answer to number 14 is false because you can't graph an exponent.

Answer:

10.16 cm

Step-by-step explanation:

1ft=254

4ft= x

so cross multiply

than the answer will be 10.16cm

Answer:

10.16 centimeters

Step-by-step explanation:

I'm not 100% sure because its super late where I live so I might have messed up . . . but I'm pretty sure its right.

  Hope This helps!!

 Sorry if it is wrong!!

Jack has a total of 35 different combinations of fruits to choose from at the store.

To calculate the number of combinations Jack can choose, we need to use the concept of combinations in mathematics. Since Jack can buy any three fruits out of the seven available options, we need to calculate the number of combinations of 7 fruits taken 3 at a time.

The formula to calculate combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of options and r is the number of options to be chosen.

In this case, n = 7 (total number of fruits) and r = 3 (fruits to be chosen). Plugging these values into the formula, we get:

C(7, 3) = 7! / (3! * (7 - 3)!)

        = (7 * 6 * 5 * 4!) / (3 * 2 * 1 * 4!)

        = (7 * 6 * 5) / (3 * 2 * 1)

        = 35

Jack has a total of 35 different combinations of fruits to choose from at the store. He can select any three fruits out of the available options, which include apples, oranges, pears, bananas, plums, grapefruit, and kiwis.

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Answer: 91

Step-by-step explanation: 3 times 34 is equal to 102... let us work out the problem together.

3 x 34 = 102

now we must divided 102 by 2 which will equal 51

Now the final step is to do 8 times 5

8 times 5 = 40

51 plus 40 = 91

this is the correct way to do the equation.

so our final answer is 91

Answer:

-34.

Step-by-step explanation:

This is an arithmetic sequence with first term a1  and common difference -2.

nth term = a1 + d(n - 1)

23rd term = 10 - 2(23-1)

= 10 - 44

= -34.

Answer:

-34

Step-by-step explanation:

The sequence starts with 10. Each subsequent term is 2 less than the previous term.

The common difference is -2.

The second term is 10 + (-2) × 1

The third term is 10 + (-2) × 2

The fourth term is 10 + (-2) × 3

Each term you subtract a multiple of -2 from 10. The multiple is 1 less than the number of the term multiplied by -2.

For term n, you get 10 + (-2) × (n - 1).

The 23rd term is:

10 + (-2) × (23 - 1) = 10 - 2 × 22 = 10 - 44 = -34