ample 8 it has been reported that 65 % of adults aged 70 and over got their flu shot last year. in a random sample of 200 adults aged 70 and over, find the mean, variance, and standard deviation for the number who got their flu shorts.

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

....... ..... ..... ...

Answer:

I think it's 1/5

Step-by-step explanation:

The ordering of the numbers from the smallest to the biggest will be -3, -✓5, -1.5, 7/2, ✓16.

It should be noted that we have to arrange the numbers from.the smallest to the biggest.

The numbers include:

-√5 = -2.24

-, 3,

-1.5,

√16 = 4

7/2 = 3.5

Therefore, the ordering of the numbers will be -3, -✓5, -1.5, 7/2, ✓16.

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The equation of the given parabola is: y = (x - 4)² + 2

The equation of the given parabola graphed below, which is concave up and has a vertex located at coordinates (4, 2), can be determined using the standard form of the equation of a parabola. The equation of the given parabola with a vertex at (4, 2) can be found using the standard form of the equation of a parabola.

The standard form of the equation of a parabola is y = a(x - h)² + k, where (h, k) is the vertex and a is the constant determined by the focus and directrix of the parabola

Since the given parabola is concave up and has a vertex located at (4, 2), we know that the equation of the parabola must be of the form: y = a(x - 4)² + 2The value of a is determined by the distance between the vertex and focus of the parabola. Since the parabola is concave up, the focus is located above the vertex and the directrix is located below the vertex, both equidistant from the vertex.

The distance from the vertex to the focus is equal to a, and the distance from the vertex to the directrix is also equal to a. Since the vertex is located at (4, 2), the focus is located at (4, 2 + a), and the directrix is located at y = 2 - a. The distance between the vertex and focus is given by the formula:

d = |y-coordinate of focus - y-coordinate of vertex|

d = |(2 + a) - 2| = |a|

Similarly, the distance between the vertex and directrix is given by:

d = |y-coordinate of directrix - y-coordinate of vertex|

d = |2 - a - 2| = |-a|

Since the distances are equal, we can equate them:

|a| = |-a|
a = ± a

However, we know that a must be positive since the parabola is concave up. Therefore, a = |a|, and we can write:

a = 2 + a - 2
a = a²
a² - a = 0
a(a - 1) = 0

Thus, a = 0 or a = 1. Since a cannot be equal to 0, we have a = 1. Therefore, the equation of the given parabola is:

y = (x - 4)² + 2

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The expected value of y when x is equals to 45 in the equation is 35.06

The equation is given as follows;

y = -2.61x + 152.51

where

Therefore,

when

x = 45

y = -2.61x + 152.51

y = -2.61(45) + 152.51

y = - 117.45 + 152.51

y = 35.06

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y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

The function x(t) = 3tu(t) is a product of a scalar 3 and a unit step function u(t). Here, u(t) is defined as:

u(t) = 0 for t < 0

u(t) = 1 for t >= 0

So, x(t) is equal to 3t for t >= 0 and equal to 0 for t < 0.

The function y(t) is the derivative of x(t) with respect to t. To find the derivative of x(t), we use the power rule for differentiation, which states that the derivative of tx(t) is x(t) + t × dx(t)/dt.

So, we have:

y(t) = dx(t)/dt = d(3tu(t))/dt = 3u(t) + 3tu'(t) = 3u(t)

Here, u'(t) is the derivative of u(t) with respect to t, which is equal to the Dirac delta function δ(t).

So, we have:

y(t) = 3u(t) = 3 for t >= 0

y(t) = 0 for t < 0

Hence, y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

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Answer:

-3x – 4y = -4

Step-by-step explanation:

Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.

Is a triangle capable of tessellation?

To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.

Every vertex, edge, and tile in a regular tesselation are identical.

However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).

Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.

Each vertex in the semiregular tessellations is the same.

Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)

The Octagon & square tiling (4,8,8) is a very common floor tiling.

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Answer:

3 qt

Step-by-step explanation:

Let's stick to one unit to facilitate things. I'm going to use quarts as the unit.

1 gal = 4 qt

Initial value = 3 gal 2 qt = 14 qt

Change = 2 gal 3 qt = 11 qt

14 qt - 11 qt = 3 qt

Answer:

B = 1/2 h(b1+b2)

Step-by-step explanation:

The estimated monthly payment for Brian's home loan would $1413.52.

To calculate the best estimate of the monthly payment for Brian's home loan, we can use the formula for calculating a fixed-rate mortgage payment.

The formula for the monthly payment of a fixed-rate mortgage is:

M = P * (r * (1+r)^n) / ((1+r)^n - 1),

where M is the monthly payment, P is the principal amount (loan amount minus down payment), r is the monthly interest rate, and n is the number of monthly payments.

In this case, Brian's principal amount is $220,000 - $22,000 = $198,000 (loan amount minus down payment). The monthly interest rate is 3.5% / 12 = 0.0029 (converted from annual interest rate to monthly rate), and the number of monthly payments is 180.

Plugging in these values into the formula, we get:

M = $198,000 * (0.0029 * (1+0.0029)^180) / ((1+0.0029)^180 - 1).

M = $198,000 * (0.0029 * (1+0.0029)^180) / ((1+0.0029)^180 - 1)

M = $1413.52

Evaluating this expression gives us the best estimate of the monthly payment. However, the calculation involves complex mathematical operations, and it is recommended to use a financial calculator or spreadsheet software to obtain an accurate estimate.

Note: It's important to consult with a financial advisor or a mortgage professional to get precise and personalized information about mortgage terms, interest rates, and monthly payments based on individual circumstances and loan options available.

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The amount that is closest to Nathan's total costs after the 15% discount and including 6% sales tax, assuming tax is applied after the discount is applied would be $624. That is option A.

The discount on sales is the amount of money that is being deducted from the original price of an item by a seller to their customers.

The original price for labor= $299.88

The original price for parts = $ 307.54

The original price for others = $ 74.71

The total original price = $682.13

The discount of on the total price = 15%.

That is;

= 15/100 × 682.13

= 10,232.95/100

= $102.32

When discount is removed from the original price;

= 682.13 - 102.32

= $579.81

When the tax is acted on the discount total sales;

= 6/100 × 579.81

= $3,478.86/100

= $34.79.

The total cost after discount and tax would be;

= 579.81 + 34.79

= $614.59

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Answer:

7, 10 and 13.

Step-by-step explanation:

If there are 3  means between 4 and 16 then:

16 is obtained by  adding the common difference 4 times:

(16 - 4)/4 = 12/4 = 3 = common difference.

So the 3 arithmetic means are 4+3, 4 +2*3, 4 + 3(3)

That is 7, 10 and 13.

Answer:

y·1.05

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer:

the answer is y = x + 1

have a good day :3

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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Answer:

the right answer is a) ∆RTS=∆MON

Answer:

y = kx

Step-by-step explanation:

Two quantities have a proportional relationship if they can be expressed in the general form y = kx, where k is the constant of proportionality. In other words, these quantities always maintain the same ratio. That is, when you divide any pair of the two values, you always get the same number k.

The ratios that represent quantities that are proportional is

15/10 and 21/14

Option B is the correct answer.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

When two ratios are equal it is said that the ratios are in proportion.

4/6 and 10/16

4/6 = 2/3

10/16 = 5/8

The ratios are not equal.

15/10 and 21/14

15/10 = 3/2

21/14 = 3/2

The ratios are equal.

25/35 and 20/24

25/35 = 5/7

20/24 = 5/6

The ratios are not equal.

9/5 and 19/10

The ratios are not equal.

Thus,

The ratio that is proportional is 15/10 and 21/14.

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No, a KNN with k = 1 cannot express any classification decision boundary given infinite data points of any class distribution.

This is because a KNN with k = 1 will always classify a new data point based on the nearest data point in the training set. Therefore, the decision boundary will always be determined by the closest data point, and cannot express any other decision boundary.

In general, a KNN with a larger k value can express more complex decision boundaries, as it takes into account the k nearest data points in the training set. However, with an infinite number of data points, it becomes impossible for a KNN with any k value to express any classification decision boundary, as there will always be an infinite number of data points closer to the new data point than the k nearest data points.

Therefore, it is important to choose an appropriate k value for a KNN classifier, as it can greatly impact the decision boundary and classification accuracy.

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Answer:

?

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = \(\frac{-1-3}{2-0}\) = \(\frac{-4}{2}\) = - 2

using (a, b ) = (2, - 1 ) , then

y - (- 1) = - 2(x - 2) , that is

y + 1 = - 2(x - 2)

Answer: A

Step-by-step explanation:

The value of x, to the nearest tenth, is approximately 4.96. The steps involved using the tangent ratio and solving for the unknown side in a right triangle.

In a triangle, the angle opposite to the side x as angle A, and the side opposite to the angle 33° as side B, and the largest side as side C. So we have:

Angle A = 90° - 33° = 57° (since the sum of angles in a triangle is 180°)

Side B = 8

Side C = 15

Side x = ?

Write the formula for the tangent ratio in terms of the sides of the triangle. For angle A, we have:

tangent(A) = opposite/adjacent

Substitute the known values into the formula and solve for the unknown side. Substituting the values we have, we get

tangent(33°) = x/8

Multiplying both sides by 8, we get:

x = 8 * tangent(33°)

Use a calculator to find the value of the tangent of 33 degrees. We get:

tangent(33°) ≈ 0.6494

Substitute the value of the tangent into the formula we obtained in step 3 and solve for x. We get

x ≈ 8 * 0.6494

x ≈ 5.1952

Round the answer to the nearest tenth, since the question asks for the value of x to the nearest tenth. We get

x ≈ 4.96

Therefore, the value of x, to the nearest tenth, is approximately 4.96.

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The line draw down as per given dimensions of standard sheet of paper 8.5x11 in then half the width of paper is 4.25 inches long approximately.

Let's consider a standard sheet of paper, which typically has dimensions of 8.5 inches by 11 inches (width by height).

If you draw a straight vertical line down half the width of the paper,

It is essentially drawing a line from the top edge to the bottom edge, dividing the paper into two equal halves.

The width of the paper is 8.5 inches.

When you draw a line down half the width, you are going from one edge to the midpoint.

Since you are going halfway, the length of the line will be half of the width,

which is 8.5 inches divided by 2, resulting in approximately 4.25 inches.

Therefore, the line you draw down half the width of the paper will be approximately 4.25 inches long.

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Answer:

either 885 more or 450 more

Step-by-step explanation:

Monday: 1000

Tuesday: 1000*1.3 = 1300

Wednesday:

I'm assuming 45% more from tuesday?

          1300*1.45 = 1885

or if not:

          1000*1.45 = 1450

either 885 more or 450 more

you can also just do 1000*1.3*1.45 = 1000*1.885 = 1885 if thats what the question means

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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The number of children and men at the party will be 30 and 15, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

There are 90 people at the party. Half of the people at the party are women. The number of women at the party is 3 times the number of men at the party. The rest of the people at the party are children.

Let the number of children be 'x', the number of men be 'y', and the number of women be 'z'. Then we have

z = 90 / 2

z = 45

Then the other equation is given as,

z = 3y

45 = 3y

y = 15

Then the number of children is calculated as,

x + y + z = 90

x + 15 + 45 = 90

x = 30

The number of children and men at the party will be 30 and 15, respectively.

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Answer:

$4.25 ?

Step-by-step explanation:

8.5/2=4.25