Find an equation of the plane through(1,1,1) that contains the linere presented by the parametric equationsx= 2t;y= 1t;z= 2 3t:

Answer:

B. p ≤ 154

Hope that helps :)

Step-by-step explanation:

The restaurant can hold 154 people or less than that.

Answer:

Step-by-step explanation:

Answer:(3,2)

Step-by-step explanation:

The value of 'x' in the given question is 27°.

Obtuse Angle may be defined as an angle that is greater than 90° and less than 180°. It may be also defined as an angle between a right angle and a straight-line angle.

From the question we can conclude that the given angles are vertically opposite to each other, and vertically opposite angles are always equal to each other.

Vertically opposite angles are formed when two lines are intersecting each other and the angles formed on each side of the intersection point are called vertically opposite angles.

Now according to the question:

[5(x-4)]°=(4x+7)°

Rearranging the terms:

(5x-20)°=(4x+7)°

=>x=27°

Therefore, the value of x is 27°.

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Answer:

Step-by-step explanation:

6

The temperature at 10,000 feet altitude will be 30.2 ° F.

We are given that:

As the airplane moves 1000 feet above the ground, the temperature drops by 1.6 ° F.

Now, the temperature on the ground is given as

Temperature on ground = 46.2 ° F

Now, the plane is at the altitude of 10,00 feet.

We need to tell the temperature at that altitude.

At 1000 feet, temperature drops by = 1.6 ° F.

At 10000 feet, the temperature will drop by = 1.6 ° F. × 10,000 / 1000

= 16 ° F.

So, the temperature will be = 46.2 ° F - 16 ° F

Temperature = 30.2 ° F

Therefore, the temperature at 10,000 feet altitude will be 30.2 ° F.

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Answer:

5902

Step-by-step explanation:

that's what it tells with my calculations

Answer:

RS = 5

QS = 18

TS = 10

TV = 15

Step-by-step explanation:

Given QV = 23 and QT = 8 and TR = RS = SV

now, we subtract the length of QT from the whole line, QV

23 - 8 = 15 then we divide this by 3 because TR = RS = SV so there must be 3 equal pieces

15 ÷ 3 = 5

RS = 5

QS = QT + TR + RS so

QS = 8 + 5 + 5

QS = 18

TS = TR + RS so

TS = 5 + 5 and

TV = TR + RS + SV

TV = 15

Step-by-step explanation:

11. Is a real numer

12. Is integer

13. Is rational

14. Is whole number

Answer:

16

Step-by-step explanation:

x+(-6)=10 Take (-6) to the other side it becomes (+6).

x= 10 + 6

x=16

A scaled copy of polygon with the scaled factor of 2 is Scale factor is defined as

It is a growing organism that falls between (0, infinity). According to the scale factor, an original figure might be either raised or decreased.

Consider two circles that appear to be the same. The word "identical" does not guarantee that both circles are of similar size. They could have various radii. One figure would be the other figure scaled down.

The ideas of ratio and proportion are intimately related to scale considerations. A given amount is multiplied or divided in ratio and proportions to create a new quantity.

A Scaled copy involves multiplying the lengths in the original figure by scale factor.

Here scale factor = 2,

Since the scale factor > 1, so there is an enlargement.

So, the scale copy's sides are 2 times of the sides of figure A.

Take the reference of grid:

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Answer:

9/28

Step-by-step explanation:

when you divide a fraction by fraction you need to multiply the left fraction by the opposite of right fraction so -7/9 becomes -9/7 and then you multiply -1/4 by -9/7. When you multiply negative with negative you get a positive value.

it's better to display fractions vertically like this to understand better

1

_

4

Answer:9/28

Step-by-step explanation:

The number of times the bacterial cell is smaller than the amoeba cell is 1.6 * 10^-10

The given parameters are:

Bacteria cell = 4 x 10^-6 m

Amoeba cell = 2.5 x 10^4 m

The number of times (n) is calculated as

n = Amoeba cell/Bacteria cell

This gives

n = (4 x 10^-6 m)/(2.5 x 10^4 m)

This gives

n = 1.6 * 10^-10

Hence, the number of times the bacterial cell is smaller than the amoeba cell is 1.6 * 10^-10

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1. A line segment can be written with just naming it by its end points and a bar above it while the name of a line requires an double-headed arrow mark above its name.

2. For constructing both a perpendicular and an angle bisector, we need to construct two arcs using a compass and their intersection point. A perpendicular bisector divided a line segment into two equal parts whereas an angle bisector divides an angle into two equal parts.

3. A perpendicular bisector can be drawn by drawing two arcs each above and below the line segment and joining using an straight edge.

1. A line and a line segment may sound quite similar however they are very different. A line, in short, is a line that never ends so it's infinite. It's the same for a line segment except at its end it is indicated by dots rather than arrows.

This difference can be seen in naming them too. A line segment is named using the initial and terminal points of the segment. Sometimes we put a 'bar' mark above its name. For example, [tex]\bar{AB}[/tex]

For a line of infinite length, it is named simply as 'line A' or 'line B' or sometimes put a double-headed arrow mark above its name.

2. A perpendicular bisector and an angle bisector are similar because they both require the need to find where two arcs meet. They are different because angle bisectors split into congruent angles meanwhile a perpendicular bisector splits into congruent segments.

Constructing a perpendicular bisector is similar in the sense that both are drawn using straight edge and compass and need to find the intersection point of the arcs. But they are different in their use as perpendicular bisector equally divides a line segment and an angle bisector equally divides an angle.

3. We have an unmarked straightedge and a compass. First put the compass at one end point A of the line. Then stretch the compass to a length more than half of the line segment AB to be bisected. In the next step, draw an arc above and one below the line. Next put the compass on the other end B of the line. Then repeat drawing two arcs, each above and below the line and also intersecting with the previous arcs. Finally join the two points got with a line cutting the line segment AB. This will be the perpendicular bisector of the line AB.

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The percentage of those who were married were also obese is: 34.7% (147/424; Option B)

Now,

The percentage of number of married participants who were obese is calculated by: dividing the former (147) by the total number of married participants(424)

=> Percentage of married participants who were obese = 147/424.

Hence, The percentage of those who were married were also obese is: 34.7% (147/424; Option B)

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(COMPLETE QUESTION:

A 2009 study analyzed data from the National Longitudinal Study of Adolescent Health. Participants were followed into adulthood. Each study participant was categorized as to whether they were obese (BMI >30) or not and whether they were dating, cohabiting, or married. The table below summarizes the results.

Dating Cohabiting Married Total

Obese 81 103 147 331

Not Obese 359 326 277 962

Total 440 429 424 1293

What percentage of those who were married were obese? (Round your answer to 1 decimal place.)

A. 32.8% (424/1293)

B. 34.7% (147/424)

C. 25.6% (331/1293)

D. 44.4% (147/331))

The time taken when the person wants to burn 250 calories will be 42.37 minutes.

From the information, the 150-pound person uses 5.9 calories per minute when walking at a speed of 4 mph.

Therefore, the time taken when the person wants to burn 250 calories will be:

= Number of calories / 5.9

= 250 / 5.9

= 42.37 minutes.

Therefore, the time taken when the person wants to burn 250 calories will be 42.37 minutes.

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The coordinates of the point B are (-5, 6)

The given parameters are

A = (-8, 6)

Point = (2, 6)

Proportion = 2/3

Because the y coordinates are the same, we can make use of only the x coordinate

So, we have

Point = Proportion * (B - A)

This gives

2 = 2/3 * (B + 8)

Multiply through by 3/2

So, we have

3 = B + 8

Subtract 8 from both sides

B = -5

Hence, the coordinates of the point B are (-5, 6)

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The probability that both are red should be 0.1423.

The possibility of picking up x number of balls among n number of balls is ⁿCₓ.

jar contains 9 red marbles and 14 blue marbles. Total number of marbles are 23.

favorable cases of picking two red marbles among 9 red marbles is ⁹C₂

And the total possible cases of picking two marbles among 23 marbles is ²³C₂

Therefore, the probability of picking both red marbles are = ( no. Of favorable cases/no. Of possible cases) = ( ⁹C₂ )/( ²³C₂ ) = 36/253 = 0.1423.

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Answer:

Step-by-step explanation:

your welcome <3

Answer:

The correct answer should be P(1, 7)

The number will be 3.

Let the number be represented by x.

Therefore based on the information, the equation will be:

(x × 4) - 1 = 1

4x - 1 = 11

Collect like terms

4x = 11 + 1

4x = 12

Divide

x = 12/4

x = 3

The number is 3.

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The sales on which Joyce earns commission is the sale beyond $20,000 which is $2,650. So the total pay for a month for Joyce in which her sales is $22,650 is $1748.75.

Joyce is paid $1,550 per month plus a commission of 7.5% on all sales of more than a $20,000 monthly quota. For the given month her sales is $22,650.

Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.

Total pay of Joyce = Her pay per month + Commission that she gets

Commission she gets is on the sales beyond $20,000.

Here, commission is on $22,650 - $20,000 = $2,650

She gets 7.5% commission. So, her commission is 7.5% * $2,650

=> 75/1000 * $2,650 = $198.75

So, the total pay of Joyce is $1,550 + $198.75

=> $1748.75 for the month.

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Step-by-step explanation:

(a)

the sum of all internal angles in a polygon with n sides is

(n - 2)×180.

since in a regular polygon all angles are equally large, we get for one internal angle :

(n - 2)×180/n

for our hexagon this means the internal angle is

(6 - 2)×180/6 = 4×30 = 120°

(b)

the area of the hexagon is (as the graphic so nicely suggests) the sum of the areas of all 6 inner triangles.

the area of a triangle is

baseline × height / 2

baseline = 10 cm

the height (from the tip of the triangle down to the baseline in a right angle) is half of 17.3 cm, because these 17.3 cm are the sum of the 2 heights of 2 triangles placed tip to tip.

so, height = 17.3/2 = 8.65 cm

the area of one of the triangles is therefore

10 × 8.65 / 2 = 5 × 8.65 = 43.25 cm²

the total area of the hexagon is then

6 × 43.25 = 259.5 cm²

The sum of 17 and 3 times x is given by the algebraic expression "17+3x" .

A mathematical construct called an algebraic expression is made up of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).

Let us take an expression 4x³+6xy+9 is an algebraic expression. Where

x,y are variables 4 and 6 are co-efficients and 9 is the constant .

In the above statement it is given that the sum of 17 and times x. Here x is a variable.

3 times x equates to 3x and when 17 is added we get the expression 17+3x.

Hence the required algebraic expression is 17+3x

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The coordinates of the point P that partitions the Line N, into the ratio 1:5 is; P(x, y) = (-14/6), (-9/6)

We are told that the point P partitions the Line N, into the ratio 1:5.

Now, the coordinates of N and M are;

N(-3, -2), M(1, 1)

The formula to find the coordinates that partition a line is;

P(x, y) = (bx1 + ax2)/(a + b), (by1 + ay2)/(a + b)

where the ratio is a:b. Thus;

Thus, the coordinates of point P here are calculated as;

P(x, y) = (5*-3 + 1*1)/(1 + 5), (5*-2 + 1*1)/(1 + 5)

P(x, y) = (-14/6), (-9/6)

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Answer: 27 days 60 miles

Step-by-step explanation: 162/6=27

6x17=102 162-102=60

Step-by-step explanation:

no wizardry is needed, as the function is already there. we only need to use it.

(a)

find d, so that 162 - 6d = 0 (0 miles are left)

162 - 6d = 0

162 = 6d

d = 162/6 = 27

it will take them 27 days.

(b)

L(17) = 162 - 6×17 = 162 - 102 = 60 miles

after 17 days they still have to lay 60 miles.

Step-by-step explanation:

Área of a circle is given as

[tex]\pi \times {r}^{2} [/tex]

Therefore you can substitute the values as follows:

[tex]3.14 \times {6}^{2} = 113.09733552923[/tex]

Answer not rounded to any decimal place and used of 3.14 as said in the instruction

The area is:

Explanation:

To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].

where:

A = area;

π = 3.14 (pi);

r = radius

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 6\ in}\end{picture}[/tex]

Plug in the data:

[tex]\sf{A=3.14\times6^2}[/tex]

[tex]\sf{A=3.14\times36}[/tex]

[tex]\sf{A=113.04\:in^2}[/tex]

Answer:

$179.01

Step-by-step explanation:

(First Step) $195 - 15% = $165.75

(Second Step) $165.75 + 8% = $179.01