during a summer thunderstorm, the temperature drops and then rises again. the rate of change of the temperature during the hour and a half after the storm began is given by t(h) = 9.5h3 − 15.5h2 + 17.4h − 10.12°f per hour

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.

Learn more about perpendicular bisector at https://brainly.com/question/11006922

#SPJ1

Answer:

Step-by-step explanation:

Answer:(3,2)

Step-by-step explanation:

Answer:

B. p ≤ 154

Hope that helps :)

Step-by-step explanation:

The restaurant can hold 154 people or less than that.

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.

Learn more about probability here:

https://brainly.com/question/11234923

Answer:

3,490,000

Step-by-step explanation:

3,487,967 = (87967) The 7 rounds up so the 8 would become 9.

Step-by-step explanation:

11. Is a real numer

12. Is integer

13. Is rational

14. Is whole number

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

To learn more about algebraic expression visit:

https://brainly.com/question/953809

#SPJ9

Answer:

The correct answer should be P(1, 7)

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)

To learn more about percentages, refer to the link: https://brainly.com/question/24304697

#SPJ4

(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 width of the rectangle is: 33m, by Pythagoras theorem.

Now,

given:

TO find: Width of rectangle = ? (say, w)

Finding:

BY Pythagoras theorem, in the rectangle ABCD,

For l = AB, w = BC and d = AC,

=> l² + w² = d²

Ob substituting the values, we get: 56² + w² = 65²

=> w² = 65² - 56²

=> w² = 4225 - 3136

=> w² = 1089

=> w = 33m

Hence, for the given values of rectangle, the width of the rectangle is 33m by Pythagoras Theorem.

To learn more about Pythagoras Theorem, refer to the link: https://brainly.com/question/654982

#SPJ4

The value of the height of the right prism is given by the formula, h = (SA - 2B) / P. It is gained by using the surface area of the right prism.

What is the right prism?

A right prism is a three-dimensional closed figure with 6 faces, 8 corners and 12 edges. It is called a right prism because, in this prism, the angle between the base and the sides is 90 degrees. All the faces of a right prism are rectangular, hence sometimes also called a right rectangular prism.

Calculation of h for the right prism

We know the  surface area of the right prism is given by:

SA = Ph + 2B

Ph + 2B = SA

Subtracting 2B from both sides of the above equation, we have,

Ph + 2B - 2B = SA - 2B

Ph = SA - 2B

Dividing both sides of an equation by P, we get,

(Ph) / P = (SA - 2B) / P

h = (SA - 2B) / P

Hence, the value of h can be found using the formula, h = (SA - 2B) / P

To learn more about the right prism, visit here:

https://brainly.com/question/14222174

#SPJ4

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.

To learn more about percentage visit:

brainly.com/question/16797504

#SPJ1

Answer: 2x2x2 or 2 cubed

Step-by-step explanation: 2x2=4 2x4=8

Answer:

5902

Step-by-step explanation:

that's what it tells with my calculations

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.

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

Answer:

Step-by-step explanation:

6

Answer:

The second answer is the correct one I believe

Answer:

second one

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°.

Learn more about Vertically opposite angle at:

brainly.com/question/13727798

#SPJ4

They will save $100 if they purchase together rather than separately.

If this week, the store is offering one free window for each purchase of 4, then the price of 5 windows will be just equal to the price of 4.

1 window = $100

5 windows = 4 x $100 = $400

If

Dave needs 7 windows  

Doug needs 8 windows

total they need together = 7+8 = 15 windows.

Buying at the offer of $400/5 windows,

they should buy 3 sets of 5 windows.

3 x 5 = 15

cost when bought together : 3 x $400

cost when bought together : $1200

If they bought separately,

Dave : 7 = 5 + 2

cost = $400 + 2($100)

cost = $600

Doug : 8 = 5 + 3

cost = $400 + 3($100)

cost = $700

cost when bought separately : $600 + $700

cost when bought separately : $1300

compare the two total costs and to determine how much they will save.

$1300 - $1200 = $100

They will save $100 if they purchase together rather than separately.

To know more about Saving money

brainly.com/question/25594963

#SPJ1

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

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:

To learn more about scaled factor refer the link:

https://brainly.com/question/22312172

#SPJ9

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)

Read more about coordinates at

https://brainly.com/question/11337174

#SPJ1

The time for the projectile to hit the ground from the given position is 1.5 s, which is obtained using the concept of time period and velocity of a projectile.

What is a projectile?

A projectile is defined as an object that has the force of gravity as the only force occurring on it. Acceleration in the projectile motion always acts vertically.

Calculation of the time taken by projectile to hit the ground

The given parameters:

The starting velocity of the projectile, u = 48 ft / s

Height of the projectile, h = 190 ft

Model of the projectile path, h(t) = - 16(t)2 + 48t + 190          —-- 1

When the projectile hits the ground, the final velocity, v = 0

differentiating equation 1 w.r.t t, we get,

(dh(t)) / (dt) = - 32t + 48

Putting dh(t) / dt = 0, we have,

- 32t + 48 = 0

32t = 48

t = 48 / 32

t = 1.5 s

Hence, the time taken by the projectile to hit the ground is 1.5 s.

To learn more about the projectile, visit here:

https://brainly.com/question/8104921

#SPJ4

Answer:

0.35

Step-by-step explanation:

3/6=1/2

7/10=0.7

1/2=0.5,0.5×0.7

=0.35

Answer: 7/20

Step-by-step explanation:

3/6*7/10= 0.35

First write down the decimal number divided by 1 like this:

0.35

1

As we have 2 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 102 = 100, so that there is no decimal point in the numerator

0.35 × 100

1 × 100

=

35

100

Since the greatest common factor of 35 and 100 is 5, we can simplify the fraction and show the same amount

35 ÷ 5

100 ÷ 5

=

7

20

Therefore, 0.35 as a fraction is 7/20

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)

Read more about Line segment Partition at; https://brainly.com/question/12959377

#SPJ1