Holly is thinking of a number.
3/4 of Holly's number is 39.

Work out the number Holly is thinking of.

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

[tex]h(x)=ax(x-7)[/tex]             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

[tex]4=a(3)((3)-7)[/tex]

[tex]4=a(3)(-4)[/tex]

[tex]\dfrac{4}{(3)(-4)}=a[/tex]

[tex]-\dfrac{1}{3}=a[/tex]

Putting [tex]a=-\dfrac{1}{3}[/tex], we get

[tex]h(x)=-\dfrac{1}{3}x(x-7)[/tex]              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

[tex]h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)[/tex]

[tex]h(1.5)=-(0.5)(-5.5)[/tex]

[tex]h(1.5)=2.75[/tex]

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

It's the one with the greater than or less than sign (the second option) because Logan wants to make money greater than or less than $1000

Mean- 6

Median- 6

Mode- 3, 4, 5, 7, 9, 10, 2, 8

Range- 8

Hope this Helped! :T

Answer:

option 3

Step-by-step explanation:

not sure if right

Answer:

D

Step-by-step explanation:

We can use two proportion to solve this problem

2 : 5 = 10 : x

x = (5 * 10)/2 = 25 feet

2 : 5 = 6 : x

x = (6*5)/2 = 15 feet

Answer:

785.5ft

Step-by-step explanation:

Given data

Diameter= 250ft

Radius= D/2= 250/2= 125ft

The total steel required can be found from the Circumference

C= 2πr

C= 2*3.142*125

C= 785.5ft

Hence the total steel required is 785.5ft    

Answer:

The slope of the line y = 1 is zero.

Answer:

m = 0

Step-by-step explanation:

The line y = 1 is a horizontal one.  All horizontal lines have the slope 0 (zero).

Answer:

a) 40 degrees b) 148 degrees

Step-by-step explanation:

a) Complementary angles are angles that in total measure 90 degrees, or form a right angle. If one angle is 50 degrees, then 90 - 50 = 40, meaning the measure of its complement will be 40 degrees.

b) Supplementary angles are similar but in total measure 180 degrees, or form a straight angle. If one angle measures 32 degrees, then 180 - 32 is equal to 148, meaning the measure of its supplement will be 148 degrees.

Answer:

h = 2A/b

Step-by-step explanation:

Area of a triangle, A = 1/2bh

Where,

b = base of the triangle

h = height of the triangle

Rearrange the formula to isolate h

A = 1/2bh

Multiply both sides by 2

2 * A = 2 * 1/2bh

2A = bh

Divide both sides by b

2A / b = bh / b

2A / b = h

Therefore,

h = 2A/b

The area of the shaded region which is inside the triangle but not in a circle is 22.43 sq. inches.

A triangle is a geometrical figure with 3 angles, 3 edges, and 3 vertices. It is one of the most basic geometrical figures.

Given that

Vertices A, B, and C of a triangle, ΔABC are centers of three circles touching each other.

As the triangle, ΔABC is an equilateral triangle,

therefore,

∠A = ∠B = ∠C = 60°. (Since the sum of all angles is 180° and the angles of an equilateral triangle are equal.)

To obtain the area of the shady region, it is needed to obtain the areas of the triangle and of the quadrants of each circle.

Area of ΔABC = [tex]\frac{\sqrt{3}}{4} a^2[/tex], where a is the length of the equal sides.

Here, a = 2 × radius of the circles

So, a = 2 × 6 = 12 inches.

Now,

Area of ΔABC = [tex]\frac{\sqrt{3}}{4} 12^2[/tex]

                        [tex]=\frac{\sqrt{3}}{4} \times144\\=\sqrt3 \times 36\\=36\sqrt3\ sq.\ inches\\= 62.35\ sq.\ inches[/tex]

Area of a quadrant of a circle = [tex]\frac{1}{4}\pi r^2[/tex]

The sum of areas of quadrants of three circles = [tex]3\times\frac{1}{4}\pi r^2[/tex]

                                                                              [tex]= 3\times\frac{1}{4}\times3.14\times 6^2\\= 3\times\frac{1}{4}\times3.14\times 36\\= 84.78\ sq.\ inches[/tex]

Area of the shaded region = The sum of areas of quadrants of three circles - Area of ΔABC

Area of the shaded region = 84.78 - 62.35

                                             = 22.43 sq. inches.

Thus the area of the shaded region is 22.43 sq. inches.

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Answer:

165

Step-by-step explanation:

Answer:

A 3/19

Step-by-step explanation:

There are 4 candies of each color. If you take out one yellow, you not only have three yellows; you have 19 candies. 3/19 is the answer.

Answer:

3/19

Step-by-step explanation:

There is an equal number of colored candies, in which there are 20 candies in all, and 5 colors:

20/5 = 4

Each color has 4 candies.

Savannah was able to obtain a yellow candy, and she does not replace it:

4/20 removing one yellow candy = 3/19

A) 3/19 is her chance of getting another yellow.

Answer:

-5

Step-by-step explanation:

Make:

(-5)³ = (-5)×(-5)×(-5) = 25×(-5) = -125

The question is incomplete. The complete question is :

Victor is selling lemonade to raise money for his school. The amount of money he collected from his sales each day is summarized on the box plot below.

What is the interquartile range of the data ?

Answer:

$ 7

Step-by-step explanation:

It is given that Victor sold lemonade in order to raise money for his school.

The money that Victor collected is shown on the diagram below.

Therefore, we find the interquartile range. It is the difference between the 3rd quartile and the 1st quartile, i.e.

IQR = [tex]$Q_3-Q_1$[/tex]

Now from the figure, the 3rd quartile is the value that is at the end of the rectangular box towards the right. Therefore, the 3rd quartile is =  $ 29

Similarly from the figure the 1st quartile at the beginning of the rectangular box to the left is = $ 22

So the interquartile range is = 3rd quartile - 1st quartile

                                               = 29 - 22

                                                = $ 7

Thus the amount of money Victor collected is $ 7.

Answer: i think its 21! how idfk but it was on some website...dont hatecrime me!

Step-by-step explanation:

Answer:

5:30 pm.

Step-by-step explanation:

First find the LCM (lowest common multiple) of 25 and 30. This is the amount of minutes it will take for the buses to meet again.

25 can be broken up into 5*5

30 can be broken up into 5*6

The most amount of 5s found in a number is two times in 25 and the most amount of 6s found in a number is once in 30, so

25*6=150

150 is the LCM. This means that in 150 minutes, the buses will be back at the bus depot together.

All we have to do now is convert 150 minutes to hours.

One hour is 60 minutes, so 150/60 is 2.5 hours, or 2 hours and 30 minutes.

2 hours and 30 minutes after 3 pm is 5:30 pm.

A- x=A

B- x=27

C- x=3

D- x=4

E- x=17

ANSWER- A and C

Hope this Helped! :T

Answer:

$6.30

Step-by-step explanation:

Answer:

The tip should be $6.30

Step-by-step explanation:

We can find 15 percent of 42$ by multiplying 42 by 0.15 (this is another way of writing down 15%) and so we get...

(42)(0.15) = 6.3

Therefore the tip should be $6.30

Answer:

£140

Step-by-step explanation:

Modal is the most common value in a sample, in this case it's 140

Answer:

631.334460 ft

Step-by-step explanation:

i think

Answer:

32 feet

Step-by-step explanation:

Since we know that the formula for finding circumference is C = π · d, and π is equal to 3.14, we reverse the formula so it fits what information we have.

We know that C = 100.48 and we also know that π = 3.14 so all we have to find is the diameter.

To do this, you divide 100.48 by 3.14 to get 32 feet as your final answer.

Answer:

The circumference of the circle is about 52.1 yards

Step-by-step explanation:

C=πd

C=2πr

C=2π(8.3)

C=16.6π

C≈16.6(3.14)

C≈52.124 yds

C≈52.1 yds

Answer:

13

Step-by-step explanation:

Answer:

I believe That the answer is c.

Step-by-step explanation:

The question shows what it should look like, and C matches the question.

Answer:

-52

Step-by-step explanation:

-11 -14 are same sign is equal to plus ,,so that is answer -52 ...

Answer:

- 11 - 41

-52 is the right answer....

Answer:

area = 32

perimeter = 30

Step-by-step explanation:

Formulas:

Area of a parallelogram: A = bh

Perimeter of a parallelogram: P = 2 ( b + s )

Where h = height s = slant height and b = base length

Define:

b = 8

h = 4

s = 7

Plug in given values into formulas and calculate

A = (8)(4)

8 * 4 = 32

A = 32

P = 2 ( 8 + 7 )

8 + 7 = 15

2(15) = 30

P = 30

Answer:

3(x + 2) = 3x + 6

Step-by-step explanation:

3(x + 2) = 3x + 6

Distribute --> 3x + 6 = 3x + 6

The pair which shows equivalent expressions are 3(x + 2) = 3x + 6.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are four equations.

A) 3(x + 2) = 3x + 6

This is equivalent, since,

3(x + 2) = 3x + (3 × 2) = 3x + 6

B) 3x + 2x= x² (3 + 2)

This is incorrect since, 3x + 2x = x(3 + 2)

C) 3x + 2 = 3(x + 2)

This is also not equivalent since we cannot take 3 outside since it is not common.

D) -3(2 + x) = -6x - 3

This is also not true since,

-3(2 + x) = (-3 × 2) + (-3x) = -6 - 3x.

Hence the equivalent expression is 3(x + 2) = 3x + 6.

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Answer:

The Anwers is C

Step-by-step explanation:

2x + y = 20. 6x - 5y = 12

Answer:

Solution given:

<J=90°[tangent to the circle is perpendicular to radius]

In right angled triangle ∆KJL

base[b]=11

hypotenuse [h]=11+7=18

perpendicular [p]=x

by using Pythagoras law

p²+b²=h²

x²+11²=18²

x²=18²-11²

x=√203

x=14.25

Answer:

Step-by-step explanation:

Given:

Conjugate of the given number is:

Divide the given number by its conjugate:

Correct choice is B