A match-seller arranges his matchboxes in a
triangular pattern as shown in Fig. 18.4. He
continues until there are 11 matchboxes in
the bottom row of the triangle. How many
matchboxes are in the complete pattern?
MATO
MATCHES
MATCHES
Fig. 18.4
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES

The exponent that is understood on the base x in the given expression is; 1

The exponent of a number tells us how many times to use the number in a multiplication. Exponents are also called Powers or Indices. For example in the exponent form ab^(x), we can say that;

The base is a and its' exponent is 1.

Applying the above to our question gives us;

If the exponent form is xy^3, then we can say that;

The base is x.

We can see that there is no exponent attached to x and as such we will use 1 as 1 will still give us the value of x.

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Answer:

y = (3/2)x + 3

Step-by-step explanation:

Point 1: (0, 3) Point: (2, 6)

            (x₁, y₁)          (x₂, y₂)

        y₂ - y₁        6 - 3            3

m = ------------ = ------------ = --------

        x₂ - x₁         2 - 0           2

y - y₁ = m(x - x₁)

y - 3 = (3/2)(x - 0)

y - 3 = (3/2)x

  +3               +3

------------------------

y = (3/2)x + 3

I hope this helps!

Answer:

8,377.58 [tex]mi^{3}[/tex]

Step-by-step explanation:

To solve for the volume of a right circular cone like the one in the picture, you use [tex]\pi[/tex][tex]r^{2}[/tex][tex]\frac{h}{3}[/tex].

Plug in the radius and height to get [tex]\pi[/tex][tex]20^{2}[/tex][tex]\frac{20}{3}[/tex].

Then solve (and round to the nearest hundredth) and you should get 8,377.58.

The bonus based upon the given formula is $2606.15 approximately

Given,

Annual salary = $48,000

Yearly sales = $76,000

Bonus is given according to the formula:

2 weeks salary + 1 percentage commission

Here,

Annual salary is given as $48,000

We have to find the weekly salary:

There is 52 weeks in a year.

So, salary for one week = Annual salary / number of weeks =  48000/52 = $923.077

Now, salary for two weeks = 923.077 × 2 = $1846.154

Rate of annual commission is 1%

The commission amount:

1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760

So,

The bonus amount = 2 weeks salary + 1 percentage commission

The bonus amount = 1846.154 + 760

The bonus amount = 2606.154

Therefore, the bonus given based upon the given formula is $2606.154

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{13}~~ = ~~\cfrac{11}{x}\implies x^2=(13)(11)\implies x^2=143\implies x=\sqrt{143}[/tex]

Answer: Eiko

Step-by-step explanation:

Eiko has the shortest time.

The percent of young men that are shorter than the mean height of young women is 2.5%.

A data set with a normal distribution has the majority of its values clustered in the middle of the range and the remaining values tapering off symmetrically toward either end.

A continuous probability distribution for a real-valued random variable is known as a "normal distribution" in statistics.

Based on the information, the percentage will be calculated thus:

Z = (69.3 - 64) / 2.7 = 1.9630

So P(Z>1.96)= 1-P(Z<1.96)

(check standard normal table)

= 1-0.975

= 0.025

= 2.5%

The percentage is 2.5%.

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Answer:the answer is b

Step-by-step explanation:

We must know the following exponent rules to help us solve this question:

[tex]3^p=\dfrac{\sqrt[3]{9}}{3}[/tex]

⇒ Rewrite [tex]\sqrt[3]{9}[/tex] as [tex]9^\frac{1}{3}[/tex]:

[tex]3^p=\dfrac{(3^2)^\frac{1}{3}}{3}[/tex]

⇒ Multiply:

[tex]3^p=\dfrac{3^\frac{2}{3}}{3}[/tex]

⇒ Subtract:

[tex]3^p=3^{\frac{2}{3}-1}[/tex]

[tex]p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}[/tex]

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

The probability that a randomly chosen applicant has over 5 years of experience is 0.2768.

It should be noted that probability simply has to do with the likelihood that an event will happen.

From the information, out of 457 applicants for a job, 271 have over 5 years of experience and 75 have over 5 years of experience.

Therefore, the probability that a randomly chosen applicant has over 5 years of experience will be:

= Number of graduate over 5 years / Number of people over 5 years experience

= 75 / 271

= 0.2768

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Notice that the slope of the line is equal to the speed

hence, the speed = 5 miles / hour

Answer:

Not 100% sure what it's asking but if it's asking what number she used to estimate the 240, she used 100 because it's one-off 99. The actual number would be 237.6

Step-by-step explanation:

Rewrite 50% as 1/2

We need a fraction that is equal to 1/2 of 1/6.
-> That fraction equals to 1/2 x 1/6 = 1/12 (or 1/6 : 2)

Answer:

1/12

Step-by-step explanation:

1/6*100/50=1/12.

The probability of picking an odd number ball in fraction form is; 6/11

We are told that a bag contains eleven balls labelled 1 through 11. These numbers are;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. This is a total of 11 numbers.

The even numbers are a total of 5 while the odd numbers are a total of 6.

Now, the probability of selecting an odd number will be;

P(selecting odd number) = Number of possible odd numbers/Number of Total Numbers

Plugging in the relevant numbers gives;

P(selecting odd number) =  6/11

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the answer is T becouse T is the time which is what you get when distance is divided by 80 mph

Answer:

3/8 barrels / minute.

Step-by-step explanation:

Rate = fraction of barrel filled / time

        = 1/4 / 2/3

        = 1/4 * 3/2

        = 3/8.

Answer:

gradient is 1/2  =  0.5

Step-by-step explanation:

y= 1/2 x−3

Swap sides so that all variable terms are on the left hand side.

1/2 x−3=y

Add 3 to both sides.

1/2 x=y+3

Multiply both sides by 2.

1/2 x = 1/2 y+3

​

Dividing by  1/2 undoes the multiplication by  1/2

x= 1/2 y+3

​

Divide y+3 by  1/2  by multiplying y+3 by the reciprocal of  1/2

​

.

x=2y+6

THE SUM OF THE INNER ANGLES IS 180°

[tex](x - 7) + (2x - 8) + 90 = 180 \\ x - 7 + 2x - 8 + 90 = 180 \\ x + 2x = 180 + 7 + 8 - 90 \\ 3x = 105 \\ \frac{3x}{3} = \frac{105}{3} \\ x = 35[/tex]

OPTION C IS THE RIGHT ANSWER.

Answer:

x= -11

It only has one solution.

Step-by-step explanation:

Angle A is located in the third quadrant and solved to be a value of  255.522 degrees.

A quadrant refers to fourth division. In a circle, a quadrant represents a quarter of a circle.

In angle calculations, there are 4 quadrants. The first quadrant is between angles 0 to 90 degrees. The second quadrant is between angles 90 to 180 degrees. The third quadrant is between angles 180 to 270 degrees. The fourth quadrant is between 270 to 360 degrees.

The each quadrant is at 90 degrees interval. and the in angle calculations, the rotation is in anticlockwise direction

cos A = 1/4

where 270°

270 degrees represent the third quadrant. Hence angle A is in the third quadrant

solving for angle A

let cos a = 1/4

a = arc cos ( 1/4 )

a = 75.522 degrees ( in first quadrant )

A = a + 180 degrees

A = 75.522 degrees + 180 degrees

A = 255.522 degrees

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Answer:

-31

Step-by-step explanation:

[tex]-38-16-(-23) \\ \\ =-38-16+23 \\ \\ =-54+23 \\ \\ =-31[/tex]

[tex]5x - 2y = 4 \\ 5x = 4 + 2y \\ \frac{5x}{5} = \frac{4 + 2y}{5} \\ x = \frac{4 + 2y}{5} ......(3)equation[/tex]

NOTE I AM SOLVING BY SUBSTITUTION

[tex]8( \frac{4 + 2y}{5} ) + 5y = - 10 \\ \frac{32 + 16y}{5 } + 5 y = - 10 \\ \frac{32 + 16y}{5} (5) + 5y(5) = - 10(5) \\ 32 + 16y + 25y = - 50 \\ 41y = - 50 - 32 \\ \\ \\ \\ 41y = - 82 \\ \frac{ - 41y}{41} = \frac{ - 82}{41} \\ y = - 2[/tex]

[tex]x = \frac{4 + 2( - 2)}{5} \\ x = \frac{4 - 4}{5} \\ x = \frac{0}{5} \\ x = 0[/tex]

ATTACHED IS THE SOLUTION

Answer: (0,-2)

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{5x-2y=4\ \ \ \ \ (1)} \atop {8x+5y=-10\ \ (2)}} \right.[/tex]

Multiply equation (1) by 5, and equation (2) by 2:

[tex]\displaystyle\\\left \{ {{25x-10y=20\ \ \ \ (3)} \atop {16x+10y=-20\ \ (4)}} \right.[/tex]

Add equations (3) and (4):

[tex]41x=0[/tex]

Divide both parts of the equation by 41:

[tex]x=0[/tex]

Let's substitute the value of x into equation (2):

[tex]8(0)+5y=-10\\0+5y=-10\\5y=-10[/tex]

Divide both parts of the equation by 5:

[tex]y=-2[/tex]

Thus, (0,-2)

Answer:

369,962

Step-by-step explanation:

If the rounding digit is 0, 1, 2, 3, or 4, drop all the digits to the right of it

If the rounding digit is 5, 6, 7, 8, or 9, add one to the rounding digit and drop all digits to the right of it

Using the slope concept, the distance from point AA to point BB ≅ 360 feet.

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

We can get, the vertical change is of 144 feet.

At point A, the angle is of 9º, while the horizontal position is of [tex]x_{A}[/tex] ,

Then, we can write,

tan 9º =  [tex]\frac{144}{x_{A} }[/tex]

[tex]x_{A}[/tex] = 144/tan 9º

Hence, tan 9º = 0.15

[tex]x_{A} =[/tex] 144/0.15

[tex]x_{A}[/tex] = 960

At point A, the angle is of 14º, while the horizontal position is of [tex]x_{B}[/tex] ,

Then, we can write,

[tex]x_{B}[/tex] = 144/tan 14º

Hence, tan 14º = 0.24

[tex]x_{B}[/tex] = 144/0.24

[tex]x_{B}[/tex] = 600

So, the distance in feet is of:

d = [tex]x_{A} -x_{B}[/tex]

d = 960 - 600

d = 360

d ≅ 360

Therefore,

A boat is heading towards a lighthouse, then the distance from point AA to point BB ≅ 360 feet.

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Equivalent equations (acceptable moves)

(1)  

4(x+3)=32

       x+3 = 8

(2)

[tex]\frac{(9x+4)}{2} =5\\\\9x+4=10[/tex]

(3)

x- 7+ 3x=25

4x-7=25

Not equivalent (unacceptable moves)

(1)

2(x+5) = 10

2x+5 =  5( 20 is wrong)

(2)

2x+4=22

2x= 22-4= 18 (26 is wrong)

(3)

[tex]\frac{(6x-1)}{3} =27\\\\6x-1=81[/tex] (9 is wrong)

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Answer:

[tex]\frac{h^6}{h^8}[/tex]

Step-by-step explanation:

1. For now, let's leave the [tex]g^{-6}[/tex] to the side and just worry about the [tex]\frac{h^8}{h^2}[/tex].

2. When you apply the exponent rule you should have learned in class, we know that when you divide two bases with exponents, the exponents subtract. So, you can subtract 8 - 2, and then the greater digit's place in the fraction stays. So, since [tex]h^8\\[/tex] is the greater number (and it's in the numerator), you put the [tex]h^6[/tex] in the numerator as well.