a rectangle has a perimeter of 3o inches and a width of 6 inches what are the dimensions of a similar rectangle with a perimeter of 20 inches?

Answer:

15 14/15

Step-by-step explanation:

8 + 7 = 15

1/3 + 3/5

5/15 + 9/15

14/15

15 + 14/15 = 15 14/15

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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Answer:

29) y = 1

31) y = x + 3

Step-by-step explanation:

Basic information:

29) Horizontal lines have a slope of 0, so in y = mx + b, the equation simplifies to y = b. Given that the y-intercept is where the line intersects the y-axis, we can see that the line intersects through (0,1), meaning that b = 1. Therefore, the equation is y = 1.

31) First, let's find the slope. Since the slope is (change in y)/(change in x), let's pick two points such as (0,3) and (1,4). As you can see, we go up one and to the right by one, meaning that the slope is 1/1 or 1. However, when writing the equation, we can just leave it as x since 1x and x are the same thing. Lastly, the y-intercept is 3 because the line intersects with the y-axis at (0,3). Therefore, the equation is y = x + 3.

Answer:29) y=1

30) y=x+3

Step-by-step explanation:

29- since the line is vertical it is moving by y, and the intercept is at 1 making the eqaution y=1

30- fill in y=mx+b, so begin by finding the "rise over run"  because it moves to the right by 1 and goes up 1 (1/1) and 1 can be refred to just as x & the y-intercept is 3 so your equation is y=x+3

Answer:

B

Step-by-step explanation:

log4x = 2.1

logx/log4 = 2.1

logx = log(4) x 2.1

logx = 1.264

x = 10^(1.264)

x = 18.38 (to two d.p)

The length of the each piece of pipe is 7 feet

What is Length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.

Given,

Total length of the pipe = 21feet

The pipe after 3 pieces = ?

We have to find the length of pipe after it is cut down into three piece

To find that we have to divide the length of the pipe with 3

The length of 3 pieces = 21/3

                                      = 7 feet

Hence, The length of each piece will be 7 feet  

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Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Answer:

7 1/2-(3+7 1/3)= -17/6=-2 5/6 ≅ -2.8333333

Step-by-step explanation:

Answer:

P = 5x + 33 = 58

Q = R = 3x+46 = 61

Step-by-step explanation:

angles in a triangle add up to 180 degrees

the angles in an isosceles triangle that correspond to the two congruent sides (are opposite the sides) are also congruent

that means that angle R = angle Q because QP and RP are congruent

angles = 5x+33, 3x+46, 3x+46

5x+33 + 3x+ 46 + 3x+46 = 180

11x + 125 = 180

subtract 125 from both sides to isolate the x and its coefficient

11x = 55

divide both sides by 11 to find x

x = 5

P = 5x + 33 = 58

Q = R = 3x+46 = 61

Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:

Course fees for continuing legal education: $1,400

Airfare and hotel room: $500

Meals provided by the hotel's restaurant: $300

Snacks from the newsstand: $10

To calculate the total amount that Bob can deduct, add up these expenses:

$1,400 + $500 + $300 + $10 = $2,210

Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

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Answer:

GH = 15

Step-by-step explanation:

given a tangent and a secant drawn from an external point to the circle, then the product of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is

FG × FH = EF²

12(12 + 2x - 1) = 18²

12(11 + 2x) = 324 ( divide both sides by 12 )

11 + 2x = 27 ( subtract 11 from both sides )

2x = 16 ( divide both sides by 2 )

x = 8

Then

GH = 2x - 1 = 2(8) - 1 = 16 - 1 = 15

The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Answer:

0.4

Step-by-step explanation:

all I got to say is that the answer is 0.4 %100

Answer:

5

Step-by-step explanation:

Answer:

He is not correct

2 boxes of eggs =1.30+1.30=2.60

1 bottle of juice cost=£2.60

2.60+2.60=£5.20

£10.00-0.90p=£9.10

9.10-5.20=£3.90

3.90/3=£1.30

1.30+1.30+1.30=£3.90

5.20+3.90=£9.10

Step-by-step explanation:

Answer:

16)  7⁻²

17) -1⁻²

Step-by-step explanation:

plug in the x=, y=, and n= into the equation.

Reflection is a rigid transformation in which the shape, the size, and the angles remain the same. Therefore, the reflection will be a figure of the same shape, but an image that will be symmetrical to the preimage.

Something like this:

Answer:

116 / 45

Step-by-step explanation:

To add fractions with unlike denominators, we need to find their common denominator.

One way to do this is by finding the least common multiple (LCM) of the denominators.

The LCM of 3, 5, 9 and 15 is 45.

We then convert each fraction so that its denominator is 45:

1/3 = 15/45

3/5 = 27/45

7/9 = 35/45

13/15 = 39/45

Now we can add the fractions:

15/45 + 27/45 + 35/45 + 39/45

To simplify, we can add the numerators and keep the common denominator:

(15 + 27 + 35 + 39) / 45

Which gives us:

116 / 45

Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.

The volume of this required figure is 190m³.

What is volume, exactly?

Volume is a term used in mathematics to describe the volume of three-dimensional space inhabited by an object or a closed surface.

                           Volume is measured in cubic units like m3, cm3, in3, etc. Volume and capacity may be used interchangeably.

Volume of a rectangular prism is the space inside the prism. It is calculated by multiplying its base area by its height.

Volume (v) = l × b × h, where l is the length, b is the breadth, and h is the height of the prism.

so volume of both the rectangular prism are to be found.

Volume of first rectangular prism = l×b×h = 5 × 4 × 5 = 100 m³.

volume of second prism = 2 × 9 × 5 = 90m³.

∴ the volume of the figure

= volume of first rectangular prism +volume of second prism

=  100m³ + 90m³

=190m³.

Thus, the volume of this required figure is 190m³.

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Answer:

The answer is 10 mph

Step-by-step explanation:

Divide 100 by 10

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Answer:

y = 2x + 3

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

m = (-1 - 3)/(-2 - 0)

m = -4/-2

m = 2

y = 2x + b

Step 2: Rewrite equation

y = 2x + 3

*You are given y-intercept (0, 3), so simply add it to your equation.

The two positive numbers are 55, and 55.

Given that,

Two positive numbers whose product is a maximum and whose sum is 110.

To Find :  Two positive real numbers with a maximum product whose sum is 110.

x + y = 110

x = 110-y

Area = xy = (110-y)y

A = 110y-y^2

Maximum A occurs when y = -b/(2a) = -110/(2*-1) = 55

x + y = 110

x + 55 = 110

x = 55

and y is also 55.

Therefore, the two positive numbers are 55, and 55.

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Answer:

eywgw6 the car is in the car is in the car is in

Step-by-step explanation:

Wu and I will be in the car is in the car is in the car is in the car is here and we can 4

Answer:

Safe fund = $24,000

Risky fund = $6,000

Step-by-step explanation:

Definition of variables:

Given information:

Convert the percentages into decimal form:

\(\implies 2.5\%=\dfrac{2.5}{100}=0.025\)

\(\implies 8\%=\dfrac{8}{100}=0.08\)

Create a system of equations from the given information and defined variables:

\(\begin{cases}0.025x+0.08y=1080\\x=4y\end{cases}\)

Substitute the second equation into the first equation and solve for y:

\(\implies 0.025(4y)+0.08y=1080\)

\(\implies 0.1y+0.08y=1080\)

\(\implies 0.18y=1080\)

\(\implies \dfrac{0.18y}{0.18}=\dfrac{1080}{0.18}\)

\(\implies y=6000\)

Substitute the found value of y into the second equation and solve for x:

\(\implies x=4(6000)\)

\(\implies x=24000\)

Therefore, the amount invested in each fund was:

Answer:

21

Step-by-step explanation:

if u divide 649 by 31 u get 20. 93 Wich u round up to 21

The average number of points scored by athlete per game is 21.

It is given that a star athlete scored 649 points during the 31 basketball games.

We have to find , the average number of points she scored per game.

What will be the value if 24 is divided into 8 parts equally ?

The value will be 3.

Total points scored in 31 basketball games = 649 points

Points scored in 1 game =

649 ÷ 31

= 20.93

≈ 21 points per game

Thus , the average number of points scored by athlete per game is 21.

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In the land area of Statesville, NC there would be 133.54 persons per square foot.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, One mile is 5280 feet so a square mile is

(5280 × 5280) = 27878400 square feet.

Therefore, The number of persons in each square foot should be,

= 322900000/27878400  persons per square foot.

= 3229000/278784 persons per square foot.

= 133.54 persons per square foot.

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Answer:

c) -10(_40)=30

Step-by-step explanation:

because -+-=+

Answer:

coordinates of A are (-4.5, 2)

coordinates of B are (0, -3.5)