GRADE
Perimeter: Change in Dimensions
A rectangle ABCD has a width of 3 inches and a length of 7 inches.
a) What is the Perimeter of the rectangle?
BINDEX
b) What is the Perimeter of the new rectangle if you double the width of rectangle ABCD? How did you find
it? How many times bigger or smaller did the new Perimeter get? (You can divide the new Perimeter over the
old one to find the times of increase/decrease)
c) What is the Perimeter of the new rectangle if you double the width and length of rectangle ABCD? How did
you find it? How many times bigger or smaller did the new Perimeter get compared to the perimeter of
rectangle ABCD?
d) Now choose a different shape of your liking and give it your own dimensions. Answer questions a), b), c)
and d) for the shape you chose.
e) Can you generalize what happens to the Perimeter if you change one of the dimensions of a shape and
what happens when you change both dimensions of the shape?
lick "Create lournal Fntn" tn antar un

Answer:

210

Step-by-step explanation:

Given:

Medals in sports = 40

Medals in dance = 25

Medals in music = 212

Total students that received medals = 55

Total students that received medals in all three categories = 6

Required:

How many students get medals in exactly two of these categories?

Take the following:

A = set of persons who got medals in sports.

B = set of persons who got medals in dance

C = set of persons who got medals in music.

Therefore,

n(A) = 40

n(B) = 25

n(C) = 212

n(A∪B∪C)= 55

n(A∩B∩C)= 6

To find how many students get medals in exactly two of these categories, we have:

n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)

=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)

Using equation 1:

=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18

Substitute values in the equation:

= 40 + 25 + 212 + 6 − 55 − 18

= 283 - 73

= 210

Number of students that get medals in exactly two of these categories are 210

The expression a/b ÷ c/d = ad/bc is A. true.

To show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc

Rational expressions are expressions of the form a/b where a and b are integers and b ≠ 0

If the rational expression a/b is to be divided by c/d, we take the reciprocal of the expression on the right side of the division sign.

So, L.H.S = a/b ÷ c/d

= a/b × 1/(c/d)

= a/b × d/c

= ad/bc

= R.H.S

Since L.H.S = R.H.S.

a/b ÷ c/d = ad/bc

So, the expression a/b ÷ c/d = ad/bc is A. true.

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Answer:

We can arrange 4 different colored balls in 24 ways.

Step-by-step explanation:

We have to find the number of ways in which we can arrange 4 different colored balls.

Firstly, we have to decide that either we use Permutation or we use Combination.

A Permutation is used when the order of arranging the numbers matters while on the other hand, a combination is used when the order of arranging the numbers doesn't matter.

So, in our question; the ordering matters to us as a ball which is placed in the first place can't be put again put in other places.

Number of ways of arranging 4 different colored balls = [tex]^{4}P_4[/tex]

                     =  [tex]\frac{4!}{(4-4)!}[/tex]          {[tex]\because ^{n} P_r = \frac{n!}{(n-r)!}[/tex] }

                     =  4! = [tex]4 \times 3 \times 2\times 1[/tex]

                     =  24 ways

Hence, we can arrange 4 different colored balls in 24 ways.

Answer:

second option

Step-by-step explanation:

Given

f(x) = (x - 7)(x + 4)(3x - 2)

To find the zeros let f(x) = 0, that is

(x - 7)(x + 4)(3x - 2) = 0

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]

zeros are x = - 4, x = [tex]\frac{2}{3}[/tex], x = 7

Hey there! I'm happy to help!

To find the volume of a cylinder, you multiply the base by the height and then divide by three. The volume of a cone is the same as the volume of a cylinder with the same dimensions divided by three.

So, since a cone's volume is 1/3 of that of a cylinder, we just divide 72 by 3!

72/3=24

Therefore, the volume of the cone is 24 feet cubed.

Have a wonderful day! :D

Answer: its 24.

Step-by-step explanation:

Answer:

Volume left in the cylinder if all the cone is made full:

[tex]\bold{345.72 \ ml }[/tex]

Step-by-step explanation:

Given

Radius of cylinder = 5 cm

Height of cylinder = 14 cm

Radius of cone = 6 cm

Height of cone = 20 cm

To find:

Liquid remaining in the cylinder if cone is made full from cylinder's liquid.

Solution:

We need to find the volumes of both the containers and find their difference.

Volume of cylinder is given by:

[tex]V_{cyl} = \pi r^2h[/tex]

We have r = 5 cm and

h = 14 cm

[tex]V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3[/tex]

Volume of a cone is given by:

[tex]V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3[/tex]

Volume left in the cylinder if all the cone is made full:

[tex]1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }[/tex]

Answer:

crystal size and rock texture     D

Step-by-step explanation:

:)

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

What is the texture?

The texture is defined as a tactile quality of an object's surface. It appeals to our sense of touch, which can evoke feelings of pleasure, discomfort, or familiarity.

The texture of an igneous rock is dependent on the rate of cooling of the melt slow cooling allows large crystals to form, fast coolng yields small crystals.

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

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Answer:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex]

Step-by-step explanation:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex] . First multiply 7*-6=-42.

Then do 16*13=208.

Simplify by dividing both by 2.

You get [tex]\frac{-42}{208}=\frac{-21}{104}[/tex].

Your final simplified answer is [tex]\frac{-21}{104}[/tex]

I hope this helps!

Answer:

(3,2)

Step-by-step explanation:

Just took the test

Answer:

3 ≤ n < 15

 1-2. not n

3-4. yes n

5-6. yes n

 7-8. yes n

9-10. yes n

11-12. yes n

13-14. yes n

15-16. not n

Step-by-step explanation:

Everything on this side is less than, < but everything on this side is greater.

Everything on this side could be equal or less, ≤ but everything on this side is

not.

I'm had a hard time with the number line, but imagine a line going through the periods and there being a dot where the yes ns end, and start.

Intervals has each point represent more than one number making the line shorter.

Answer:

x^2 +4x + y^2 -2y +1 =0

Step-by-step explanation:

First we need to find the radius

Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2

A circle can be written in the form

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x--2)^2 + (y-1)^2 = 2^2

(x+2)^2 + (y-1)^2 = 4

FOIL ing

x^2 +4x+4  + y^2 -2y +1 = 4

Combining like terms

x^2 +4x + y^2 -2y +5 -4 =0

x^2 +4x + y^2 -2y +1 =0

Answer and Step-by-step explanation:

Answer:

x^2 +4x + y^2 -2y +1 =0

Step-by-step explanation:

First we need to find the radius

Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2

A circle can be written in the form

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x--2)^2 + (y-1)^2 = 2^2

(x+2)^2 + (y-1)^2 = 4

FOIL ing

x^2 +4x+4  + y^2 -2y +1 = 4

Combining like terms

x^2 +4x + y^2 -2y +5 -4 =0

x^2 +4x + y^2 -2y +1 =0

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 ​minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72​, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is given by = P(X > 82 min)

       P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)

                                                           = 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)

                                                           = 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)

                                                           = 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 ​minutes, then we conclude that the population mean must be more than 72​, since the probability is so low.

Answer:

Step-by-step explanation:

From the given data

mean, u = 72

Standard deviation [tex]\rho[/tex] = 23

A) Probability that a randomly selected time interval between eruptions is longer than 82​minutes

[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]

B)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]

C)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]

D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases

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The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.

Yellow: 3 spaces out of 6, so the probability is 3/6 = 1/2

Red: 2 spaces out of 6, so the probability is 2/6 = 1/3

Blue: 1 space out of 6, so the probability is 1/6

multiplying the probability of each color by 150:

Yellow: 1/2 * 150 = 75 times

Red: 1/3 * 150 = 50 times

Blue: 1/6 * 150 = 25 times

Terefore The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.

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Answer:

370 mm²

Step-by-step explanation:

The area of this figure can be calculated by taking the whole figure as a full rectangle, and consider the part that is cut out from the middle of the shape as another rectangle.

Find the area of the cut-out part and subtract from the area of the full rectangular shape to get the area of the composite figure.

=>Area of full rectangular shape:

Length = 30 mm

Width = 15 mm

Area = L * B = 30*15 = 450 mm²

=>Area of the cut-out Rectangle part:

Length = 10 mm

Width = 8 mm

Area = 10*8 = 80 mm²

=>Area of composite figure = 450 mm² - 80 mm² = 370 mm²

Answer:

40 m

Step-by-step explanation:

The perimeter of the flat, orange shape is the sum of all the sides that forms a boundary around the shape.

The shape is made up of 4 triangles having 2 equal side lengths each, which surrounds the center square.

Each side length of the triangle, that forms a boundary round the shape = 5 m.

There are 8 of this equal side length.

Perimeter = 8(5m) = 40 m

Answer:

On day 0 (starting day), the percentage of petri dish occupied by bacteria was 2.44%

Step-by-step explanation:

Rate of growth = 2  (i.e. doubles every day)

Petri dish was filled to 100% on day 12.

Let

P(0) = percentage of Petri dish occupied on day 0, then

equation of percentage a  function of time in x days

P(x) = P(0)*r^x  ......................(1)

where

100% = P(12) = p(0) * 2^12 = 4096 P(0)

=>

P(0) = 100% / 4096 = 0.0244%

Next, to find percentage on February 14 (Valentine's day!)

Day 0 is February 9, so February 14 is the fifth day, so x=5.

Substitute x=5 in equation (1) above,

P(x) = P(0)*r^x  

P(5) = P(0)*2^5

P(5) = 0.0244*2^5 = 0.0244*32 = 0.781%

Ans. the 0.781% of the petri dish was filled with bacteria after 5 days on February 14th.

Answer:

0.0244%

Step-by-step explanation:

A = p(1 + r)^t

The future amount is 100, for 100 percent. From February 9 to February 21, there are 12 days. The rate of growth is 100% since the amount doubles each day. t = 12, for 12 days. p = beginning percentage.

100 = p(1 + 1)^12

log 100 = log [p(1 + 1)^12]

2 = log p + 12 log 2

log p = 2 - 12 log 2

p = 10^(2 - 12log 2)

p = 0.0244

Answer 0.0244%

Answer:

1/3

Step-by-step explanation:

Let's say you picked the blue one first. You have a 2/3 chance of doing that, and now you're left with 2. Now, to pick the green one, you have a 1/2 chance. Multiply that and you  see that you have a 1/3 chance of picking it last.

Answer:

1/3.

Step-by-step explanation:

The probability that the red cube WON'T be picked on the first draw is 2/3. This is because there is a 1/3 probability of picking a green cube, added to a 1/3 probability of picking a blue cube.

The probability that the red cube WON'T be picked on the second draw is 1/2.  This is because one cube has already been picked, so there are two remaining. You can only pick one of the two.

(2/3) * (1/2) = (2 * 1) / (3 * 2) = 2 / 6 = 1/3.

Hope this helps!

Answer:

Number of different cones made = 18

Step-by-step explanation:

Given:

Types of cone = 2

Number of flavors = 3

Number of toppings = 2

Find:

Number of different cones made

Computation:

Number of different toppings = 1(peanuts) + 1(sprinkles) + 1(both) = 3

Number of different cones made = Types of cone × Number of flavors × Number of different toppings

Number of different cones made = 2 × 3 × 3

Number of different cones made = 18

Answer: [tex]2.25\sqrt{3}[/tex]

Not sure what you mean by terms of pi, unless you want us to find the area of the sector, not the triangle.

Step-by-step explanation:

Assuming you mean the area of the triangle...

First draw an altitude from the 120 degree angle to the opposite base.  You will find that the altitude will also be a median.  This forms 2 30-60-90 right triangles.  Thus, the height of the altitude is 1.5 and the base of the triangle is 1.5*root3.  Thus, the base of the triangle is [tex]3\sqrt{3}[/tex] and the height is 1.5.  Thus, the area of the triangle is [tex]2.25\sqrt{3}[/tex]

Answer:

(0,-3)

Step-by-step explanation:

this is your answer..................

Answer:

Excess of income over expenditure is ₹1,185,500.

Step-by-step explanation:

Note: The data in this question are merged together. They are therefore sorted before answering this question. See the attached pdf file for the sorted question.

The question is now answered as follows:

Question: Prepare Income and Expenditure A/c. for the year ending 31-03-2014.

Answer and explanation:

Note: See the attached excel file for the Income and Expenditure A/c. for the year ending 31-03-2014.

Both receipts and payments account and income and expenditure account are prepared by not-for-profit organizations such as charity organizations, human right campaign, clubs, etc.

Receipts and payments account is an account gives a summary of all the cash transitions, cash received and paid, that the organization engaged in during a particular period. It is similar to the cash book prepared by profit making organizations. The receipts and payments account is prepared in or to determine the balance of cash in hand or at bank or bank overdraft at the end of the period.

Income and expenditure account is an account gives a summary of all incomes and expenses of an organization during a particular period. It is similar to the trading and profit and loss account prepared by profit making organizations. The income and expenditure account is prepared in order to determine whether there is a surplus or a deficit balance during the period.

Answer:

7.55

Step-by-step explanation:

3/x = x/19

x² = 57

x = 7.54983....

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

2x - 2(-2x + 5) = 2

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

Answer: 42w

Step-by-step explanation:

Subtracting a negative is like adding.

Answer:

4

Step-by-step explanation:

y=mx+b

b=y-intercept.

In this case...

mx=-5<-- this is the slope of the line.

b=4<-- y intercept.

Hope this helps, any further questions, please feel free to ask.

Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( [tex]\frac{x-\mu }{\sigma}[/tex]  > [tex]\frac{2.3-\mu }{\sigma}[/tex] )

P (z  > [tex]\frac{2.3-1.9 }{0.3}[/tex]  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( [tex]\frac{x-\mu }{\sigma }[/tex] <  [tex]\frac{a-\mu }{\sigma }[/tex] )

[tex]\frac{a-1.9 }{0.3 } = -1.55[/tex]

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

Answer:

x = 1

Step-by-step explanation:

Using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

3[tex]log_{2}[/tex] (2x) = 3

[tex]log_{2}[/tex] (2x)³ = 3

(2x)³ = 2³

8x³ = 8 ( divide both sides by 8 )

x³ = 1 ( take the cube root of both sides )

x = 1

Answer:

x=1 is the correct answer

Step-by-step explanation:

got it right on edge!!!!

Answer:

i believe a=105, b=29, and c=45

Answer:

Sine angle of <ACB = 38.68°

Step-by-step explanation:

Hello,

To solve this problem, we need a good representation of the sides and the angle.

See attached document for better illustration.

Assuming it's a right angled triangle,

AC = hypothenus

AB = opposite

BC = adjacent

AC = 40

BC = 25

AB = 25

From trigonometric ratios

Sinθ = opposite/ hypothenus

Sinθ = AB / AC

Sinθ = 25 / 40

Sinθ = 0.625

θ = sin⁻¹0.625

θ = 38.68°

Sine angle of <ACB = 38.68°