Finding missing side length given two similar triangles

The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²

The surface area of sphere = 324π inches²

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the surface area of the Sphere be = S

Let the dimensions of the rectangular box be L x W x H

12 inches x 14 inches x 18 inches

Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum

From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere

So , Height of the Box = Diameter of the Sphere

And , Radius of the sphere = Height of the Box / 2

                                             = 18 / 2

Radius of the sphere = 9 inches

Now ,

Surface Area of a Sphere = 4πr²

r = 9 inches

Substituting the values in the equation , we get

Surface Area of a Sphere S = 4 x π x ( 9 )²

                                              = 4 x π x 81

                                              = 324π inches²

Therefore , the value of S is 324π inches²

Hence , The surface area of sphere = 324π inches²

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Using the z-distribution to test the hypothesis, it is found that:

a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.

b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:

[tex]H_0: p = 0.581[/tex]

At the alternative hypothesis, it is tested if the proportion is different, hence:

[tex]H_1: p \neq 0.581[/tex]

A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

The equation calculating the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed as follows:

For this problem, the value for these variables is given as follows:

[tex]\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}[/tex]

z = -1.44.

The critical value for a two-tailed test is with a significance level of 0.05 is:

|z| = 1.96.

The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.

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Answer: Yes

Step-by-step explanation:

Because if you keep going it will reach 86, since it's added by 4, so 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86.

how long does it take Peter to clean a room by himself is[tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
What does "rate" mean mathematically?

A rate is a unique ratio where the two words are expressed in several units.

Let Peter take time to clean 1 room be = t
Let Parker take time to clean 1 room be = t+15
Total Time taken by both to clean to room T= 110
Equation for total time taken to clean 2 room by both
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{T}[/tex]

[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{110}[/tex]
By taking LCM

[tex]\frac{2t+15}{t^{2}+15} =\frac{1}{55}[/tex]
By cross multiplication in above equation

[tex]110t+825=t^{2} +15t[/tex]
[tex]t^{2}-95t-825=0[/tex]

Hence the answer is   [tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]

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The distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

The points are (3, π/6) and (2, π/3)

The polar coordinate system is the system that represent a point by a distance from a fixed reference point and angles from a reference direction

The distance between the two points

d = [tex]\sqrt{r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2)}[/tex]

(3, π/6) is the coordinates of first point

(2, π/3) is the coordinates of second point

Substitute the values in the equation

d = [tex]\sqrt{3^2+2^2-2(3)(2)cos(\pi/6 - \pi /3)}[/tex]

d = [tex]\sqrt{9+4-12(\frac{\sqrt{3} }{2} )}[/tex]

d = [tex]\sqrt{13-6\sqrt{3} }[/tex]

d = 1.614 units

Hence, the distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

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The equation of the linear function is y=8x+(-8).

What do you mean by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to data in the given question,

We have points (0,-8) and (1,0), thus

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8[/tex]

Then

y=8x+b

Points (0,-8) means that when x=0, y=-8 and we use this to find b,

y=8x+b

-8=8(0)+b

-8=0+b

b=-8

So, y=8x+(-8)

Therefore, the equation of the linear function is y=8x+(-8).

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Answer:

Depends on the gravitational force. On Earth, one pound equals 4.41N.

Step-by-step explanation:

The formula for Newton's Second Law of Motion is F=ma, which is Force = mass × acceleration.

The SI unit of mass is the kilogram (kg), so we'll have to convert one pound to kilograms. For practical purposes, one pound equals 0.45kg.

The gravitational force of the Earth is 9.8m/s^2. It is worth noting that each planetary body has its own gravitational force in respect to its mass.

Force = mass × acceleration = 0.45kg × 9.8m/s^2 = 4.41N

This number is only applicable on Earth, and may and will change on a planetary body with a mass different from Earth's.

The probability that the selections are both boys is 7/10

The given parameters in the question are

Seventh grade

Boys = 7

Girls = 3

Eight grade

Boys = 4

Girls = 4

The probability of selecting a boy is calculated as

P(Boy) = Number of boys/Number of students

So, we  have

Seventh grade

Boys = 7

Girls = 3

P(boy) = 7/10

Eight grade

Boys = 4

Girls = 4

P(boy) = 4/8

The probability that the selections are both boys is

P = P(boy) * P(boy)

So, we have

P = 7/10 * 4/8

Evaluate

P = 7/20

Hence, the probability is 7/20

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Sophie determine that the function describing the cost of dinner is linear if you order X eggrolls your dinner will cost 1.50x + $10 what is the per egg roll fee?

1.50x + $10

per egg roll fee is $1.50

Answer:

521 mm2

Step-by-step explanation:

Formulas:

area of circle= 3.14 x radius x radius

area of semicircle = 0.5 x 3.14 x radius x radius

diameter of circle= 20mm

radius=0.5x20mm=10mm

area of trapezium= 0.5 x (base+base) x height

Working:

area of semicircle= 0.5 x 3.14 x 10mm x 10mm = 157mm2

area of trapezium = 0.5 x (20mm+32mm) x 14mm = 364mm2

total area of figure= 157mm2 + 364mm2 =521mm2

The required change in height of the missile is 16100 feet.

Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.

Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.

here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.

Thus, the required a change in height of the missile is 16100 feet.

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Based on the given equation and the given value of (), the value of 5() from the equation is 490

If

() = 94 + 2 + 2

The equation can be solved by substituting the value of () into 5()

Substituting is the method of inserting the known value of a variable into an equation to solve for the value of the equation.

Then,

(5)()

= 5(94 + 2 + 2)

= 5(98)

= 490

So therefore, the value of 5() is given by 490.

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The number of adult tickets were sold is 130 tickets.

Given,

In the question:

Total tickets were sold for the school play is 390 tickets.

The number of student tickets sold was two times number of adult tickets sold.

To find the how many adult tickets were sold?

Now, According to the question:

Based on the given conditions:

Let the number of adult tickets be x.

Formulate the condition:

x × (1 + 2) = 390

x × 3 = 390

Simplify

x = 390/3

x = 130

Hence, The number of adult tickets were sold is 130 tickets.

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The total change in yards where the team started is 3x

The given parameters in the question are:

Yards per play = unknown

Number of plays = 3 consecutive plays

Represent the yards per play with x

So, we have

Yards per play = x

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = x * 3

Evaluate

Total change = 3x

Hence, the total change is 36 yards

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Answer:

B; 14 cents/1 ounce

Step-by-step explanation:

So you were given the information that there is 140 cents per 10 ounces. Now, we have to get that into a unit rate, which is a number over 1. It would have to be B because the info. was cents/ounces and typically money is over amount.

So you do 140/10

That equals out to 14/1

So it is 14 cents/1 ounce.

Hope this helps!!! :)

Solution to the fraction  (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9) = -38

Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects

To simplify the fraction into a simple form the following steps are followed;

Evaluate (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)

(-7 + 3) x 9 + ⅖ x (-1.1 - 3.9)

Add the numbers

(-4) x 9 + ⅖ x (-1.1 - 3.9)

Evaluate the exponent

(-4) x 9 + ⅖ x (-5)

Multiply the number

-36 + ⅖ x (-5)

-36 -10/5

Subtract the number from each other

-36 -10/5

=-36-2

Answer = -38

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The kilograms of dough that Emmett prepare if he worked for 4 hours is 20 kilograms.

A proportional relationship simply means the relationship that has an equivalent ratio as well as a constant.

In this case, Emmett prepared 10 kilograms of dough after working 2 hours. The kilograms per hour will be:

= 10/2

= 5 kilograms per hour

Therefore, in 4 hours, the kilograms will be:

= Number of hours × 5 kilograms

= 4 × 5

= 20 kilograms

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Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

Answer:

  -8, -5

Step-by-step explanation:

You want the second column of matrix B given matrices A and AB.

Matrix B can be found by left-multiplying AB by A^-1, as shown in the attachment.

The second column of matrix B is ...

  [tex]\left[\begin{array}{c}-8\\-5\end{array}\right][/tex]

The order of the energy levels starting from the highest is:

3. Can hold a maximum of 32 electrons

1. Can hold a maximum of 18 electrons.

2. Can hold a maximum of eight electrons.

4. Can hold a maximum of two electrons.

When a shell gets bigger, it can retain more electrons, and has greater electron energies the further it is from the nucleus.

Two electrons can fit in the first shell, which is closest to the nucleus. Eight electrons can fit in the second shell. 18 electrons can fit in the third shell then 32 electrons can fit inside of the last shell.

The shell that can contain 32 electrons has the highest energy level

Following this relationship, it shows that the arrangement is done using the number of electrons to arrive at 3,  1,  2,and 4

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Answer:

[tex]\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]

Step-by-step explanation:

Two cards are drawn randomly from a well-shuffled deck of cards without replacement. Find the probability of getting both face cards in succession.

In a deck of 52 cards, there are three face cards (J, Q, and K) in each of four suits (clubs, diamonds, hearts, and spades). That means there are 12 face cards in total (J♣, Q♣, K♣, J♦, Q♦, K♦, J♥, Q♥, K♥, J♠, Q♠, K♠).

The probability of drawing a face card the first time, then, is 12 out of 52.

There is now one less face card in the deck, as well as one less card in the deck. Therefore, the probability of drawing a face card a second time is 11 out of 51.

The probability, then, of drawing two face cards in succession is:

[tex]\frac{12}{52}\times{\frac{11}{51}}=\frac{132}{2652}=\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]

The answer to the inequality is  -55 < 49. That is -55 is less than 49.

What is inequality?

This refers to the relationship between two values that are not equal. It can be represented with the following symbols; < less than,> greater than, ≥ greater than or equal to,≤ less than or equal to, and  ≠ not equal to.

The given equation States that;

5(11 − ) < + 49

5*11- < +  49

-55  < +49

Therefore, -55 is less than 49.

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Dilation entails altering a figure's size.

Because the is larger than, Isaiah's assertion is untrue.

Although dilation is not a hard transformation, the angles of the figures it dilates remain unchanged.

The aforementioned claim suggests that,

The dimensions of and should be equal.

However, it is evident that;

are not equivalent.

In reality

greater than

Therefore, Isaiah's assertion is false.

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The inequality will be represented by p ≥ 33 for at least 15 points.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Mark must score at least 11 points to have an average of 10 points per game.

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...

 (8+14+10+20+5++p)/6 ≥ 15

 57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify

 p ≥ 33

Mark must score at least 33 points in the next game to average at least 15 points per game.

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The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.

What is congruent triangles?

When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.

Main Body:

First let us find the co-ordinates of both the triangles.

A= (3,5)

B = (-2, 3)

C= (-4,-1)

A' =(10,-5)

B'= (5, -3)

C' =(3,1)

Distance between two points =  d=√((x₂ – x₁)² + (y₂ – y₁)²).

In ΔABC

Distance of side AB =  √((3 –(-2) )² + (5 –3 )²)

                                 = √5² +2²

                                 = √29

Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)

                                 = √20

Distance of side CA = √((3-(-4) )² + (5-(-1) )²)

                                 = √7² + 6²

                                 = √85

Distance of side A'B' = √((10 -5)² + (-5-(-3))²

                                   = √(5² +2²)

                                   = √29

Distance of side B'C' = √ ((5-3)² + (-3 -1)² )

                                  = √ (2)² +4²

                                  = √20

Distance of side C'A' = √((10-3)² + ( -5-1)²)\

                                   = √(7)² + 6²

                                   = √85

This shows each side of ΔABC is equal to side of ΔA'B'C'.

hence the triangles are congruent.

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Answer:

E and X

Step-by-step explanation:

look for the 6 then behind it

Answer:

X and E

Step-by-step explanation:

"axes" is the plural of axis. The x-axis is the flat line marked with numbers and arrows at the ends. Its labelled x on the right side.

The y-axis is the up-and-down line marked with numbers and arrows at the ends, labelled y at the top.

The origin is where the two axes cross.

Points J, E, X and P are all on the axes. But X and E are 5 units from the origin (where the lines cross) J and P are 9 units from the origin.

2, 6 and 10 were labelled on the axes, but each tick mark is an evenly spaced amount. So the 5 was unlabelled, but it is understood to be 5. See image.