Wesley makes spherical fish tanks with a diameter of 30. A customer requests a smaller tank with half the volume of the tank that Wesley usually makes.
What is the approximate diameter of the smaller tank?
Round to the nearest tenth.

Step-by-step explanation:

since PQRT is a rhombus,

URQ=TPU

y=180-90-24=66

x=180-32-90-24=34

Answer:

1/6

Step-by-step explanation:

Each roll is independent.  So the probability of rolling a six is 1/6, regardless of the previous rolls.

Answer:

Probability of (one club and one heart) = 0.1275 (Approx)

Step-by-step explanation:

Given:

Total number of cards = 52

Each suits = 13

FInd:

Probability of (one club and one heart)

Computation:

Probability of one club = 13 / 52

Probability of one heart = 13 / 51

Probability of (one club and one heart) = 2 [(13/52)(13/51)]

Probability of (one club and one heart) = 0.1275 (Approx)

Answer:

D. 0.1275

Step-by-step explanation:

Justo took the Pre-Test on Edg (2020-2021)!!

Answer:

[tex] \mathsf{ {5x}^{2} + 28x + 21}[/tex]

Option A is the right option.

Step-by-step explanation:

Let's find the area of large rectangle:

[tex] \mathsf{(3x + 6)(2x + 4)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses

[tex] \mathsf{ = 3x(2x + 4) + 6(2x + 4)}[/tex]

Calculate the product

[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}[/tex]

Multiply the numbers

[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 24}[/tex]

Collect like terms

[tex] \mathsf{ = {6x}^{2} + 24x + 24}[/tex]

Let's find the area of small rectangle

[tex] \mathsf{(x - 3)(x - 1)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses

[tex] \mathsf{ = x( x - 1) - 3(x - 1)}[/tex]

Calculate the product

[tex] \mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}[/tex]

Multiply the numbers

[tex] \mathsf{ = {x}^{2} - x - 3x + 3}[/tex]

Collect like terms

[tex] \mathsf{ = {x}^{2} - 4x + 3}[/tex]

Now, let's find the area of shaded region:

Area of large rectangle - Area of smaller rectangle

[tex] \mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}[/tex]

Collect like terms

[tex] \mathsf{ = {5x}^{2} + 28x + 21}[/tex]

Hope I helped!

Best regards!

Answer:

Step-by-step explanation:

Hello,

For any function f which has an inverse function we can write

[tex]x=(f^{-1}of)(x)=(fof^{-1})(x)=f(f^{-1}(x))[/tex]

This is why, in practice, to find the inverse of f we will consider f(x) = y and we will look for x as a function of y, so we switch x and y and solve for y. Let's do it.

Step 1 - The function f(x) can be written as a variable.  [tex]\boxed{y}=f(x)[/tex]

f(x) = y = 5x + 2

Step 2 - switch the variables x <-> y

x = 5y + 2

subtract 2 to both parts of the equation

<=> x - 2 =  5y + 2 - 2 = 5y

divide by 5 both parts of the equation

[tex]<=> y=\dfrac{x-2}{5}[/tex]

It means that the inverse of f is as below.

[tex]\boxed{ \ f^{-1}(x)=\dfrac{x-2}{5}\ }[/tex]

Step 3 - Find the inverse of g(x)

We already found that the inverse of f is g, so the inverse of g is f.

Let's do it again.

[tex]g(x)=y=\dfrac{x-2}{5} \ \ \text{ switch x and y } \\ \\ x= \dfrac{y-2}{5} \ \ \text{ solve for y }\\ \\ y-2=5x \ \ \text{ mulitply by 5 both parts of the equation } \\ \\ y = 5x+2 \ \ \text{ add 2 to both parts of the equation }[/tex]

And we found what we already known, meaning f is the inverse of g.

[tex](gof)(x)=(fog)(x)=x[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answers and Step-by-step explanation:

Step 1:

We want to find the variable that ff(x) represents. Well, we know it can't be x because we already have x on the other side of the equation: ff(x) = 5x + 2.

So, ff(x) must equal y.

Since ff(x) = y, we know then that ff(x) = y = 5x + 2. And our equation is:

y = 5x + 2

Step 2:

Let's switch the variables now. This means that what used to be y will be x and what used to be x will be y:

y = 5x + 2  ⇒  x = 5y + 2

Subtract 2 from both sides:

5y = x - 2

Divide by 5 from both sides:

y = (x - 2)/5

Step 3:

Let's find the inverse of g(x) by doing the exact same thing as we did with ff(x):

g(x) = y = (x - 2)/5

Switch the variables:

y = (x - 2)/5  ⇒      x = (y - 2)/5

Multiply by 5 on both sides:

5x = y - 2

Add 2 to both sides:

y = 5x + 2

Notice that this is the exact same as ff(x)! This means that ff(x) and g(x) are inverses.

Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

There are 15 points on a circle.

We need three points to form a triangle

Therefore the number of triangles = 15 choose 3 ​= 15!/(3!x12!)​ = (15x14x13)/(3x2x1) = 5x7x13 = 455

Hence the number of triangles formed is 455

Answer:

C. rotation, then translation

Step-by-step explanation:

edge 2021

I think it's C "rotation, then translation"

not 100% sure so check other answers too

Answer:

(B), in which the first two values are 2 and 10.

Step-by-step explanation:

We can tell that this is a proportional relationship because we can examine the numbers in there.

(2,10)

(4,20)

and (6,30).

If you notice, the x value times 5 gets us the y value for every single point there.

Therefore, B is proportional and it's equation is y = 5x.

Hope this helped!

Answer:

B.

Step-by-step explanation:

B. Is the only one that proportional because,

(2,10)

(4,20)

(6,30)

All these x values multiply by 5 to get the y value.

So the equation is y = 5x meaning it is linear and it goes through the origin which makes it proportional.

Thus,

answer choice B is correct.

Hope this helps :)

Answer:

Option (A).

Step-by-step explanation:

[tex]8\frac{4}{5}[/tex] is a mixed fraction and can be written as,

[tex]8\frac{4}{5}=8+\frac{4}{5}[/tex] [Combination of a whole number and a fraction]

When we multiply this mixed fraction by 7,

[tex]7\times 8\frac{4}{5}=7\times (8+\frac{4}{5})[/tex]

          [tex]=(7\times 8)+(7\times \frac{4}{5})[/tex] [Distributive property → a(b + c) = a×b + a×c]

          [tex]=56+\frac{28}{5}[/tex]

          [tex]=56+5\frac{3}{5}[/tex]

          [tex]=56+5+\frac{3}{5}[/tex]

          [tex]=61+\frac{3}{5}[/tex]

          [tex]=61\frac{3}{5}[/tex]

Therefore, [tex]7\times 8\frac{4}{5}=61\frac{3}{5}[/tex] will be the answer.

Option (A) will be the correct option.

Answer:

Whenever a-5<0 or a<5

Step-by-step explanation:

So if you have an absolute value, that turns into two equations. The one we care about is -(a-5)=5-a. After distributing the negative through the left side of the equation, you'll get that 5-a=5-a, which is an identity. But you can only say that abs(a-5)=5-a when a-5<0. To see a visual representation of this, graph both sides of the equation in desmos.

Answer:

w²-30w+210=0

Step-by-step explanation:

2w + 2l = 60 , w + l = 30, l = 30 - w

wl = 210

w(30-w) -210 = 0

30w - w²-210 = 0

w²-30w+210=0

Answer: C

Step-by-step explanation:

The open dot means its not equal to X and the placement is -14.5

Answer:

56

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{35+20}{20}[/tex] = [tex]\frac{32+?}{32}[/tex] ( cross- multiply )

20(32 + ?) = 1760 ( divide both sides by 20 )

32 + ? = 88 ( subtract 32 from both sides )

? = 56

Answer:

[tex]\boxed{56}[/tex]

Step-by-step explanation:

We can use ratios to solve since the triangles are similar.

[tex]\frac{20}{32} =\frac{35}{x}[/tex]

Cross multiplication.

[tex]20x=35 \times 32[/tex]

Divide both sides by 20.

[tex]\frac{20x}{20} = \frac{35 \times 32}{20}[/tex]

[tex]x=56[/tex]

Step-by-step explanation:

[tex] \sqrt{p} = \sqrt[r]{w - {as}^{2} } [/tex]

Find raise each side of the expression to the power of r

That's

we have

Send w to the left of the equation

Divide both sides by - a

We have

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

3

1/5

3/4

3/4

Step-by-step explanation:

Coefficient is a number that is always written in front of a term.

3xy^3=3

xy/5=1/5

3/4xy=3/4

3/4x^2y=3/4

Hope this helps ;) ❤❤❤

Answer:

Because the triangle is isosceles, the base angles are congruent, meaning that the angles that are not right angles are x and x. Since the sum of angles in a triangle is 180°, we can write:

90 + x + x = 180

x + x = 90

2x = 90

x = 45°

Answer:

45 degrees

Step-by-step explanation:

This triangle is "isosceles..." two legs are equal.  Thus, the triangle has two 45 degree angles.  The indicated angle is 45 degreees.

Answer: C) Plane: 235 km/h, Wind: 24 km/h

Step-by-step explanation:

Given that :

Average Speed while flying with a tailwind = 259km/hr

Return trip = 211km/hr

Let the speed of airplane = a, and wind speed = w

Therefore ;

Average Speed while flying with a tailwind = 259km/hr

a + w = 259 - - - (1)

Return trip = 211km/hr

a - w = 211 - - - (2)

From (2)

a = 211 + w

Substitute the value of a into (1)

a + w = 259

211 + w + w = 259

211 + 2w = 259

2w = 259 - 211

2w = 48

w = 48/2

w = 24km = windspeed

Substituting w = 24 into (2)

a - 24 = 211

a = 211 + 24

a = 235km = speed of airplane

Answer:

$4

Step-by-step explanation:

2 Bracelets + 3 rings = $26

2 rings = $12

3 rings = x

To get the cost of 1 ring you divide 12 by 2 and the answer you get is 6.

The total cost of the 3 rings is $18( $6*3)

Then you subtract the cost of both 2 bracelets and 3 rings($26) from the cost of 3 rings($18). The answer is $8. ( THIS IS THE COST OF 2 BRACELETS)

1 BRACELET= $4( $8/2)

Answer:

130

Step-by-step explanation:

just did test on plato/edmentum..it was correct

84 (the answer above) is incorrect

Answer:

Hi sorry for late respond but the answer in 130!!

Step-by-step explanation:

Answer:

432 aquariums

Step-by-step explanation:

To determine the number of aquariums the factory made, find the volume of 1 aquarium, then divide the total volume of water required.

Solution:

Volume of triangular prism aquarium = triangular base area × length of triangular prism

Volume = ½*b*h*l

Where,

b = 8 ft

h = 4 ft

l = 3 ft

Volume = ½*8*4*3 = 4*4*3

Volume = 48 ft³

Number of aquarium made = Volume of water required ÷ volume of 1 aquarium

= 20,736 ÷ 48 = 432 aquariums

Answer:

1.76m/s ; 1.76m/s ; 1.74m/s, 0.86m/s

Step-by-step explanation:

Given the following :

Distance jogged in first direction (A to B) = 300m

Time taken = 2 minutes 50s = (2*60) + 50 = 120 + 50 = 170s

Distance jogged in opposite direction (B to C) = 100m

Time taken = 1minute = 60s

Recall:

Speed = distance / time

Therefore Average speed from A to B

Average speed = 300m/ 170s = 1.764 = 1.76m/s

Average Velocity = Displacement / time

Displacement = 300m ; time = 170s

= 300m / 170s = 1.76m/s

Average speed (A to C)

Therefore, average speed = total distance / total time taken

Total distance = (300 + 100)m = 400m

Total time taken = (170 + 60)s = 230s

Average speed = 400m / 230s

= 1.739m/s = 1.74m/s

Average velocity:

Displacement = distance between initials position and final position.

Initial distance covered = 300m. Then 100m was jogged in the opposite direction.

Distance between starting and ending positions, becomes : (300 - 100)m = 200m

200 / 230 = 0.87m/s

Answer:

[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

[tex]a^2-5ab+3ab-15b^2[/tex]

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]

which is the final factorization.

Answer:

[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]

=================================================

Explanation:

For choice C, the x values are out of order, so it might be tricky at first. I recommend sorting the x values from smallest to largest to get -2, -1, 0, 1, 2. Do the same for the y values as well. Make sure the correct y values stay with their x value pairs. You should get the list of y values to be 4, 2, 1, 1/2, 1/4

Check out the attached image below for the sorted table I'm referring to

We can see the list of y values is going down as x increases. This is a good sign we have decay. Further proof is that we multiply each term by 1/2 to get the next one

4 times 1/2 = 2

2 times 1/2 = 1

1 times 1/2 = 1/2

1/2 times 1/2 = 1/4

and so on. Effectively we can say the decay rate is 50%

Answer: 22

Step-by-step explanation:

She sold two tubs of Oatmeal Raisins and it's 6 dollars a tub so we can do 6*2 or 6+6 (doesn't matter). We get $12. Then, she also sells 2 tubs of Peanut Butter, and since it's $5 a tub, then we do 5*2 or 5+5 to get 10. We add 12 and 10 (12+10) and get 22.

I'm not sure if this is right because you added $22, $24, $20, and $11 and I'm not sure what the purposes of those are.

Answer:

b. Contains four right angles.

Step-by-step explanation:

A parallelogram has two pairs of opposite sides that are both congruent and parallel, as does a rectangle.

A parallelogram usually does NOT have four right angles, but a rectangle does. b Contains four right angles is the difference between a parallelogram and a rectangle.

The diagonals of a parallelogram bisect each other, and so do the rectangle's diagonals.

The opposite angles of parallelograms are congruent, and all four angles of a rectangle are congruent, so this is a similar aspect of both a parallelogram and a rectangle.

Hope this helps!

Answer:

divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125

Answer:

Length = 8x - 3.2

Step-by-step explanation:

Perimeter = 4(Length)   [Since it's a square so all the sides are equal]

Given that Perimeter = 32x - 12.8

32x - 12.8 = 4(Length)

Dividing both sides by 4

=> Length = [tex]\frac{4(8x-3.2)}{4}[/tex]

=> Length = 8x - 3.2

Now, Three equivalent expressions to find the perimeter

=> Perimeter = 32x - 12.8

=> Perimeter = 4(8x - 3.2)   [Perimeter = 4 (Length)]

=> Perimeter = 2(16x - 6.4)

Answer:

[tex]\boxed{8x-3.2}[/tex]

Step-by-step explanation:

The perimeter is 32x - 12.8 of a square.

Use formula for perimeter of a square.

[tex]P=4a[/tex]

[tex]P=perimeter\\a=side \: length[/tex]

[tex]32x - 12.8=4a[/tex]

Solve for side length.

[tex]\frac{32x - 12.8}{4} =a[/tex]

[tex]8x-3.2=a[/tex]

Three equivalent expressions for perimeter:

32x - 12.8

⇒ 8(4x - 1.6)

⇒ 4(8x - 3.2)

⇒ 2(16x - 6.4)

Answer:

The explicit formula for the sequence is

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

Hope this helps you

Answer:

[tex]\huge\boxed{a_n=-6n+44}[/tex]

Step-by-step explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

[tex]a_n=a_1+(n-1)(d)[/tex]

Substitute:

[tex]a_1=38;\ d=-6[/tex]

[tex]a_n=38+(n-1)(-6)[/tex]         use the distributive property

[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]

Answer:

927.0 cm²

Step-by-step explanation:

Step 1: find Z

m < Z = 180 - (28 + 118) (sum of ∆)

= 180 - 146

Z = 34°

Step 2: Find side XY using the law of sines

[tex] \frac{XY}{sin(34)} = \frac{42}{sin(28)} [/tex]

Cross multiply

[tex] XY*sin(28) = 42*sin(34) [/tex]

[tex]XY*0.469 = 42*0.559[/tex]

Divide both sides by 0.469

[tex]\frac{XY*0.469}{0.469} = \frac{42*0.559}{0.469}[/tex]

[tex]XY = 50.06[/tex]

XY ≈ 50 cm

Step 3: find the area.

Area of ∆ = ½*XY*YZ*sin(Y)

XY ≈ 50 cm

= ½*50*42*sin(118)

= 25*42*0.8829

Area = 927.045

Area ≈ 927.0 cm² (nearest tenth)

Answer:

34 adults and 11 children

Step-by-step explanation:

15 times 11 is 165dollars for kids

25 times 34 adults equals 850 dollars

add it and its 1015

Answer:

34 and 11

Step-by-step explanation: