Which type(s) of symmetry does the following object have?
Select all that apply.
diagonal line of symmetry
no symmetry
vertical line of symmetry
horizontal line of symmetry
rotational symmetry

The rate at which the amount of water in the tank is changing is -3 gallons per minute. The negative sign indicates that the water level is decreasing.

In the given scenario, the tank initially contains 13 gallons of water and after three minutes, it contains 4 gallons of water. To determine the rate at which the amount of water is changing, we calculate the difference in the water level and divide it by the time elapsed.
The change in water level is 4 gallons (final amount) - 13 gallons (initial amount) = -9 gallons. The negative sign indicates that the water level is decreasing.
The time elapsed is 3 minutes.
To find the rate of change, we divide the change in water level (-9 gallons) by the time elapsed (3 minutes):
Rate of change = -9 gallons / 3 minutes = -3 gallons per minute.
Therefore, the rate at which the amount of water in the tank is changing is -3 gallons per minute. The negative sign signifies a decrease in the water level.

Learn more about rate here
https://brainly.com/question/30907190



#SPJ11

Answer:

4.25

Step-by-step explanation:

Take your cost and divide it by the number of tickets.

55.25/13 = 4.25

21.25/5 = 4.25

No matter which pair you use, the answer is 4.25

Answer:

3a-2a+7-4

a+3

Step-by-step explanation:

like and unlike terms arranging

and add and subtraction

The vertices of the ellipse are (-4,2) and (4,2), since these points lie on the major axis of the ellipse which is horizontal.

Two of the focuses given in the issue, (−4,2) and (4,2), are both situated on a similar even line. This implies that the significant hub of the oval should be level. Two different focuses given in the issue, (2,2) and (- 9,2), are likewise situated on this level line. Thusly, the focal point of the oval is the midpoint between the focuses (- 4,2) and (4,2), which is (0,2).

The other two focuses given in the issue, (−5,5) and (−5,−1), are situated on an upward line that goes through the focal point of the oval. This implies that the minor pivot of the oval should be vertical.

The vertices of the oval are the places where the significant hub meets the circle. Since the significant hub goes through the focuses (−4,2) and (4,2), the vertices of the oval are (- 4,2) and (4,2).

In this way, the vertices of the oval are (- 4,2) and (4,2).

To learn more about vertices of ellipse, refer:

https://brainly.com/question/9525569

#SPJ4

Answer:

Step-by-step explanation:

One antifreeze solution is 26% alcohol and another is 11% alcohol how much of each mixture should be added to make 24 l of a solution that is 21% alcohol?

Let us represent

First solution =>x

Second solution => y

System of equations

x + y = 24.....Equation 1

x = 24 - y

26% × x + 11% × y = 21% × 24

= 0.26x + 0.11y = 5.04... Equation 2

The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

Learn more about Abelian groups

brainly.com/question/33613547

#SPJ11

The required expression for part A ⇒ 2x(3x-8)

The required expression for part B ⇒2x(3x-8)

Part A:

The area of the rectangular space is given by the expression 6x²-16x, which is equal to the length times the width. We are given that the width of the rectangular space is 2x.

Therefore, we can write:

length x width = area

length x (2x) = 6x²-16x

length = (6x²-16x) / (2x)

Simplify the expression for length by factoring out 2x from the numerator:

length = 2x(3x-8)

So the expression for the length of the rectangular space is 2x(3x-8).

Part B:

To prove that our expression for the length is correct, we can multiply it by the width and show that we get the original expression for the area:

length x width = 2x(3x-8) x (2x)

                        = 4x²(3x-8)

                        = 12x³ - 32x²

Now we can compare this result with the original expression for the area, which is 6x²-16x.

We can simplify the original expression by factoring out 2x:

6x²-16x = 2x(3x-8)

We can see that the expression we obtained by multiplying the length and the width is equivalent to the original expression for the area, so our expression for the length is correct.

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

Answer:

The answer is 4914

Step-by-step explanation:

Answer:4914

Step-by-step explanation:

Answer:

$0.25

Step-by-step explanation:

Let's represent the comics by assigning it the letter C.

20C = $5.00

C = $5.00/20

= $0.25

We can confirm this by using the example where he uses 30 comics.

30C = $7.50

C = $7.50/30

= $0.25.

Therefore each comic costs $0.25

Answer:

SSS

Step-by-step explanation:

Since all three sides of the triangle are congruent, we don't need to prove anything else, so we would use SSS (Side-Side-Side)

There is a 0.0876 percent probability that six or more pages will include mistakes. There is a 1.64 x 10⁻⁶ chance that more than 10 pages may include mistakes.

Information about possibility of occurrence is provided by probability. For instance, weather patterns are used by meteorologists to predict the possibility of rain. In order to understand the relationship between exposures and the risk of health outcomes, epidemiology uses probability theory.

a) Chance that six or more pages may have mistakes:

To get this probability, we can utilise the binomial probability formula:

P(X>=6) = 1-P(X<6)

where X is the number of pages with errors.

P(X<6) = P(X=0)+P(X=1)+P(X=2) +P(X=3)+P(X=4)+P(X=5)

For each term, using the binomial probability formula, we obtain:

P(X < 6) = 0.9124

Therefore, P(X >= 6) = 1 - P(X < 6) = 1 - 0.9124 = 0.0876

Hence, there is a 0.0876 percent chance that six or more pages will include errors.

b) Chance that there are errors on more than 10 pages:

Using the same method, we can discover:

P(X > 10) = P(X = 11) + P(X = 12) + ... + P(X = 200)

To find the likelihood, we can use a calculator or software because performing the math by hand can be very time-consuming. Using a calculator for the binomial distribution, we obtain:

P(X > 10) = 1.64 x 10⁻⁶ (rounded to 3 decimal places)

Hence, there is a roughly 10% chance that there will be errors on more than 10 pages. 1.64 x 10⁻⁶.

c) Probability that none of the pages contain errors:

P(X = 0) can be calculated using the binomial probability formula:

P(X = 0) = (200 choose 0) * (0.009)⁰ * (1 - 0.009)²⁰⁰

= 0.8196

As a result, 0.8196 percent of the pages are likely to be error-free.

d) Probability that fewer than five pages contain errors:

P(X<5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

Again, using the binomial probability formula for each term, we get:

P(X < 5) = 0.8151

Hence, the likelihood that fewer than five pages are mistake-free is 0.8151.

To know more about probability visit:-

https://brainly.com/question/30034780

#SPJ1

To find the slant height of a cone, given the lateral area and the radius, we can use the formula:

Lateral Area = πrℓ

where "r" is the radius and "ℓ" is the slant height.

In this case, the given lateral area is 1753 square centimeters, and the radius is 31 cm.

1753 = π * 31 * ℓ

To find the slant height, we can rearrange the formula:

ℓ = 1753 / (π * 31)

Using the value of π as approximately 3.14159, we can now calculate the slant height:

ℓ ≈ 1753 / (3.14159 * 31)

ℓ ≈ 17.85

Therefore, the slant height of the cone, to the nearest tenth, is approximately 17.9 centimeters.

Learn more about approximately here:

https://brainly.com/question/31695967

#SPJ11

Answer:

x = 16

Step-by-step explanation:

Probabilities are used to determine how likely it is for an event to happen.

(1) A roll of two dice

Let the dice be A and B. The sample space of each is:

\(A = \{1,2,3,4,5,6\}\\B = \{1,2,3,4,5,6\}\)

To get the sample space (S) of the sum of the dice, we simply add up the individual element of both dice. So, we have:

\(S = \{(1+1),(1+2),(1+3),(1+4),(1+5),(1+6),.............,(6+1),(6+2),(6+3),(6+4),(6+5),(6+6)\}\)

This gives

\(S = \{2,3,4,5,6,7,.............,7,8,9,10,11,12\}\)

The complete sample space is:

\(S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12\}\)

\(n(S) = 36\) --- the total outcomes

The probability of rolling a sum of 7 is:

\(P(7) = \frac{n(7)}{n(S)}\)

Where

\(n(7) = 6\) ---- number of 7's in the sample space

So, we have:

\(P(7) = \frac 6{36}\)

\(P(7) = 0.167\)

The probability of rolling a sum of 7 is 0.167

(2) Restaurant

We have:

\(Soup = \{A,B,C,D\}\)

\(Salads = \{1,2,3\}\)

To get the sample space (S), we simply pick the individual elements of the above data. So, we have:

\(S = \{A1, A2, A3,B1, B2, B3,C1, C2, C3,D1, D2, D3\}\)

(3) Disjoint events

Events are said to be disjointed if they cannot happen at the same time. 3 examples are:

(4) Bob and Sarah

Let

\(A \to\) Bob gets to work on time

\(B \to\) Sarah gets to work on time

\(P(A) = 80\% \\ P(B) = 90\%\\P(A\ n\ B) = 72\%\)

The probability that Bob OR Sarah is late for work is represented as:

\(P(A'\ or\ B')\)

This is calculated using:

\(P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')\)

Where:

\(P(A') = 1 - P(A) = 1 - 80\% = 20\%\)

\(P(B') = 1 -P(B) = 1 - 90\% =10\%\)

\(P(A\ n\ B') = P(A) \times P(B') = 20\% \times 10\% = 2\%\)

So, we have:

\(P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')\)

\(P(A'\ or\ B') = 20\% + 10\% - 2\%\)

\(P(A'\ or\ B') = 28\%\)

\(P(A'\ or\ B') = 0.28\)

The probability that Bob OR Sarah is late for work is 0.28

(5) Jake's Pizza

Let

\(A \to\) The proportion of time they deliver on time

\(B \to\) You get your pizza for free

So:

\(P(A) = 92\%\)

You get your pizza for free if they didn't deliver within 30 minutes.

This means that:

\(P(B) = 1 - P(A)\) --- Complement rule

So, we have:

\(P(B) = 1 - 92\%\)

\(P(B) = 0.08\)

The probability that you get your pizza for free is 0.08.

(6) Students and Soccer

Let:

\(A \to\) Probability that a student likes soccer

So:

\(P(A) = 54\%\)

If all 3 selected students like soccer, the probability is calculated as:

\(Pr = P(A) \times P(A) \times P(A)\)

\(Pr = P(A)^3\)

\(Pr = 54\%^3\)

\(Pr = 0.157\)

The probability that all 3 selected students like soccer is 0.157

(7) Students and Soccer

Let:

\(A \to\) Probability that a student likes soccer

\(B \to\) Probability that a student does not like soccer

So:

\(P(A) = 54\%\)

\(P(B)= 1 - P(A)= 1 - 54\% = 46\%\) ---- Complement rule

If all 4 selected students do not like soccer, the probability is calculated as:

\(Pr = P(B) \times P(B) \times P(B) \times P(B)\)

\(Pr = P(B)^4\)

\(Pr = 46\%^4\)

\(Pr = 0.045\)

The probability that all 4 selected students do not like soccer is 0.045

(8) Marbles

\(Blue = 6 \\ Green = 4 \\ Red = 5\)

When the green marble is selected, we are left with

\(Blue = 6 \\ Green = 3 \\ Red = 5\)

The probability of selecting a red marble at this point is:

\(P(Red) = \frac{Red}{Blue + Green + Red}\)

\(P(Red) = \frac{5}{6+3+5}\)

\(P(Red) = \frac{5}{14}\)

\(P(Red) = 0.357\)

The probability that the next marble you draw is red is 0.357

(9) Studying for test

Let

\(A \to\) Students got an A

\(B \to\) Students studied for test

So:

\(P(A\ n\ B) = 60\% \\ P(B) = 75\%\)

The probability that a student got an A given that they studied for the test is  represented as:

\(P(A | B)\)

So, we have:

\(P(A | B) = \frac{P(A\ n\ B)}{P(B)}\)

\(P(A | B) = \frac{60\%}{75\%}\)

\(P(A | B) = 0.80\)

The probability that a student got an A given that they studied for the test is  0.80

Read more about probabilities at:

https://brainly.com/question/16693319

Q9.1: To justify the proposal, we need to compare the benefits of the road expansion (in terms of reduced travel time) with its costs. The value of time represents the monetary value individuals place on their time spent traveling. In this case, the value of time is $1.5 per minute.

First, let's calculate the reduction in travel time resulting from the road expansion. We compare the two road performance functions: t1​ = 30 + 6×10−6q and t2​ = 20 + 3×10−6q. By subtracting t2​ from t1​, we can determine the time savings: Δt = t1​ - t2​ = (30 + 6×10−6q) - (20 + 3×10−6q)    = 10 + 3×10−6q Next, we multiply the time savings by the number of trips (q) to obtain the total time savings: Total Time Savings = Δt × q = (10 + 3×10−6q) × q Now, we can determine the monetary value of the time savings by multiplying the total time savings by the value of time ($1.5 per minute): Monetary Value of Time Savings = Total Time Savings × Value of Time                             

= (10 + 3×10−6q) × q × $1.5  If the monetary value of the time savings exceeds the construction cost of $9.6×107, then the proposal is justified. Q9.2: To determine the construction cost at which the proposal becomes justified, we set the monetary value of the time savings equal to the construction cost and solve for q: (10 + 3×10−6q) × q × $1.5 = $9.6×107 By solving this equation for q, we can find the corresponding construction cost at which the proposal becomes justified.

Learn more about total time savings here: brainly.com/question/33195786

#SPJ11

The range of the function is

\(y \leqslant 1\)

Answer:

Graph B

Step-by-step explanation:

The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.

Answer: \(z = \frac{4.7}{6.5}\)

Step-by-step explanation:

original equation: 3.1 + 6.8z - 2.4 = 0.3z - 4

Start by adding simplifying like terms on each side (terms with no variables, and the terms with variables, in this case: z)

3.1 - 2.4 = 0.7

0.7 + 6.8z = 0.3z - 4

Then begin to transfer segments from one side to the other so you can isolate the terms with no variables and variables. To move them to the other side, you will need to use the opposite value (positive/negative) of what they are right now.

0.7 + 6.8z = 0.3z - 4

-0.7              -0.7

6.8z = 0.3z - 4.7

-0.3z    -0.3z

6.5z = 4.7

When you are this far into the equation, you will want to divide both sides by whatever your variable (z) is being multiplied by (6.5)

\(z = \frac{4.7}{6.5}\)

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

To know more about depreciation, refer here:

https://brainly.com/question/30531944

#SPJ11

The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

learn more about gain here:

https://brainly.com/question/31218742

#SPJ11

Answer:

:)

Step-by-step explanation:

its either A or D hope it helps

Answer:

The answer is C)Spelling Scores vs. Hours Spent Studying

Step-by-step explanation:

This is the answer because if you look at all of the other options, then you will see that they have a steeper slope, you could also calculate and find for slope if u are still unsure :) hope this helps

The graph that has a trend line with the least slope is the History Scores vs. Hours Spent Studying graph

The slope of a line is the quotient of the change in the vertical values to the corresponding horizontal values

Check below on how the trend line with the least slope can be determined

From the question, we have:

The slope (m) is calculated using:

m = (y₂ - y₁)/(x₂ - x₁)

So, we have:

The line 3 has the least slope

i.e. m₃ = 2.5

Hence, the graph that has a trend line with the least slope is the History Scores vs. Hours Spent Studying graph

Read more about slope at:

https://brainly.com/question/1884491

9514 1404 393

Answer:

  one solution (11, 4)

Step-by-step explanation:

Both equations describe curves with positive slope. The y-intercept of the line (-7) is less than that of the root function (-2), so the line must intersect the root function in exactly one place. There is one solution.

__

Solved in the conventional way, the equation would become a quadratic, with two solutions. One of them is extraneous. (That is why I prefer a graphical solution.)

Given ...

  x -y = 7

  y = √(3x +3) -2

We can substitute for y to get ...

  x -7 = √(3x +3) -2

  x -5 = √(3x +3)

  x^2 -10x +25 = 3x +3 . . . . . . square both sides

  x^2 -13x +22 = 0 = (x -11)(x -2) . . . . . gives solutions x=11, x=2

The value x=2 does not satisfy the equation ...

  x -7 = √(3x +3) -2   ⇒   2 -7 = √(3·2 +3) -2   ⇒   -5 = 1 (false)

Answer:

Step-by-step explanation:

Option A: ∠ BDC ≅ ∠ADB is the missing statement in the proof.

This statement is needed to complete the proof by showing that triangles ∆ABC and ∆ADB are similar by the AA criterion.

Answer:

1.00

Step-by-step explanation:

The exponential function that goes through points (0,12) and (2,300) is \(y = 12(5)^x\).

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The coordinate points are (0,12) and (2,300).

The exponential function has form \(y=ab^x\).

So, the x values are 0,2 and y values are 12,300.

Substitute the first x and y values in the equation -

\(12=ab^0\)

a = 12 ...... equation (1)

Substitute the second x and y values in the equation -

300 = ab² ...... equation (2)

Substitute the value of equation (1) in equation (2) -

300 = (12)b²

b² = 300 / 12

b² = 25

b = √25

b = 5

Substitute the values of a and b in exponential function -

\(y = 12(5)^x\)

Therefore, the exponential function is \(y = 12(5)^x\).

To learn more about exponential function from the given link

brainly.com/question/12626186

#SPJ1

This equation holds true, which confirms that AB is indeed the hypotenuse of the right triangle.

If the Pythagorean equation holds for all right triangles and ∠C is a right angle, then we can use the Pythagorean theorem to show that side AB is indeed the hypotenuse of the triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So in this case, we have side AB as the hypotenuse, and sides AC and BC as the other two sides.

According to the Pythagorean theorem, we have:
AB^2 = AC^2 + BC^2

Since ∠C is a right angle, AC and BC are the legs of the triangle. By substituting these values into the equation, we get:
AB^2 = AC^2 + BC^2
AB^2 = AB^2

This equation holds true, which confirms that AB is indeed the hypotenuse of the right triangle.

Know more about hypotenuse here:

https://brainly.com/question/2217700

#SPJ11