Volume with fractions

What is the volume of this rectangular prism? 1/2cm 1/2cm 3cm

Answer:

32,  2√7

Explanation:

given: \(\sf \bold x^2+6x+2=0\)

using quadratic formula:   \(\boxed{\boxed{\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a}}}\)

solve using the equation:

given a > β

solve:

and

The percentage of Chihuahuas that weigh more than 5 pounds is approximately 2.28%.

We have,

We need to find the area under the normal distribution curve to the right of the value x = 5.

We can use the standard normal distribution with a mean of 0 and a standard deviation of 1 by converting the original problem to a standard normal distribution.

z = (x - μ) / σ

where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.

In this case,

x = 5, μ = 4, and σ = 0.5.

z = (5 - 4) / 0.5 = 2

We can use a standard normal distribution table or calculator to find that the area to the right of z = 2 is approximately 0.0228.

Therefore,

The percentage of Chihuahuas that weigh more than 5 pounds is approximately 2.28%.

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Given:

Find-:

The proportion and value of x

Explanation-:

The proportion is:

Because of side ratio is:

So, the value of x is:

The value of "x" is 12.

Answer:

x = 12 units.

Step-by-step explanation:

In similar polygons, corresponding sides are in same ratio.

Let the unknown side be 'x.

  \(\sf \dfrac{x}{15}=\dfrac{32}{40}\\\\\\\)

    \(\sf x = \dfrac{32}{40}*15\\\\ x = \dfrac{4}{5}*15\\\\ x = 4*3\\\\x = 12\)

Brett and his family need to start hiking no later than 4:20 PM to reach their camping spot and set up camp before it gets dark.

To calculate the latest time Brett and his family can start hiking, we need to subtract the total time required for hiking and setting up the camp from the sunset time.

Total time required:

Hiking time: 2 hours 55 minutes = 2.92 hours

Setting up camp time: 1 hour 10 minutes = 1.17 hours

Total time required = Hiking time + Setting up camp time = 2.92 hours + 1.17 hours = 4.09 hours

Now, subtract the total time required from the sunset time:

Sunset time: 8:25 PM

Latest start time = Sunset time - Total time required

Latest start time = 8:25 PM - 4.09 hours

To subtract the hours and minutes, we need to convert 4.09 hours into minutes:

0.09 hours * 60 minutes/hour = 5.4 minutes

So, the latest start time is 8:25 PM - 4 hours 5.4 minutes:

Latest start time = 8:25 PM - 4 hours 5.4 minutes = 4:20 PM

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Answer:

∠DEC = 83º

Step-by-step explanation:

∠BAC and ∠ABC combine is 105º.

∠ACB is 75º.

∠ECD is 75º.

180º-75º-22º=83º

Step-by-step explanation:

3.

the left cup is the summary of 2 cylinders.

the right cup is just a cone.

the volume of a cone is

pi×r²×h/3 = pi×3.5²×6/3 = pi×12.25×2 = pi×24.5 =

= 76.93 in³

the volume of a cylinder is

pi×r²×h

the first cylinder is

pi×3²×1.5 = pi×9×1.5 = pi×13.5 = 3.14×13.5 = 42.39 in³

the second cylinder is

pi×2²×2.25 = pi×4×2.25 = pi×9 = 28.26 in³

in total the cup has

42.39 + 28.26 = 70.65 in³

so, the cone has the larger volume by 6.28 in³ ≈ 6 in³.

that would be 3.479827 fl.oz. ≈ 3 fl.oz. of water.

I have no idea on what scale you need to quantify the amount of water. I just guessed.

2.

here we need the surface area.

the object consists of a large prism (or block) and a cylinder.

we don't need the bottom area for neither, as the cylinder is simply on top of the prism, and its bottom is not going to be painted either.

we need 5 sides of the prism :

front and back

left and right

top (and we need the full top, because the area the cylinder is covering up is the same area for the top of the cylinder).

and the we need to add only the side wall of the cylinder the "mantle".

so,

front and back rectangles are 10×3 × 2 = 60 in²

left and right rectangles are 10×3 × 2 = 60 in²

the top rectangle (square) is 10×10 = 100 in²

the cylinder mantle is

circumference of the circle × height

2×pi×r×h = 2×pi×4×6 = 3.14×48 = 150.72 in²

so, in total we have

60 + 60 + 100 + 150.72 = 370.72 in² ≈ 371 in²

Answer:

Question 2: 320.48 in^2

Question 3: 6.28 in^3

Step-by-step explanation:

Question 2)

The question tells us that the shape will be covered in paint. This means that we need to find the surface area instead of volume. In the question, I’ll find the surface area of the two individual shapes (The cylinder and the rectangular prism) and take away parts that will not be covered in paint.

Rectangular Prism

1. ((10x10)+(10x3)+(10x3))x2 — All rectangular prisms have 2 sides with the same area. Since there are 6 sides total, all we need to do is find 3 sides of different sizes and multiply them by 2. The number we get is 320 in^2.

2. We will not be painting the bottom, so we can take the area of the bottom away. The area of the bottom is 10x10, which is 100. 320 - 100 is 220 in^2.

3. We are also not painting the area where the cylinder is touching the top (The circle-shaped area). The formula of finding the area of a circle is radius x radius x pi. Since the radius is 4 and pi can be rounded to 3.14, the area of the circle will be 4x4x3.14, which is 50.24 in^2. We can take that away from 220, so 220 - 20.24 is 169.76 in^2.

Cylinder

1. 4x4x3.14 — We know that one side of the cylinder (The base) will not be painted, so all we need to do is find the area of one of the bases. Radius x Radius x pi, in this case, is 50.24 in^2.

2. (((4+4)x3.14)x6) — Now we need to find the area of the side of the cylinder. The area of the side is base x height. The base length is the perimeter of the circle. The equation of the circle perimeter is (radius + radius) x pi. In numbers, it will be 8x3.14 which is 25.12. The height of the side is 6, so the equation will be 25.12 x 6, which is 150.72.

3. The surface area of the cylinder (excluding the base at the bottom) is 150.72 in^2.

Since the rectangular prism and the cylinder is stuck together and is considered as a whole, we add the two numbers together. 169.76 + 150.72 = 320.48 in^2!

Question 3)

The amount of water the cups can hold is the same size as the volume of individual cups. In order to find out the amount of water each cup can hold, we need to find the volume first.

Cup #1

1. (2x2x3.14)(2.25) — This is the base times the height of the bottom cylinder. The formula to find a circle is radius x radius x pi, and the height was 2.25. The volume of this shape will be 28.26 in^3.

2. (3x3x3.14)(1.5) — The area of the bottom is radius x radius x pi, and the height was 1.5 If we multiply all of these numbers together, we get 42.39 in^3.

3. Now that we found the two cylinders of the first cup, we can add them together. 28.26 + 42.39 = 70.65.

4. The area of cup #1 is 70.65 in^3.

Cup #2

1. (3.5 x 3.5 x 3.14)(6)(1/3) — The formula for finding the area of a cone is base x height x 1/3. The area of the base is radius x radius x pi, and the height is 6. Then we multiply by 1/3 (or divide by 3). Then, we get 76.93 in^3.

2. The volume of cup #2 is 76.93 in^3.

The question asks: How much more water will the larger cup hold?

Comparing 70.65 in^3 (First cup) and 76.93 in^3 (Second cup), we know that the second cup is bigger. To find the difference in the amount of water it can hold, we can subtract 70.65 from 76.93. This equals 6.28 in^3.

The final answer for Question 3 will be 6.28 in^3!

The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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To determine the probability of at least 48 meteors per hour appearing during the Geminid meteor shower, we can use statistical calculations based on the average and variance provided.

Additionally, by watching for an additional hour, the probability of at least 48 meteors per hour will rise.

The problem provides the average number of meteors per hour as 50 and the variance as 9 meters squared. The distribution of meteor counts can be assumed to follow a normal distribution due to the Central Limit Theorem.

(a) To find the probability of at least 48 meteors per hour appearing during a 4-hour observation, we can calculate the cumulative probability using the normal distribution. By using the average and variance, we can determine the standard deviation as the square root of the variance, which in this case is 3.

With this information, we can calculate the z-score for 48 meteors using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Once we have the z-score, we can look up the corresponding probability in a standard normal distribution table or use a statistical calculator.

(b) By watching for an additional hour, the probability of at least 48 meteors per hour will rise. This is because the longer the astronomer observes, the more opportunities there are for meteors to appear. The average number of meteors per hour remains the same, but the overall count increases with each additional hour, increasing the chances of observing at least 48 meteors in a given hour.

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Answer: 1249 hrs

Step-by-step explanation:

Sophia walked for 12 km to get to her aunt's house.

She did this at a speed of 5km/h which means that the time taken was:

Time = Distance / Speed

= 12 / 5

= 2.4 hours

2.4 in hours:

= 0.4 * 60 minutes

= 24 minutes

= 2 hours 24 minutes

If she left at 1025, she would arrive at:

= 1025 + 2 hours 24

= 1249 hrs

Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

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Answer:

110 is the answer

hope this helps

have a good day :)

Step-by-step explanation:

Answer: 5

the scale length of 15cm and 3cm is 15/3 = 5

Step-by-step explanation:

\((3 + 7) + 6 = 3 + (7 + 6)\)

Answer:

B. 5x^4 - 28x^2 + 25x - 6

Step-by-step explanation:

the steps r in the pic above

Answer:

2.31

Step-by-step explanation:

1.65 * 1.4 = 2.31

Answer:

X = 4; Y= 2

Step-by-step explanation:

Answer:

Is this a complete question?

Answer:

There are 28 marbles in the box. Some are red (12), others are yellow (6) and others are blue (10).

If in this box there 28 marbles and 6 of them are yellow, we substract to get the quantity of marbles that aren't yellow: 28-6 = 22

So 22 of the 28 marbles aren't yellow: 22/28, which we can simplify dividing the numerator and denominator by 2: 11/14

Answer:

1.divide

2.minus

3.times

Answer:

C

Step-by-step explanation:

because you cannot sell negative pizzas.

The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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Two supplementary angles equal 180 degrees.

Let the first angle = x

The second angle is 30 degrees more so this would be x + 30

Now add the two angles together to equal 180:

X + x+ 30 = 100

Combine like terms:

2x + 30 = 180

Subtract 30 from both sides:

2x = 150

Divide both sides by 2:

X = 75

One angle = x = 75

The other angle is x + 30 = 75 + 30 = 105

The smaller angle is 75 degrees.

To determine the linear meters of fence that will be painted, we need to find the perimeter of each triangle that makes up the block, and then multiply that perimeter by 8. Total length of fence needs to be pained is, 5104 meters.

Identify each of the 3 triangles that make up the quadrilateral ABCD.

For each triangle, measure the length of each side using a ruler or measuring tape.

Add up the lengths of all the sides of each triangle to find the perimeter of that triangle.

Once you have found the perimeter of each triangle, multiply that value by 8 to get the total length of fence that will be painted.

Sides of triangle 1: 23 m, 93 m, 90 m

Sides of triangle 2: 93 m, 93 m, 48 m

Sides of triangle 1: 88 m, 20 m, 90 m

The perimeter of the first triangle is 206 meters.
The perimeter of the second triangle is 234 meters.

The perimeter of the third triangle is 198 meters. Then the total length of fence that will be painted is,

Total length of fence = (206 + 234 + 198) x 8 = 5104 meters

Therefore, we can use this procedure to determine the linear meters of fence that will be painted.

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--The complete question is, Consider the lengths obtained in the previous session of one of the sections of the planters to answer the following questions. (The previous question answer for length are shown in image) Write the procedure you will use to determine the linear meters of fence that will be painted. Also, find the length that needs to be painted.--

The value of x in the similar triangles are:

a. x = 80 ft.

b. x = 16 ft.

Similarity among two or more triangle is a common relations when the properties of the triangles are compared. But in this case, the triangle are NOT congruent.

Considering the triangles in the given question,

1. Comparing the properties of the similar triangles, we have;

So that,

30/ x = 50/ 80

50x = 4000

x = 4000/ 50

  = 80

x = 80 ft.

2. Comparing the properties of the two triangles, we have;

4.5/ 12 = 6/ x

4.5x = 72

x = 72/ 4.5

  = 16

x = 16 ft

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Answer:

A) 210 B) 0.18

Step-by-step explanation:

got it right

Answer+Step-by-step explanation:

m = man's age

s = son's age

m=s+36

(m+8)=3*(s+8)

Resolves to: s=10, m=46

So the man is 46 (=10+36).

In 8 years, son is 18 (=10+8), man is 54 (=3*18 and 46+8), thank you.

The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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Answer:

Check explanation

Step-by-step explanation:

Monday = 3 1/4 hours

Tuesday = 1 3/4 hours

Wednesday = 2 2/3 hours

Thursday = x hours

Friday = 5 1/2 hours

Total hours worked = 16 1/2 hours

Total hours worked = Monday + Tuesday + Wednesday + Thursday + Friday

16 1/2 = 3 1/4 + 1 3/4 + 2 2/3 + x + 5 1/2

33/2 = 13/4 + 7/4 + 8/3 + x + 11/2

33/2 = 39+21+32+66/12 + x

33/2 = 158/12 + x

33/2 - 158/12 = x

x = 198-158/12

x = 40/12

= 3 4/12

x = 3 1/3 hours

Earnings per hour = $7.50

Total earnings = Earnings per hour * Total hours worked

= 7.50 * 16 1/2

= 7.50 * 33/2

= 7.50 * 16.5

= $123.75

Amount needed to purchase a game player = $146.25

Amount needed more =$146.25 - $123.75

= $22.5

More hours needed to work = Amount needed more / Earnings per hour

= $22.5 / $7.50

= 3 hours

Therefore,

Alice needs to work 3 hours more

Main Answer: Only one triangle can be drawn with side lengths of 3 units, 4 units, and 5 units and no matter how they are oriented,it will always have the same shape and size.

Supporting Question and Answer:

What is the condition for determining if a triangle can be formed with a given set of side lengths?

The condition for determining if a triangle can be formed with a given set of side lengths is to check whether the sum of the lengths of any two sides is greater than the length of the third side, as stated by the Triangle Inequality Theorem. If this condition is not satisfied, then the three sides cannot form a triangle.

Body of the Solution:

The correct answer is:(A) triangles, because triangles with the same three side lengths are the same shape and size no matter how they are positioned.

This is because, according to  the Side-Side-Side congruence criterion, if the three sides of one triangle are equal in length to the three sides of another triangle, then the two triangles are congruent,which means they have the same angles and size. Since a triangle is determined by its three side lengths, and the side lengths of the given triangle are fixed at 3, 4, and 5 units, there is only one unique triangle that can be formed with these side lengths. It is important to note that the position or orientation of the triangle does not affect its shape or size, hence any other triangles that may appear to have the same side lengths would be congruent to the original triangle, and thus be considered the same triangle.

Option (B) is incorrect because reflection changes the orientation of the triangle, but does not change its shape or size.

Option (C) is incorrect because the order in which the sides are written does not affect the shape or size of the triangle.

Option (D) is incorrect because, as explained earlier, a triangle can be formed with side lengths of 3, 4, and 5 units.

Final Answer:  Therefore, Only one triangle can be drawn with side lengths of 3 units, 4 units, and 5 units and the correct option is:

(A) triangles, because triangles with the same three side lengths are the same shape and size no matter how they are positioned.

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The correct answer is A) triangles, because triangles with the same three side lengths are the same shape and size no matter how they are positioned.

Triangles with side lengths of 3 units, 4 units, and 5 units can be drawn in many different ways, but they will have the same shape and size. This is because the side lengths are relatively small compared to the overall size of the triangle, so the shape of the triangle is not significantly affected by the orientation of the sides.

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On solving the provided query we have Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

The facts (3) ABCD and AB are insufficient to demonstrate that ABCD is a parallelogram.

The diagonals are bisected by each other, which is a characteristic of parallelograms, according to statement (1).

According to statement (2), opposing sides of a parallelogram are congruent and parallel, which is another characteristic of parallelograms.

Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

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