A square of side 18 inches is cut to make an open box with equal squares cut from each corner. The volume of the box to be 432 cubic inches. We have to find the minimum length of the sides of the squares cut from each corner.
Let x be the length of the sides of the squares cut from each corner. The length of the open box will be (18 - 2x), since we are cutting x length from each corner.Height of the box will be x. Volume of the box V = Length × Width × Height We know that, V = 432 cubic inches Given, V = Length × Width × Height We have, Length = (18 - 2x) Width = (18 - 2x)
Height = xV
[tex](18 - 2x) × (18 - 2x) × x= (18 - 2x)² × x= x(324 - 72 x + 4x²)[/tex]
=432 cubic inches
x(4x² - 72x + 324) - 432 = 0 Now, solving this equation, we get: 4x² - 72x + 324 - 432/x = 0 Multiplying both sides by x, we get: 4x³ - 72x² + 324x - 432 = 0 Factorizing it, we get:
4(x - 6)² (x - 3) = 0x = 3, 6 As the length of the side can not be negative.
Therefore, the minimum length of the side of the square cut from each corner be 3 inches.Volume, V of the box as a function of x can be calculated as follows:V = x(324 - 72x + 4x²)
= 4x³ - 72x² + 324 x cubic inches. Answer: Therefore, the minimum length of the side of the square cut from each corner should be 3 inches.
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Maria is buying 5 tickets to a play that cost $17 each. She decides to calculate the total cost y doing the following calculation: 5($10)+5($7) = $50+$35= $85 at property is Maria using that allows her to calculate the total cost in this way?
The correct total cost of the 5 tickets is $85.
The calculation that Maria is using to calculate the total cost of the tickets is incorrect. She is multiplying the number of tickets by $10 and $7 separately, instead of multiplying the number of tickets by the cost per ticket.
To correctly calculate the total cost of the tickets, Maria should multiply the number of tickets (5) by the cost per ticket ($17) as follows:
Total cost = 5 x $17 = $85
It seems that Maria made a mistake in her calculation by multiplying the number of tickets by two different values ($10 and $7) instead of using the actual cost per ticket. This mistake leads to an incorrect total cost of $50 + $35 = $85.
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Classify each number according to its value. 4. 2 × 10-6 2. 1 × 10-3 3. 1 × 10-2 3. 2 × 10-5 3. 5 × 10-4 5. 8 × 10-3 5. 2 × 10-4.
The given numbers can be classified into two categories: small values and very small values (closer to zero). All the given numbers have values that are either small or very small, with some being closer to zero than others based on the number of places the decimal point is moved to the left.
In scientific notation, numbers are expressed as a product of a decimal number between 1 and 10, and a power of 10. The power of 10 indicates the number of places the decimal point is moved to the right (if the exponent is positive) or to the left (if the exponent is negative).
Based on the given numbers:
1. 2 × 10^(-6): This number is very small, as the exponent is negative and indicates that the decimal point is moved 6 places to the left.
2. 1 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.
3. 1 × 10^(-2): Similar to the previous number, this is also a small value, with the exponent indicating a movement of 2 places to the left.
4. 2 × 10^(-5): This number is very small, with the exponent indicating a movement of 5 places to the left.
5. 5 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.
6. 8 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.
7. 2 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.
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What is a positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees and a negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees?
the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.
To find th positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees, and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees,
we can use the following formulas:For a positive coterminal angle, add 360 degrees repeatedly until we reach the desired range.For a negative coterminal angle, subtract 360 degrees repeatedly until we reach the desired range.
Let's start with the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees.
To find this angle, we need to add 360 degrees repeatedly until we reach a value between 500 degrees and 1000 degrees.
So, we can write:47 + 360 = 407 (not in range)
407 + 360 = 767 (not in range)
767 + 360 = 1127 (not in range)
1127 + 360 = 1487 (not in range)
1487 + 360 = 1847 (not in range)
1847 + 360 = 2207 (not in range)
2207 + 360 = 2567 (not in range)
2567 + 360 = 2927 (not in range)
2927 + 360 = 3287 (not in range)
3287 + 360 = 3647 (not in range)
3647 + 360 = 4007 (not in range)
4007 + 360 = 4367 (not in range
4367 + 360 = 4727 (not in range)
4727 + 360 = 5087 (not in range
5087 + 360 = 5447 (not in range
)5447 + 360 = 5807 (not in range)
5807 + 360 = 6167 (not in range)
6167 + 360 = 6527 (not in range)
6527 + 360 = 6887not in range)
6887 + 360 = 7247 (not in range
)7247 + 360 = 7607 (not in range)
7607 + 360 = 7967 (not in range)
7967 + 360 = 8327 (not in range)
8327 + 360 = 8687 (not in range)
8687 + 360 = 9047 (not in range)
9047 + 360 = 9407 (not in range)
9407 + 360 = 9767 (not in range
)9767 + 360 = 10127 (not in range)
10127 + 360 = 10487 (not in range)
10487 + 360 = 10847 (not in range)
10847 + 360 = 11207 (in range)
Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 11207 - 10847 = 360 degrees.
To find the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees, we need to subtract 360 degrees repeatedly until we reach a value between -500 degrees and 0 degrees. So, we can write:
47 - 360 = -313 (not in range)
-313 - 360 = -673 (not in range)
-673 - 360 = -1033 (not in range)
-1033 - 360 = -1393 (not in range
-1393 - 360 = -1753 (not in range)
-1753 - 360 = -2113 (not in range)
-2113 - 360 = -2473 (not in range)
-2473 - 360 = -2833 (not in range
-2833 - 360 = -3193 (not in range
-3193 - 360 = -3553 (not in range)
-3553 - 360 = -3913 (not in range)
-3913 - 360 = -4273 (not in range)
-4273 - 360 = -4633 (not in range)
-4633 - 360 = -4993 (in range)
therefore, the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is -4993 - (-5183) = 190 degrees.
Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.
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Eric is working for an ad firm. He is responsible for storyboarding. Help him specify the different types of audio in the storyboard.
primary audio
secondary audio
background audio
He can make a note of scenes where surrounding noise is required.
>
He can make a note of external microphone to record audio simultaneously while
recording video.
He can make a note of additional music that he wants to add while editing.
Specify primary audio , secondary audio (sound effects/music), and background audio (ambient music) in the storyboard. Note scenes with surrounding noise, use an external microphone for recording, and plan additional music for editing.
In storyboarding for an ad firm, Eric needs to consider three types of audio: primary audio, secondary audio, and background audio. Primary audio refers to the main audio component that drives the narrative or delivers important information in the ad. This can include dialogue, voiceover, or any sound directly related to the main subject. Secondary audio supports the primary audio and adds depth to the storytelling. It can include sound effects, ambient noise, or music that complements the visuals. Background audio provides the overall atmosphere and mood of the ad. It can include ambient music or soundscapes that create the desired emotional tone.
Additionally, Eric should make notes of scenes where surrounding noise is required. This means capturing the environmental sounds that enhance the authenticity and realism of the ad, such as street noise, nature sounds, or crowd reactions. He should also consider using an external microphone to simultaneously record audio while filming the video. This ensures high-quality audio capture and reduces the reliance on the camera's built-in microphone, which may not provide optimal sound recording. Lastly, Eric can make a note of any additional music he intends to add during the editing process. This can involve selecting appropriate background tracks, jingles, or any other musical elements that enhance the overall impact of the ad. By carefully considering these audio aspects during storyboarding, Eric can create a compelling and immersive ad experience for the audience.
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Determine the period. Acellus
Answer: 15
Step-by-step explanation:
Period=distance between 2 top points.
15
The sum of two times a number and 9 is five times the difference of a number and six.
Using algebraic equations, the value of the number assumed to be x is 13.
Let's assume that the number in question be "x". Thus, the expression can be written as:
2x + 9 = 5 (x - 6).
Let's solve this equation and find the value of x:
Distributing the 5 across the parentheses,
2x + 9 = 5x - 30
Subtracting 2x from both sides,
we get, 3x = 39
Dividing both sides by 3,
x = 13
Thus, the number is 13.
Thus, we have found the number by forming and solving an equation.
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An open cylinder with internal radius r cm has a 2-cm wall and is 9r cm long. Express the volume of material in the wall of the cylinder as a polynomial function in terms of r
The volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]\(r\)[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .
To find the volume of material in the wall of the open cylinder, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder. The outer cylinder has a radius of [tex]\(r + 2\)[/tex]cm, while the inner cylinder has a radius of [tex]r[/tex] cm. The length of both cylinders is [tex]9r[/tex] cm.
The volume of the outer cylinder can be calculated using the formula: [tex]\(V_{\text{outer}} = \pi \cdot (r + 2)^2 \cdot 9r\) cm^3[/tex].
The volume of the inner cylinder can be calculated using the formula: [tex]\(V_{\text{inner}} = \pi \cdot r^2 \cdot 9r\) cm^3[/tex].
To find the volume of material in the wall, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
[tex]\[V_{\text{wall}} = V_{\text{outer}} - V_{\text{inner}} = \pi \cdot (r + 2)^2 \cdot 9r - \pi \cdot r^2 \cdot 9r= 9\pi r(r + 2)^2 - 9\pi r^3= 9\pi r[(r + 2)^2 - r^2]= 9\pi r[4r + 4].\][/tex]
Simplifying further:
[tex]\[V_{\text{wall}} = 36\pi r^2 + 36\pi r \text{ cm}³ = 36\pi(r^2 + r).\][/tex]
Therefore, the volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]r[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .
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use the distributive property to create true equations 8(3+6) brainly
Here are some true equations that use the distributive property to distribute 8(3+6):
8(3+6) = 8(3) + 8(6) = 24 + 48 = 72
8(3+6) = (83) + (86) = 24 + 48 = 72
8(3+6) = (83) + 68 = 24 + 48 = 72
The distributive property can be used to distribute any number of factors over a sum. In this case, we are distributing the factor 8 over the sum 3+6. We can do this by multiplying each term in the sum by 8 and then adding the products together. This gives us 24 + 48 = 72.
what is the value of x in the figure below
Answer:
24
Step-by-step explanation:2x+42= 90
2x=90-42
2x=48
x=24
Step-by-step explanation:
2x°+42°=90°
2x+42°-42°=90°-42°
2x/2=48°/2
x=24°
But Iam not sure I just try
To prove that AAGE and A OLD are congruent by
SAS, what other information is needed?
1) GE = LD
2) AG=OL
3) AGE= OLD
4) AEG = ODL
To prove that AAGE and AOLD are congruent by SAS, the other information that is needed is: GE = LD.Explanation:To prove that two triangles are congruent using SAS (side-angle-side) postulate, we need to know.
Two sides and the angle between them in one triangle are congruent to the corresponding sides and angle in the other triangle.So, given AG = OL, AGE = OLD, and AEG = ODL, we can conclude that two angles and a side are equal in both triangles.However, to apply the SAS postulate, we need to have another pair of equal sides in both triangles. And that is given by GE = LD. Hence, option 1) is the correct answer.Other options don't provide the necessary information to prove the congruence of the two triangles using SAS.
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a field project superintenint earns an annual salary of 72800
A field project superintendent earns an annual salary of $72,800. This is a piece of information about the annual salary of a field project superintendent.
A field project superintendent is a person responsible for overseeing and managing construction projects. This position is responsible for ensuring that the construction project is completed on time, within budget, and in accordance with safety and quality standards. This person must have a thorough understanding of construction principles and techniques, as well as the ability to read and interpret blueprints and specifications.
A salary is a fixed amount of compensation paid to an employee for their work. The amount of salary is typically determined by the employee's position, job duties, and level of experience. Salaries are usually paid on a monthly or bi-weekly basis.
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Estimate pet car populations for several European countries in 2002 are shown below. If each car population doubles by 2010, which values will be closest to the average pet car population for these countries in 2010? A.) 9 million B.) 15 million C.) 18 million D.) 12 million
The value closest to the estimated average pet car population for European countries in 2010 is 15 million.
Given the table for pet car populations in 2002, we need to estimate the average pet car population for European countries in 2010 after each car population has doubled.
It can be observed that in 2002, Spain and Italy had the lowest pet car population while Germany and the United Kingdom had the highest.
In order to find the estimated average pet car population for European countries in 2010, we first need to find the pet car population for each country in 2010 after doubling their 2002 population.
The results are shown in the table below:
|Country|Pet car population in 2002
|Pet car population in 2010|
|-|-|-|
|France|22 million
|44 million|
|Germany|
30 million|
60 million|
|Italy|
8 million|
16 million| |Spain|6 million|12 million| |United Kingdom|28 million|56 million|
To find the estimated average pet car population for European countries in 2010, we need to sum up the pet car populations for all the countries in 2010 and then divide by the total number of countries (which is 5).
Adding all the pet car populations in 2010:
44 million + 60 million + 16 million + 12 million + 56 million = 188 million
The estimated average pet car population for European countries in 2010, closest to the calculated value, would be:
188 million/5 ≈ 38 million
Now, we need to find which of the given options is closest to this value. We can see that the option closest to 38 million is D.) 12 million.
However, this value is not the answer since it is too low compared to the estimated average.
Therefore, we can rule out option
D.) as the answer.
Now, we can look at the remaining options to determine which is closest to the average.
Option A.) 9 million is clearly too low, and
option C.) 18 million is too high.
Therefore, the answer is
option B.) 15 million,
which is the value closest to the estimated average pet car population for European countries in 2010.
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ALMN, LM || OP. Given that NL=35, NO=20, and NM=49, find NP.
L
O
N
M
NP =
Answer:
NP=28
Step-by-step explanation:
20/35=x/49
cross multiply
35x=20x49
35x=980
x-980/35
x=28
A 14ft ladder leans against the side of a house the angle of elevation of the ladder is 74 how high is the top of the ladder from the ground round to the nearest tenth
The top of the ladder is approximately 44.1 feet from the ground.
To find out how high the top of the ladder is from the ground, we need to use trigonometry, specifically the tangent function since we have the angle of elevation and the length of the adjacent side. Here are the steps to solve the problem:
Step 1: Label the diagram and identify the angle of elevation and the adjacent side.
Label the base of the ladder as the adjacent side (a), the height of the ladder as the opposite side (o), and the length of the ladder as the hypotenuse (h).Identify the angle of elevation as the angle between the adjacent side and the hypotenuse.
In this case, the angle of elevation is 74°.
Step 2: Write out the formula and substitute the given values.Tanθ = o/aTan74° = o/a Solve for o: o = a * tan74°
Step 3: Substitute the value of a and use a calculator to find o.
Substitute the value of a, which is 14 feet, and use a calculator to find o. o = 14 * tan74°o ≈ 44.1 feet (rounded to the nearest tenth)Therefore, the top of the ladder is approximately 44.1 feet from the ground.
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PP 02. 10
2) Mr. Edwin Lazo paid Php 13,600. 00 for a television serMUT UN UN
P16,000. 0. What is the rate of discount?
4. 15%
B. 16%
C. 18%
D. 20%
that regularly sells at Php 1580. 00 is on sale at 30% off. What is the
The rate of discount is 30%. The regular price of the television set is Php 1580, and it is being sold at a discount of 30%.
To find the sale price, we can use the formula:
Sale price = Regular price - (Discount rate × Regular price)
Substituting the given values, we get:
Sale price = 1580 - (0.30 × 1580)
Sale price = 1580 - 474
Sale price = 1106
Therefore, the sale price of the television set is Php 1106. This means that Mr. Edwin Lazo paid Php 13,600.00 for an item that originally cost Php 1580.00 but was on sale at Php 1106.00.
To calculate the rate of discount, we can use the following formula:
Discount rate = (Regular price - Sale price) / Regular price x 100%
Substituting the given values, we get:
Discount rate = (1580 - 1106) / 1580 x 100%
Discount rate = 474 / 1580 x 100%
Discount rate = 0.3 x 100%
Discount rate = 30%
Therefore, the rate of discount is 30%.
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The volume of a cube is 407cm3.
Work out the length of its side rounded to 1 DP.
Given, the volume of a cube is 407cm³.Let's assume that a is the length of a side of the cube. We know that the volume of a cube = a³So,
a³ = 407Take the cube root of both sides to find the value of a.
a = (407)^(1/3)≈ 7.96cm(rounded to 1 decimal place)
Hence, the length of the side of the cube rounded to 1 DP is 7.96 cm (more than 100 words).
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Tressa has 57.9 points in a competition. She loses 8.6 points. Write and evaluate an addition expression to determine Tressa's current score.
To write and evaluate an addition expression to determine Tressa's current score, we need to subtract the number of points she loses from her original score. The original score is 57.9 points and she loses 8.6 points.
So, Tressa's current score can be determined by adding the difference (which is -8.6) to her original score. Therefore, the addition expression to determine Tressa's current score can be written as:
57.9 + (-8.6)
To evaluate this expression, we simply need to add the numbers:
57.9 + (-8.6) = 49.3
Therefore, Tressa's current score is 49.3 points.
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PLEASE, I REALLY NEED HELP HOW DO I DO A VERBAL EXPLANATION FOR THIS??? PLEASE
The radical form of[tex](-3x^3)^-^2/3 is 1 / (9x^2)[/tex].
To rewrite the expression[tex](-3x^3)^-^2/3[/tex] as a radical, we can use the fact that a negative exponent indicates that the base is in the denominator. Therefore, we can rewrite the expression as:
[tex]1 / (-3x^3)^(^2^/^3^)[/tex]
Using this concept, we can rewrite the exponent -2/3 as [tex]3\sqrt(1/-3^2)[/tex], where 3√ is the cube root. We also need to take the cube root of the absolute value of -3x^3 to ensure that the result is always positive.
To find the radical form, we can simplify the expression under the radical by raising it to the power of 3/2:
[tex](-3x^3)^(^2^/^3) = [(-3)^(^2^/^3^) * (x^3)^(^2^/^3^)]^3 = [(9 * x^2)^(^1^/^3^)]^3 = 9x^2[/tex]
Substituting this back into the original expression gives:
1 / (-3x^3)^(2/3) = 1 / (9x^2).
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Marissa bought x shirts that cost $19. 99 each and y pairs of shorts that cost $14. 99 each. The next day she went back to the store and bought 3 more shirts that cost $19. 99 each and 4 more pairs of shorts that cost $14. 99 each. Which expression represents the total amount Marissa spent? StartFraction x 3 over 19. 99 EndFraction StartFraction y 4 over 14. 99 EndFraction StartFraction 3 x over 19. 99 EndFraction StartFraction 4 y over 14. 99 EndFraction 19. 99 (x 3) 14. 99 (y 4) (3 x) 19. 99 (4 y) 14. 99.
The expression that represents the total amount Marissa spent is (x * 19.99 + y * 14.99) + (3 * 19.99 + 4 * 14.99).
In summary, the expression (x * 19.99 + y * 14.99) represents the cost of the initial purchase, where x is the number of shirts and y is the number of shorts. The expression (3 * 19.99 + 4 * 14.99) represents the cost of the additional purchase the next day, where 3 is the number of shirts and 4 is the number of shorts. By adding both expressions together, we get the total amount Marissa spent.
The first part of the expression, x * 19.99, calculates the cost of the x shirts at $19.99 each. Similarly, the second part, y * 14.99, calculates the cost of the y pairs of shorts at $14.99 each. These two terms represent the initial purchase.
The next part of the expression, 3 * 19.99, calculates the cost of the 3 additional shirts bought the next day. Similarly, 4 * 14.99 calculates the cost of the 4 additional pairs of shorts. These two terms represent the additional purchase.
By adding the cost of the initial purchase and the additional purchase, we obtain the total amount Marissa spent on shirts and shorts.
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your planning w dinner party with the budget of 50$ and a menu that consists of 1 main dish 2 side dish and 1 dessert
This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!
If you're planning a dinner party with a budget of $50 and a menu that consists of 1 main dish, 2 side dishes, and 1 dessert, there are plenty of affordable options you can choose from. Here's a sample menu that should fit within your budget:Main Dish: Baked Chicken - $10Ingredients:4 chicken leg quarters - $6.004 tbsp olive oil - $0.501 tbsp salt - $0.101 tbsp pepper - $0.101 tbsp garlic powder - $0.101 tbsp paprika - $0.10Directions:Preheat oven to 400°F. Combine salt, pepper, garlic powder, and paprika in a small bowl.
Drizzle chicken with olive oil and rub spice mixture onto chicken. Place chicken in a baking dish and bake for 45-50 minutes until chicken is cooked through.
Side Dish 1: Garlic Roasted Potatoes - $4Ingredients:6 medium-sized potatoes - $1.501/4 cup olive oil - $0.751 tbsp salt - $0.101 tbsp pepper - $0.101 tb sp garlic powder - $0.10Directions:Preheat oven to 400°F. Wash potatoes and cut them into small cubes.
Combine potatoes with olive oil, salt, pepper, and garlic powder in a large mixing bowl. Spread the potatoes out in a single layer on a baking sheet and bake for 30-35 minutes until golden brown and crispy.
Side Dish 2: Sauteed Green Beans - $3Ingredients:
1 lb green beans - $2.001/4 cup butter - $0.501 tbsp garlic - $0.101/2 tbsp salt - $0.051/2 tbsp pepper - $0.05Directions:Bring a pot of water to a boil and blanch green beans for 2-3 minutes. Drain and rinse under cold water. Combine flour, rolled oats, brown sugar, butter, cinnamon, and nutmeg in a mixing bowl. Use your hands to mix the ingredients together until crumbly. Spread the topping over the apples and bake for 35-40 minutes until golden brown and crispy.
Total cost: $25This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!
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You pick a card from a standard deck, look at it, then pick a second card. Since a standard deck of 52 cards has 13 hearts and 13
diamonds, is the probability of drawing a heart and then a diamond 13/52 x 13/52
Yes, the probability of drawing a heart and then a diamond from a standard deck of 52 cards is indeed (13/52) x (13/52).
To calculate the probability of two independent events occurring, we multiply their individual probabilities. In this case, the probability of drawing a heart on the first card is 13 out of 52 because there are 13 hearts in a standard deck of 52 cards. The probability of drawing a diamond on the second card is also 13 out of 52 since there are 13 diamonds in the deck.
Therefore, the probability of drawing a heart and then a diamond is:
(13/52) x (13/52) = (169/2704) = 1/16 ≈ 0.0625 ≈ 6.25%
So, the probability of drawing a heart and then a diamond from a standard deck is 13/52 multiplied by 13/52.
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Three people share seven brownies. How many brownies should each person get?
Three people share seven brownies. Each person should get 2 brownies since 2 is the closest value that is less than 2.33 since the answer should be a whole number.
Explanation: We can calculate the number of brownies each person should get by dividing the total number of brownies by the number of people that will share them. Since three people are to share 7 brownies, we divide 7 by 3.Thus, each person should get 2 and 1/3 of a brownie. This value, however, cannot be the answer since it should be a whole number. Therefore, we take the closest b number that is less than 2.33, which is 2. This implies that each person should get 2 brownies.
In essence, we will have shared 6 brownies since 2 x 3 is equal to 6. So, one brownie will be left. This means that the brownie should be shared among the three people. Each person will receive two brownies and the remaining one brownie should be shared equally among the three. So, each person should get two and one-third pieces of brownies.
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Farid has two types of sticks: short ones, measuring 1 cm and long ones, measuring 3 cm. With which of the combinations below can he make a square, without breaking or overlapping the sticks?
Farid can make a square by using a combination of two short sticks and two long sticks.
To form a square without breaking or overlapping the sticks, the length of each side of the square must be equal. In this case, we have two types of sticks: short ones measuring 1 cm and long ones measuring 3 cm.
To determine which combinations can form a square, we need to consider the lengths of the sides and the total length of the sticks.
1. Using only short sticks (1 cm each):
To form a square, we need four equal sides. Since each short stick measures 1 cm, the total length of the four sides would be 4 cm. This combination does not work as the total length is too small to form a square.
2. Using only long sticks (3 cm each):
Similarly, using only long sticks would result in a total length of 12 cm for the four sides. This combination also does not work as the total length is too large to form a square.
3. Using a combination of short and long sticks:
In this case, we can combine short and long sticks to create a square. For example, using two short sticks and two long sticks would give us a total length of 2 cm + 2 cm + 3 cm + 3 cm = 10 cm. This combination can form a square with each side measuring 2.5 cm.
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MICE The average length of the head and body of a western harvest mouse is 2.9 inches. The average length of the tail is 2.8 inches. First, estimate the total length of the mouse. Then find the actual total length.
Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.
The given information states that the average length of the head and body of a western harvest mouse is 2.9 inches, while the average length of the tail is 2.8 inches. To estimate the total length of the mouse, we can add these two measurements together:
Estimated total length = Average length of head and body + Average length of tail
Estimated total length = 2.9 inches + 2.8 inches
Estimated total length = 5.7 inches
Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.
It's important to note that this estimate represents the average length and may not accurately reflect the actual total length of each individual mouse. There may be variations in the lengths of different mice within the population. Factors such as genetics, age, and environment can influence the actual total length of a mouse. Therefore, the estimate serves as a general approximation and the actual total length of each mouse may differ slightly from the estimate of 5.7 inches.
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Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below.Based on this work, what is the solution to the system?(-4, -4)(0, 0)no solutioninfinitely many solutions
The solution to the system of equations is (-4, 4).
The system of equations is: x + y = -8 and x - y = 0
Mr. Brown can find the solution to the system of equations by solving it using the elimination method as follows:
x + y = -8 (Equation 1)
x - y = 0 (Equation 2)
Add Equation 1 and Equation 2.
Doing so will eliminate y from the equations and solve for x.
x + y + x - y = -8 + 0
2x = -8 x = -4
Substitute x = -4 into any of the original equations to solve for y.
Let's use Equation 2: x - y = 0 -4 - y = 0
y = -(-4) y = 4
Therefore, the solution to the system of equations is (-4, 4).
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54 cu. In. 72 cu. In. 36 cu. In. 80 cu. In. Dimensions of Rectangular Prism Volume of Rectangular Prism 4 in. , 3 in. , 6 in. 6 in. , 3 in. , 2 in. 4 in. , 5 in. , 4 in. 2 in. , 9 in. , 3 in.
The dimensions of a rectangular prism can be matched with the volume of the rectangular prism as follows:
4 in., 3 in., 6 in. = 72 in³6 in., 3 in., 2 in. = 36 in³4 in., 5 in., 4 in. = 80 in³2 in., 9 in., 3 in. = 54 in³How to match the dimensions to the volumeTo match the dimensions of the rectangular prism to the volume we need to know the formula or the volume of a rectangular prism. That is;
length * breadth * height.
So, for the dimensions given, we would simply multiply all the side lengths to arrive at the final volume of the rectangular prism. For the first one,
4 * 3 * 6 = 72 in³
6 * 3 * 2 = 36 in³
4 * 5 * 4 = 80 in³
2 * 9 * 3 = 54 in³
The results represent the final volumes of the rectangular prisms.
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In 7 hours, operators at a call center make 4,732 telemarketing calls. Write an equation to represent how to find the number of phone calls made per hour. Using the equation from part A, how many calls did the center make per hour.
The call center made approximately 676 calls per hour. In 7 hours, operators at a call center make 4,732 telemarketing calls.
To represent the number of phone calls made per hour at the call center, we can use the equation:
Number of phone calls made per hour = Total number of phone calls / Number of hours
Given that in 7 hours, operators at the call center made 4,732 telemarketing calls, we can substitute the values into the equation to find the number of calls made per hour:
Number of phone calls made per hour = 4,732 / 7
Performing the division:
Number of phone calls made per hour = 676
Therefore, the call center made approximately 676 calls per hour.
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In ΔABC, the measure of ∠C=90°, the measure of ∠A=5°, and BC = 3 feet. Find the length of CA to the nearest tenth of a foot
Select each expression that has a value of 15 when x = 15 D A - 10 3 DB 15.521 * * OC (3,015 - ) - 186 OD 2022-30 DE -25 what is the answer?
The expressions that have a value of 15 when x = 15 include the following:
A. x/3 + 10
C. (3,015 ÷ x) - 186
How to evaluate each of the expression?Based on the information provided, we would determine the output value of each of the given expression by substituting 15 for the value of x as follows;
Expression = x/3 + 10
Expression = 15/3 + 10
Expression = 5 + 10
Expression = 15 (True).
Expression = 15,521 ÷ x
Expression = 15,521 ÷ 15
Expression = 1034.73 (False).
Expression = (3,015 ÷ x) - 186
Expression = (3,015 ÷ 15) - 186
Expression = 201 - 186
Expression = 15 (True).
Expression = 20x² ÷ 30
Expression = 20(15)² ÷ 30
Expression = 4500 ÷ 30
Expression = 150 (False).
Expression = 20x²/5 - 25
Expression = 20(15)²/5 - 25
Expression = 900 - 25
Expression = 875 (False).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
PLEASE HELP ME ANSWER ASAP Q2
The length of the side /CD/ is 6√3 square units. Option A
What is the sine of an angle?
The trigonometric function known as the sine of an angle describes the ratio between the lengths of the hypotenuse and the side opposite the angle in a right triangle. The sine function, sometimes known as "sin", is described as follows:
Sin = opp/adj
The sine function can be used to determine how a right triangle's angles and sides match up.
Let the altitude /CD/ be x
Using the sine of an angle;
Sin 60 = √3/2
√3/2 = x/12
x = √3/2 * 12
x = 6√3 square units
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