The correct function combinations for the given expressions are: Expression 1 with Function D, Expression 2 with Function A, Expression 3 with Function C, and Expression 4 with Function B.
To determine the correct function combinations for the given expressions, let's analyze each expression and its corresponding function.
Expression 1: 2x + 5
Function D: Linear function
Expression 1 is a linear function with a coefficient of 2 and a constant term of 5. Therefore, the correct function combination for Expression 1 is Function D.
Expression 2: x^2 + 3x + 2
Function A: Quadratic function
Expression 2 is a quadratic function with a squared term, a linear term, and a constant term. Thus, the correct function combination for Expression 2 is Function A.
Expression 3: √x
Function C: Square root function
Expression 3 represents a square root function, denoted by the radical symbol (√). Therefore, the correct function combination for Expression 3 is Function C.
Expression 4: |x|
Function B: Absolute value function
Expression 4 represents an absolute value function, indicated by the vertical bars surrounding the variable x. Hence, the correct function combination for Expression 4 is Function B.
In conclusion, the correct function combinations for the given expressions are Expression 1 with Function D, Expression 2 with Function A, Expression 3 with Function C, and Expression 4 with Function B.
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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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Suppose you live in a world with only 5p and 7p coins. What's the largest amount that can't be made with these coins?
23p is the largest amount that can't be made with these coins.
The problem you are referring to is known as the "Frobenius coin problem" or the "Coin-change problem." In this case, we have coins of denominations 5p and 7p, and we want to find the largest amount that cannot be made using a combination of these coins.
To solve this problem, we can use a mathematical concept called the "Frobenius number." The Frobenius number is given by the formula:
Frobenius number = (5p * 7p) - (5p + 7p)
In this case, the Frobenius number is:
Frobenius number = (5 * 7) - (5 + 7) = 35 - 12 = 23
Therefore, the largest amount that cannot be made using only 5p and 7p coins is 23p.
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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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Solve the problem by entering and solving an equation.
What is the temperature in degrees Fahrenheit of a freezer kept at -30°C?
The equation is
(x -
The temperature is
degrees Fahrenheit.C
The temperature in degrees Fahrenheit of a freezer kept at -30°C is -22°F, indicating an extremely cold temperature below freezing point.
To convert the temperature from Celsius to Fahrenheit, we can use the formula:
°F = (°C * 9/5) + 32
Substituting -30°C into the formula:
°F = (-30 * 9/5) + 32
°F = (-54) + 32
°F = -22
Therefore, the temperature in degrees Fahrenheit of a freezer kept at -30°C is -22°F. This indicates that the freezer is extremely cold since -22°F is significantly below freezing point (32°F). The negative sign indicates that it is below zero on the Fahrenheit scale, emphasizing the low temperature of the freezer.
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he subjectively determined maximum amount a customer would pay for a product is its ______ price. Multiple choice question. overwhelming exploitative unfair reservation
The subjectively determined maximum amount a customer would pay for a product is its reservation price. The main answer is reservation.
An individual's reservation price is the highest price they are prepared to pay for a product or service. The maximum amount that an individual is willing to pay for a product or service is referred to as the reservation price, which is determined subjectively based on the individual's perception of the product's or service's worth.
To put it another way, the maximum amount a buyer will pay for an item is determined by his or her perception of the item's worth, which is influenced by the buyer's individual tastes and preferences.For example, if a person is willing to pay $50 for a pizza, that is their reservation price for a pizza. If the price of the pizza is higher than their reservation price, they are likely to leave without making a purchase. A reservation price is influenced by factors such as product quality, perceived benefits, personal income, and budget constraints.
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In TUV, the measure of ZV=90°, the measure of ZT=24º, and TU = 7. 1 feet. Find the length of UV to the nearest tenth of a foot.
This equation has no real solutions. It seems there might be an error in the given information or the problem setup. Please double-check the values and conditions provided to ensure accuracy.
To find the length of UV, we can use the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides multiplied by the cosine of the included angle.
Let's denote the length of UV as x. According to the given information, we have TU = 7.1 feet and ZT = 24º. ZV is given as 90º, indicating that triangle TUV is a right triangle.
Applying the Law of Cosines, we can write:
x^2 = (7.1)^2 + UV^2 - 2(7.1)(UV)cos(24º)
Since ZV = 90º, the cosine of 90º is 0, so the equation simplifies to:
x^2 = (7.1)^2 + UV^2
Now, we substitute the given values:
x^2 = (7.1)^2 + x^2
Simplifying, we get:
0 = (7.1)^2
This equation has no real solutions. It seems there might be an error in the given information or the problem setup. Please double-check the values and conditions provided to ensure accuracy.
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Darius filled up his gas tank with 24 gallons of gas. For each mile that he drives, he uses 0.06 gallons of gas. Which formula represents the number of gallons of gas left after driving n miles?
The formula that represents the number of gallons of gas left after driving n miles is 24 - 0.06n.
Darius initially filled up his gas tank with 24 gallons of gas. For each mile he drives, he consumes 0.06 gallons of gas. To determine the number of gallons of gas left after driving n miles, we need to subtract the amount of gas used from the initial amount.
Let's consider the amount of gas used for n miles. Since Darius uses 0.06 gallons of gas for each mile driven, the total amount of gas used for n miles can be calculated as 0.06n. To find the number of gallons of gas left, we subtract the gas used from the initial amount: 24 - 0.06n.
Therefore, the formula that represents the number of gallons of gas left after driving n miles is 24 - 0.06n. This formula allows us to calculate the remaining gas in the tank based on the number of miles driven by Darius.
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Francis ran miles in of an hour. How many miles can Francis run in one hour?
If Francis ran 7.5 miles in 1/2 hour, then the distance he covered in one hour will be: m/x = 7.5/(1/2) = 15 miles. We need the value of x in order to determine the distance he covered in one hour.
Given that Francis ran m miles in x hours.
To find how many miles can Francis run in one hour, we need to calculate how much distance he can cover in one hour.
Since he ran m miles in x hours, we can find how many miles he can run in 1 hour using unitary method as follows:
In x hours, he can run m miles.
Therefore, in 1 hour, he can run m/x miles or we can say that the speed of Francis is m/x miles per hour (mph).
Therefore, Francis can run (m/x) miles in one hour. According to the question, Francis ran miles in of an hour, we don't have the value of x, we cannot determine the exact distance he covered in 1 hour.
For instance, if Francis ran 5 miles in 1/2 hour, then the distance he covered in one hour will be:m/x = 5/(1/2) = 10 miles.
Similarly, if Francis ran 7.5 miles in 1/2 hour, then the distance he covered in one hour will be: m/x = 7.5/(1/2) = 15 miles. Thus, we need the value of x in order to determine the distance he covered in one hour.
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A $290.00 designer purse is on sale at an outlet mall. The discounted price of the purse is $174.00. What percent is the purse being discounted by? The purse is discounted by Don't forget to include a percent sign, %, in your answer.
The purse is discounted by 44.83%, Divide the difference by the original price. In this case, 116.00 / 290.00 = 0.3962.
To find the percentage discount, we can use the following formula:
(original price - discounted price) / original price * 100 = percent discount
In this case, the original price is $290.00 and the discounted price is $174.00. So, the percent discount is:
(290.00 - 174.00) / 290.00 * 100 = 44.83%
Therefore, the purse is discounted by 44.83%.
Here is a step-by-step explanation of how to find the percentage discount:
Subtract the discounted price from the original price. In this case, 290.00 - 174.00 = 116.00.
Divide the difference by the original price. In this case, 116.00 / 290.00 = 0.3962.
Multiply the result by 100. In this case, 0.3962 * 100 = 44.83.
Therefore, the purse is discounted by 44.83%.
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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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The range of doses for Losartan per day is 70 to 90 milligrams. What would be the corresponding range for doses in micrograms?
The corresponding range for Losartan doses in micrograms is 70,000 to 90,000 micrograms per day.
To convert the range of Losartan doses from milligrams to micrograms, we need to multiply the milligram values by 1,000.
The lower end of the range, 70 milligrams, can be converted to micrograms by multiplying it by 1,000: 70 mg * 1,000 = 70,000 micrograms.
Similarly, the upper end of the range, 90 milligrams, can be converted to micrograms: 90 mg * 1,000 = 90,000 micrograms.
Therefore, the corresponding range for Losartan doses in micrograms is 70,000 to 90,000 micrograms per day. This means that the dosage range for Losartan can vary from 70,000 micrograms to 90,000 micrograms per day, depending on the specific prescription or treatment plan.
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x(a-b)+2=c(x+3)-dsolve the equation for the variable x in terms of a,b,c, and d.
To solve the equation [tex]\(x(a-b) + 2 = c(x+3) - d\)[/tex] for the variable [tex]\(x\)[/tex] in terms of [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex], we can follow these steps:
1. Expand the equation by distributing the terms on both sides:
[tex]\(xa - xb + 2 = cx + 3c - d\)[/tex]
2. Rearrange the equation by isolating the terms containing [tex]\(x\)[/tex] on one side:
[tex]\(xa - cx = xb - d - 3c + 2\)[/tex]
3. Factor out [tex]\(x\)[/tex] on the left side of the equation:
[tex]\(x(a - c) = xb - d - 3c + 2\)[/tex]
4. Divide both sides of the equation by [tex]\((a - c)\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\(x = \frac{{xb - d - 3c + 2}}{{a - c}}\)[/tex]
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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.
Chloe wants to buy a hoodie that costs $\$32.75$. She empties her wallet and finds she only has three $\$10$ bills, eight quarters, and a pile of dimes. What is the minimum number of dimes that must be in her pile so she can pay for the hoodie?
Chloe wants to buy a hoodie that costs $\$32.75$. She empties her wallet and finds she only has three $\$10$ bills, eight quarters, and a pile of dimes. Thus, she needs at least 8 dimes to be able to pay for the hoodie. She needs at least 8 dimes in her pile so she can pay for the hoodie.
We are required to find the minimum number of dimes that must be in her pile so she can pay for the hoodie. Let us start the solution with the conversion of the given $\$10$ bills into dollars.The three $\$10$ bills are worth $\$30$ in total. She needs $\$2.75$ to be able to pay for the hoodie. To avoid having any extra cents left, we should use only quarters and dimes in this purchase. Let d be the number of dimes needed.Then, the number of quarters needed is equal to (275 − 10d)/25. Since the number of quarters is given to be 8, we can use this to form the equation: (275 − 10d)/25 = 8Multiplying both sides of the equation by 25, we have:275 − 10d = 200d = (275 − 200)/10= 7.5She needs at least 7.5 dimes to pay for the hoodie, which is not possible.
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The minimum number of dimes that must be in her pile so she can pay for the hoodie is 297 dimes.
Given that Chloe wants to buy a hoodie that costs 32.75.
She empties her wallet and finds she only has three $10$ bills, eight quarters, and a pile of dimes.
We need to find the minimum number of dimes that must be in her pile so she can pay for the hoodie.
In order to solve this, we first need to convert the given amount into cents.
Since, there are three $10 dollar bills, then the total amount of money Chloe has is:
[tex]$\text{Total money}= 3 \times 10 + 8 \times 25 = 305$[/tex] cents
Chloe needs 3275 cents to pay for the hoodie.
Therefore, the minimum number of dimes that must be in her pile so she can pay for the hoodie is:
[tex]$\frac{3275 - 305}{10} = 2970/10 = \boxed{297}$[/tex] dimes.
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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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write the equation of a line perpendicular to 2x+5y=10 that passes through (10,-3)
The equation of the line perpendicular to 2x + 5y = 10 that passes through the point (10, -3) is y = (-5/2)x + 22.
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line has the equation: 2x + 5y = 10.
First, let's rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope:
2x + 5y = 10
5y = -2x + 10
y = (-2/5)x + 2/5
From this equation, we can see that the slope of the given line is -2/5.
To find the slope of the line perpendicular to this line, we take the negative reciprocal of -2/5. The negative reciprocal is obtained by flipping the fraction and changing its sign:
Negative reciprocal of -2/5: -(5/2) = -5/2.
So, the slope of the line perpendicular to 2x + 5y = 10 is -5/2.
Now we have the slope (-5/2) and a point (10, -3) that the line needs to pass through. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) represents the given point and m is the slope.
Using the point (10, -3) and the slope -5/2, we can substitute the values into the equation:
y - (-3) = (-5/2)(x - 10)
y + 3 = (-5/2)(x - 10)
To simplify further, we distribute -5/2:
y + 3 = (-5/2)x + 25
y = (-5/2)x + 22
Therefore, the equation of the line perpendicular to 2x + 5y = 10 that passes through the point (10, -3) is y = (-5/2)x + 22.
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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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James has a balance of $1,230 on his credit card that has an APR of 24%. He currently pays the minimum monthly payment of $30. 75. If James wants to pay off his balance in 18 months, determine the monthly payment he would need to make. Choose the following modification with the least cuts to his current expenses that will allow James to pay off his balance in 18 months. Income Wages $3,015. 00 Expenses Rent $1250. 00 Utilities $432. 45 Food/Clothes $345. 00 Entertainment $255. 00 Car $360. 00 Credit Card $30. 75 Cell Phone $103. 89 Net Income $237. 91 a. James can eliminate $83 from Food/Clothes. B. James can eliminate $25 from Food/Clothes and $27 from Entertainment. C. Addison can eliminate $15 from Food/Clothes and $22 from Entertainment. D. The minimum payment is enough to pay off the balance within 24 months.
To pay off his credit card balance of $1,230 with a 24% APR in 18 months, James needs to increase his monthly payment. The least impactful modification to his expenses would be to eliminate $83 from Food/Clothes.
James currently pays the minimum monthly payment of $30.75, which is not sufficient to pay off his balance in the desired timeframe. To determine the monthly payment required, we need to calculate the interest accrued over 18 months. The formula to calculate monthly interest is (APR/12) * balance. In this case, the monthly interest would be (24%/12) * $1,230 = $24.60.
To pay off the balance within 18 months, James needs to cover both the monthly interest and reduce the principal amount. Let's assume the monthly payment is P. Each month, James will pay P - $24.60 towards the principal. Since he wants to pay off the balance in 18 months, the equation becomes: 18 * (P - $24.60) = $1,230.
Simplifying the equation, we get 18P - $442.80 = $1,230. Rearranging and solving for P, we find that James needs to make a monthly payment of approximately $94.04.
Among the given options, the least impactful modification to James' expenses would be to eliminate $83 from Food/Clothes, which would cover most of the increased monthly payment.
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The total cost for Baydan and three of her friends to go ice skating and be represented by the expression 4x+36 the four friends pay and amount x to rent the ice skates and admission fee. How much is the admission fee for one person?
We know that the total cost for all four friends is 4x + 36, so we can set up an equation: 4x + 4a = 4x + 36 Subtracting 4x from both sides: 4a = 36 Dividing both sides by 4: a = 9.
Therefore, the admission fee for one person is 9.
In the given expression 4x + 36, the term 4x represents the amount each friend pays for renting the ice skates, and the constant term 36 represents an additional cost or admission fee for all four friends.
To find the admission fee for one person, we need to divide the constant term 36 by the number of friends, which is 4.
Admission fee for one person = 36 / 4
Calculating this expression, we get:
Admission fee for one person = 9
Therefore, the admission fee for one person is 9.
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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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A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay. excluding tax, for the shirt?
The customer will pay 0.85x - 5 dollars for the shirt. This is calculated by taking 15% off the original price (0.85x) and subtracting the coupon amount of 5 dollars.
To calculate the price the customer will pay for the shirt, we need to consider the original price, the discount percentage, and the coupon.
Let's denote the original price of the shirt as x dollars. The sale price after a 15% discount would be (100% - 15%) of x, which can be expressed as 0.85x dollars.
Next, the customer has a coupon for 5 dollars off the sale price. Therefore, the final price the customer will pay is the sale price minus the coupon amount. It can be expressed as 0.85x dollars - 5 dollars.
So, the price the customer will pay for the shirt, excluding tax, is given by the expression 0.85x - 5 dollars.
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Weights of newborn babies are skewed-right with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. What percent of newborn babies would have weights between 5.1 pounds and 9.9 pounds?
Approximately 95.44% of newborn babies would have weights between 5.1 pounds and 9.9 pounds.
To find the Percentage of newborn babies with weights between 5.1 pounds and 9.9 pounds, we can use the z-score formula and the z-score table.
Given:
x₁ = 5.1 pounds
μ = 7.5 pounds
σ = 1.2 pounds
Calculating the z-scores:
z₁ = (x₁ - μ) / σ
z₁ = (5.1 - 7.5) / 1.2
z₁ = -2.0
x₂ = 9.9 pounds
z₂ = (x₂ - μ) / σ
z₂ = (9.9 - 7.5) / 1.2
z₂ = 2.0
Using the z-score table, we can find the probabilities associated with these z-scores.
The z-score of -2.0 corresponds to a probability of 0.0228, and the
z-score of 2.0 corresponds to a probability of 0.9772.
To find the percentage of newborn babies with weights between 5.1 pounds and 9.9 pounds, we subtract the probability of 5.1 pounds and less from the probability of 9.9 pounds and less:
P(5.1 ≤ x ≤ 9.9) = P(x ≤ 9.9) - P(x ≤ 5.1)
= 0.9772 - 0.0228
= 0.9544
Multiplying this result by 100, we find that approximately 95.44% of newborn babies would have weights between 5.1 pounds and 9.9 pounds.
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The dealership bought a used car for $3,200 and sold the car for $8,950. What percentage was the mark-up? Round to the nearest tenth of a percent.
To calculate the mark-up percentage, we need to find the difference between the selling price and the buying price, and then express that difference as a percentage of the buying price.
Buying price: $3,200
Selling price: $8,950
Mark-up = Selling price - Buying price = $8,950 - $3,200 = $5,750
Now, we'll calculate the mark-up percentage:
Mark-up percentage = (Mark-up / Buying price) * 100
Mark-up percentage = ($5,750 / $3,200) * 100 = 179.6875
Rounding to the nearest tenth of a percent, the mark-up percentage is approximately 179.7%.
Therefore, the mark-up percentage for the used car is 179.7%.
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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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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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Suppose that y is directly proportional to x and that y = 28 when x = 7. Find the constant of proportionality k. Then, find y when x = 16.
Given that y is directly proportional to x and y = 28 when x = 7, we need to find the constant of proportionality (k). Then, we can use this constant to find the value of y when x = 16.
When two variables, y and x, are directly proportional, their relationship can be expressed as y = kx, where k is the constant of proportionality.
Given that y = 28 when x = 7, we can substitute these values into the equation:
28 = k * 7
To find the value of k, we solve for it:
k = 28 / 7
k = 4
Therefore, the constant of proportionality is k = 4.
Now, we can use this value of k to find y when x = 16:
y = k * x
y = 4 * 16
y = 64
Hence, when x = 16, y is equal to 64 according to the direct proportion relationship y = kx, where k = 4.
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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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Determine the period. Acellus
Answer: 15
Step-by-step explanation:
Period=distance between 2 top points.
15
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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The number of miles, m, a car can travel varies directly with the amount of gas, g, in
its fuel tank. If k is the constant of variation, which equation represents that
situation?
A)m = g+
B)m = kg
k
C)m
9
Dm =
9
k
The equation that represents the situation where the number of miles a car can travel varies directly with the amount of gas in its fuel tank is option B: m = kg.
In a direct variation, the relationship between two variables can be expressed using the equation y = kx, where y represents the dependent variable, x represents the independent variable, and k is the constant of variation. In this case, the number of miles, m, is the dependent variable, and the amount of gas, g, is the independent variable.
The equation m = kg represents the direct variation between m and g, where k is the constant of variation. This means that for every unit increase in g, there will be a corresponding unit increase in m, and the ratio between m and g will remain constant.
Options A, C, and D do not correctly represent the concept of direct variation. Option A is missing the constant of variation, option C uses a constant value of 9 instead of k, and option D has the incorrect placement of variables and constant.
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