a person standing 20 feet from a street light casts a shadow as shown. how many times taller is the streetlight than the person? assume the triangles are similar.
Using the concept of similar triangles to calculate the scale factor, the height of the streetlight is 3 times the height of the person.
Length of shadow cast = 10 feets
Height of person = 6 feets
Distance of person from streetlight light = 20 feets
Since the triangles are similar :
Comparing the length of both triangles :
Bigger triangle = 30 feets Smaller triangle = 10 feetsThe scale factor is :
(Bigger triangle / Smaller triangle) = (30/10) = 3 Therefore, the scale factor is 3Using the scale factor ; the height of the streetlight will be :
Height of person × 3 = 6 feets × 3 = 18 feetsHeight of streetlight = 18 feets
Height of person = 6 feets
Therefore, the streetlight is (18/6 = 3) 3 times the height of the person.
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The price of a radio was lowered by $6, then raised by $3. If the original price was $45, what is the current price?
$7.50 for 5 pounds ?
The graph shows the relationship between the distance a truck can travel and the amount of gasoline used. (5,35) What is the unit rate for the distance traveled to the amount of gasoline used? (1,7) Enter your answer in the box. mpg
Answer:
y=7x or the answer is 7
Step-by-step explanation:
i took the test in (k12)
If a and b are both positive numbers and a < b, what must be true about their absolute values?
a bike race is 6 miles long by noon tammy had ridden 3/4 of the distance. at this rate how long will it take her to finish the race.
Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3200 + 9x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $150 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
Final Answer:
The revenue function is R(x) = 150x.
The profit function is P(x) = -0.1x² + 141x - 3200.
To make a profit, Gymnast Clothing should manufacture between approximately 23.07 and 1386.93 pairs of cleats. Because they cannot manufacture a fraction of a cleat, they should manufacture at least 24 pairs and no more than 1386 pairs.
Explanation:
Let's start by defining the revenue and profit functions for Gymnast Clothing.
**Revenue Function:**
The revenue function, R(x), is calculated by multiplying the number of cleats sold, x, by the selling price per pair of cleats. Since Gymnast Clothing sells cleats at $150 per pair, the revenue function is:
R(x) = 150x
**Cost Function:**
The cost function, C(x), is given as:
C(x) = 3200 + 9x + 0.1x²
**Profit Function:**
The profit function, P(x), represents the money made after subtracting costs from the revenue. It's defined as the difference between the revenue function and the cost function:
P(x) = R(x) - C(x)
Substitute R(x) with the revenue function and C(x) with the cost function to get:
P(x) = 150x - (3200 + 9x + 0.1x²)
Simplify the profit function by combining like terms:
P(x) = -0.1x² + 141x - 3200
This is the profit function, which tells us how the profit varies with the number of x pairs of cleats manufactured and sold.
**Determining the Number of Cleats to Manufacture for Profit:**
To figure out how many cleats Gymnast Clothing should manufacture to make a profit, we need to determine when the profit P(x) is greater than zero:
P(x) > 0
In other words, we want to find the values of x for which:
-0.1x² + 141x - 3200 > 0
Solving this inequality for x gives us the interval within which manufacturing the cleats will be profitable. Based on the solution to the inequality, the number of pairs of cleats that Gymnast Clothing should manufacture to make a profit is between approximately 23.07 and 1386.93 pairs.
Summary:
- The revenue function is R(x) = 150x.
- The profit function is P(x) = -0.1x² + 141x - 3200.
- To make a profit, Gymnast Clothing should manufacture between approximately 23.07 and 1386.93 pairs of cleats. Because they cannot manufacture a fraction of a cleat, they should manufacture at least 24 pairs and no more than 1386 pairs.
Revenue: [tex]\( R(x) = 150x \)[/tex]. Profit: [tex]\( P(x) = -0.1x^2 + 141x - 3200 \).[/tex] Solve [tex]\(-0.1x^2 + 141x - 3200 > 0\)[/tex] for profit.
To find the exact values for the revenue and profit functions, we'll use the given cost function and selling price.
1. Revenue Function [tex](\(R(x)\))[/tex]: The revenue is given by the product of the number of units sold [tex](\(x\))[/tex] and the selling price per unit[tex](\$150):[/tex] [tex]\[ R(x) = 150x \][/tex]
2. Profit Function [tex](\(P(x)\)):[/tex] The profit is the difference between revenue and cost: [tex]\[ P(x) = R(x) - C(x) \][/tex]
Given that the cost function is [tex]\(C(x) = 3200 + 9x + 0.1x^2\),[/tex] we substitute this into the profit function: [tex]\[ P(x) = 150x - (3200 + 9x + 0.1x^2) \][/tex]
Simplify the expression:
[tex]\[ P(x) = -0.1x^2 + 141x - 3200 \][/tex]
So, the exact functions are:
1. Revenue Function: [tex]\[ R(x) = 150x \][/tex]
2. Profit Function: [tex]\[ P(x) = -0.1x^2 + 141x - 3200 \][/tex]
To find how many cleats Gymnast Clothing should manufacture to make a profit, we set the profit function greater than zero and solve for x: [tex]\[ -0.1x^2 + 141x - 3200 > 0 \][/tex]
Solving this inequality will provide the exact values of x for which the company makes a profit within the given range [tex]\(0 \leq x \leq 500\)[/tex]. This involves factoring, using the quadratic formula, or graphing to determine the valid range of x values for profit.
If g (n)n-2, then what is the value of g(10)?
What is 1.888 as a mixed number
We have that 1.888 as a mixed number is
[tex]\frac{9}{5}=1\frac{4}{5}[/tex]
From the Question we are told that
1.888 is given
Generally
[tex]1.8888 \approx\frac{9}{5}[/tex]
Therefore
the Mixed number is given as
[tex]\frac{9}{5}=1\frac{4}{5}[/tex]
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Which numbers are a distance of 3.2 units from −4 on a number line?
9514 1404 393
Answer:
-7.2, -0.8
Step-by-step explanation:
Those numbers are ...
-4 ± 3.2 = {-4 -3.2, -4 +3.2} = {-7.2, -0.8}
The numbers -7.2 and -0.8 are a distance of 3.2 from -4 on the number line.
(-16)^-2 = please help
At the end of the day, a pharmacist counted and found she has 4/3 as many prescriptions for antibiotics as she did tranquilizers. She had 84 prescriptions for the two types of drugs. How many prescriptions did she have for tranquilizers?
By using algebra to model the problem, we find that the pharmacist had 36 prescriptions for tranquilizers.
Explanation:In the given problem, we need to find out the number of prescriptions for tranquilizers. We know that the pharmacist has 4/3 as many prescriptions for antibiotics as tranquilizers. We also know that the total number of prescriptions for both the drugs is 84. We can make a mathematical model out of this information and solve for the number of tranquilizer prescriptions.
Let us suppose the number of tranquilizer prescriptions is x. Then the number of antibiotic prescriptions would be 4/3*x. Together, these prescriptions add up to 84.
So, we can write the equation: x + 4/3*x = 84
To make the equation simpler we can multiply the entire equation by 3 which transforms the equation into: 3x + 4x = 252
Combining like terms gives us: 7x = 252
Finally, dividing both sides of the equation by 7 gives us the solution: x = 252 / 7
So, x = 36
Therefore, we conclude that the pharmacist had 36 prescriptions for tranquilizers.
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What adds to be the bottom number but also multiplies to be the top?
The student is asking about fractions. In a fraction, the denominator (bottom number) represents the total number of equal parts the whole is divided into, while the numerator (top number) signifies the parts we're considering. When multiplying, the numerators and denominators multiply separately to form the new fraction.
Explanation:The student is referring to the concept of fractions. In a fraction, the number on the bottom (the denominator) is the total number of equal parts into which a whole is divided, and the number on the top (the numerator) is the number of those parts we are considering. To clarify by using an example, let’s take 2/4. In this scenario, the denominator is 4, which means our whole is divided into 4 equal parts. The numerator is 2, which shows that we're referring to 2 out of those 4 parts. When multiplying fraction, the numerators multiply to create the new numerator and denominators multiply to create the new denominator. Hence, 2/4 multiplied with 3/4 would produce 6/16.
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helppppppppppppppppppppppp
lots of points
first number is x , second number is y
y = x-6
so answer is B 22-6 = 16
B (22,16)
What is the greatest common divisor of 8, 16, and 24?
Alan needs 36 quarts of paint to paint the basement of his house. If 1 gallon is equal to 4 quarts, how many gallons of paint should Alan buy?
4 gallons
9 gallons
18 gallons
36 gallons
How do u use 18,801,310 in expanded from using exponents
Daphne wants to buy a coat that cost $80. The store that sells the coat has multiple locations. The sales tax in each county is shown in the table. How much more would the coat cost in Delaware county than Fairfield county? Delaware tax rate is 7.25 Fairfield tax rate is 6.5 Franklin tax rate is 6.75
The coat would cost $0.60 more in Delaware County than in Fairfield County.
To determine how much more the coat would cost in Delaware County compared to Fairfield County, we need to calculate the total cost of the coat in both counties, including their respective sales tax rates, and then find the difference between these two amounts.
First, let's calculate the total cost of the coat in Delaware County:
1. Original price of the coat: $80
2. Sales tax rate in Delaware County: 7.25%
The sales tax amount in Delaware County is calculated as:
[tex]\[\text{Sales tax} = \text{Original price} \times \left(\frac{\text{Sales tax rate}}{100}\right) = 80 \times \left(\frac{7.25}{100}\right) = 80 \times 0.0725 = 5.80\][/tex]
So, the total cost in Delaware County is:[tex]\[\text{Total cost} = \text{Original price} + \text{Sales tax} = 80 + 5.80 = 85.80\][/tex]
The sales tax amount in Fairfield County is calculated as:
[tex]\[\text{Sales tax} = \text{Original price} \times \left(\frac{\text{Sales tax rate}}{100}\right) = 80 \times \left(\frac{6.5}{100}\right) = 80 \times 0.065 = 5.20\][/tex]
So, the total cost in Fairfield County is:
[tex]\[\text{Total cost} = \text{Original price} + \text{Sales tax} = 80 + 5.20 = 85.20\][/tex]
Now, let's find the difference in total costs between Delaware County and Fairfield County:
[tex]\[\text{Difference} = \text{Total cost in Delaware County} - \text{Total cost in Fairfield County} = 85.80 - 85.20 = 0.60\][/tex]
kens new car goes 26 miles per gallon of gasoline. the cars tank holds 14 gallons. how far will ken be able to drive on a full tank of gas
The temperature of a freezer started at 18 degrees celsius. After cooling for a few hours, the freezer had a temperature of -12 degrees celsius. What is the difference between the new and colder temperature of the original temperature
The freezer's temperature decreased by 30 degrees Celsius from its original temperature of 18 degrees Celsius to reach -12 degrees Celsius.
The temperature change in the freezer is calculated by finding the difference between the final temperature and the initial temperature.
In this case, the freezer started at 18 degrees Celsius and cooled down to -12 degrees Celsius.
To determine the difference, subtract the initial temperature from the final temperature:
-12 degrees Celsius (final temperature) - 18 degrees Celsius (initial temperature) = -30 degrees Celsius.
The negative sign indicates a decrease in temperature.
Therefore, the temperature of the freezer decreased by 30 degrees Celsius.
This temperature change represents the amount by which the freezer's internal temperature dropped during the cooling process.
It's crucial to note that the negative value signifies a colder temperature than the initial state.
The cooling process might be influenced by factors such as the freezer's capacity, insulation, and cooling mechanism.
Temperature changes is essential for various applications, including food preservation and scientific experiments where precise temperature control is crucial.
The freezer experienced a temperature decrease of 30 degrees Celsius, resulting in a colder temperature of -12 degrees Celsius from its initial state of 18 degrees Celsius.
how can the statement below be rewritten as a conditional statement in if-then form? Two angles with angle measures that add up to 180 degrees form a linear pair.
A) If two angles form a linear pair, then one of their angle measures is 180 degrees.
B) If a linear pair has angle measures that add up to 180 degrees, then there are more than two angles.
C) If the measures of two angles add up to 180 degrees, then they form a linear pair.
D) If there are two angles, then their angle measures must add up to 180 degrees.
C) If the measures of two angles add up to 180 degrees, then they form a linear pair.
The statement below be rewritten as a conditional statement If the measures of two angles add up to 180 degrees, then they form a linear pair. Option C is correct.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Rewrite the following sentence into a conditional statement. A linear pair is created when the measurements of two angles sum up to 180 degrees.
Hence,option C is correct.
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Which statement is true regarding the given logical statement? If a number is a square number then 1, then it has at least one factor other than 1 and itself.
A) An equivalent statement is "all numbers having at least one factor other than 1 and itself are square numbers."
B) The hypothesis is "a number is a square number greater than 1."
C) The conclusion is "a number is a square number greater than 1."
D) A counterexample for this conditional statement is 49.
Answer: B
Step-by-step explanation: B
The correct statement is B) The hypothesis is 'a number is a square number greater than 1.' This correctly identifies the 'if' part of the logical statement, whereas A), C) and D) are incorrect interpretations.
Explanation:The given logical statement is 'If a number is a square number then it has at least one factor other than 1 and itself.' In examining the answer choices, 'B) The hypothesis is "a number is a square number greater than 1." correctly identifies the hypothesis or the 'if' part of the logical statement. A) is incorrect as it reverses the conditions and conclusions. C) is incorrect as the conclusion is the part following 'then' and D) is incorrect as 49, being a square number, upholds the conditions stated in the logical statement, and thus cannot be a counterexample.
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W at is 1/8 in decimal form
A local hamburger shop sold a combined total of 622 hamburgers and cheeseburgers on Sunday. There were 72 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Sunday?
you are making balloon arrangements for a birthday party. There are 16 white balloons and 24 red balloons . Each arrangement must be identical .What is the greatest number of arrangements you can make using every balloon
The greatest number of arrangements using every balloon is an illustration of the highest common factors (HCF).
The greatest number of arrangements you can make using every balloon is 8.
Given that:
[tex]White = 16[/tex]
[tex]Red = 24[/tex]
To determine the greatest number of arrangements, we simply calculate the HCF of 16 and 24.
We have:
[tex]16 = 2\times 2\times 2 \times 2[/tex]
[tex]24 = 2\times 2\times 2 \times 3[/tex]
The highest common factor is:
[tex]HCF =2 \times 2 \times 2[/tex]
[tex]HCF =8[/tex]
Hence, the greatest number of arrangements you can make using every balloon is 8.
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Can I get help please!!
What's more precise 11ft:122in
help me plz I don't understand
hans made $264 for 12 hours of work. at the same rate, how many hours would he have to work to make $198
Which pair of numbers have a greatest common factor of 2?
Select each correct answer.
4 and 6
10 and 2
6 and 12
2 and 24
Except for pair (6, 2), all pairs (4, 6), (10, 2), and (2, 24) have the greatest common factor of 2.
Given that,
Which pair of numbers have the greatest common factor of 2 from the options is to be determined.
The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers includes.
Here,
The greatest common factor of 4 and 6 is 2.
The greatest common factor of 10 and 2 is 2.
The greatest common factor of 6 and 12 is 6.
The greatest common factor of 2 and 24 is 2.
Thus, except pairs 6 and 12 all pairs (4, 6), (10, 2), and (2, 24) has greatest common factor of 2.
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