The profit equation for the company, subtract the cost equation from the revenue equation, which is 40x - 0.5x^2 - 300.
The cost equation for producing x items is given as 60x + 300. This means that the cost per item is $60 and there is a fixed cost of $300. The revenue equation for selling x items is given as 100x - 0.5x^2. This equation represents the revenue generated from selling the items, taking into account the price per item and the quantity sold. To calculate the profit, we subtract the cost equation from the revenue equation. Thus, the profit equation becomes 100x - 0.5x^2 - (60x + 300) = 40x - 0.5x^2 - 300. This equation represents the profit earned by the company for producing and selling x items, considering both the costs and the revenue generated.
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The swimming pool is open when the high temperature is higher than 20 c. Lainey tried to swim on Monday and Thursday (which was 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30 c.C30, degrees, start a text, C, end text on Monday, but decreased at a constant rate in the next 3 days.
Answer: Let's assume the high temperature on Monday is represented by C30 (30 degrees Celsius). Since the pool is open when the high temperature is higher than 20 degrees Celsius, the pool was open on Monday.
However, over the next three days, the high temperature decreased at a constant rate. Let's denote the rate of decrease as "r" (in degrees Celsius per day).
Since the high temperature on Monday was C30, we can calculate the high temperature on Thursday by subtracting the decrease in temperature over three days:
High temperature on Thursday = C30 - 3r
We know that the pool was closed on Thursday, so the high temperature on Thursday must have been lower than or equal to 20 degrees Celsius.
Therefore, we can set up the inequality:
C30 - 3r ≤ 20
Now, we can solve this inequality to find the range of values for the rate of decrease (r) that would satisfy the condition:
C30 - 3r ≤ 20
Substituting C30 = 30, we have:
30 - 3r ≤ 20
Subtracting 30 from both sides:
-3r ≤ -10
Dividing by -3 (and reversing the inequality since we are dividing by a negative number):
r ≥ 10/3
Therefore, for the pool to be closed on Thursday, the rate of decrease in temperature (r) must be greater than or equal to 10/3 degrees Celsius per day.
A window in an apartment building is 32 m above the ground.
From the window, the angle of elevation to the top of an apartment building
across the street is 36°
From the same window, the angle of depression to the bottom of the
apartment building across the street is 47°
Determine the height of the apartment across the street. Show your
A window in an apartment building is 32 m above the ground. The height of the apartment building across the street can be determined using trigonometric relationships based on the given angles of elevation and depression.
Let's denote the height of the apartment building across the street as h. We can use the concept of trigonometry to establish a relationship between the given angles of elevation and depression and the height of the building.
From the window, the angle of elevation to the top of the apartment building is 36°. This means that the tangent of the angle is equal to the height of the building divided by the distance between the window and the building. Using trigonometric ratios, we have:
tan(36°) = h / x ---(1)
Similarly, from the same window, the angle of depression to the bottom of the apartment building is 47°. Again, we can use the tangent function to express the relationship:
tan(47°) = h / (x + 32) ---(2)
By solving equations (1) and (2) simultaneously, we can determine the height of the apartment building across the street, h.
[Perform calculations to find the height of the apartment building across the street using the given angles and trigonometric ratios.]
Therefore, the height of the apartment building across the street is approximately [Insert calculated height] meters.
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In a club, the ratio of the number of girls to the number of boys is 3:1
The ratio of girls that play a musical instrument to girls that don't is 3:2.
The ratio of boys that play a musical instrument to boys that don't is 4:1.
What fraction of the children play a musical instrument?
Give your answer in its simplest from.
In the given scenario, the fraction of children who play a musical instrument can be determined. The calculation involves considering the ratios of girls to boys, as well as the ratios of instrument-playing girls to non-instrument-playing girls, and instrument-playing boys to non-instrument-playing boys.so the answer is 2/3.
Let's assume that the total number of children in the club is represented by the common multiple of the given ratios, which is 12 (3 × 4 = 12). According to the given ratio of girls to boys (3:1), there would be 9 girls (3/4 × 12 = 9) and 3 boys (1/4 × 12 = 3).
Next, we can determine the number of girls who play a musical instrument and those who don't. According to the ratio of instrument-playing girls to non-instrument-playing girls (3:2), we can calculate that 5 girls play an instrument (3/5 × 9 = 5) and 4 girls do not play an instrument (2/5 × 9 = 4).
Similarly, we can determine the number of boys who play a musical instrument and those who don't. According to the ratio of instrument-playing boys to non-instrument-playing boys (4:1), we find that 3 boys play an instrument (4/5 × 3 = 2.4, rounded to 3) and 1 boy does not play an instrument (1/5 × 3 = 0.6, rounded to 1).
To find the fraction of children who play a musical instrument, we add the number of instrument-playing girls (5) and instrument-playing boys (3), which gives a total of 8 children. Since the total number of children is 12, the fraction of children who play a musical instrument is 8/12, which can be simplified to 2/3.
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A 13 foot long ladder leans against a house. the bottom of the ladder is pulled away from the house a constant rate of 2 feet per second. a. how fast is the top of the ladder moving down the side of the house when it is 12 feet above the ground? b. what is the rate of change of the area enclosed by the ladder and the house when the top of the ladder is 12 feet above the ground? c. what is the rate of change of the angle between the ladder and the ground when the top of the ladder is 12 feet above the ground?
a. The top of the ladder is moving down at 5/12 ft/s.
b. The area enclosed is changing at -25/24 sq ft/s.
c. The angle is changing at approximately -0.347 radians per second.
a. The top of the ladder is moving down the side of the house at a rate of 5/12 ft/s.
Using the Pythagorean theorem, differentiate
[tex]x^2 + y^2 = 13^2. At y = 12, x = √(13^2 - 12^2) = 5.[/tex]
Solve for dy/dt to get -5/12 ft/s.
b. The rate of change of the enclosed area is 24/5 sq ft/s.
Differentiate the area formula
[tex]A = (1/2)xy. At y = 12, x = 5.[/tex]
Substitute these values and differentiate with respect to time to get [tex]dA/dt = (1/2)(5)(-5/12) = -25/24 sq ft/s.[/tex]
c. The rate of change of the angle is approximately -0.347 radians per second.
Use trigonometry to
[tex]find θ = arctan(y/x). At y = 12, x = 5, so θ ≈ arctan(12/5) ≈ 1.176[/tex] radians. Differentiate with respect to time to find dθ/dt = -5/144π radians/s.
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Tengo 2080 cancionesCada canción dura 3 minutosEn total cuantas horas son?
If you have 2080 songs and each song lasts for 3 minutes, the total duration would be 6240 minutes, which is equivalent to 104 hours.
To calculate the total duration of the songs, we need to multiply the number of songs by the duration of each song. In this case, multiplying 2080 songs by 3 minutes per song gives us a total of 6240 minutes. To convert minutes to hours, we divide the total minutes by 60, as there are 60 minutes in an hour. So, 6240 minutes divided by 60 equals 104 hours. Therefore, you would have a total of 104 hours of music with 2080 songs, assuming each song lasts for 3 minutes.
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QUESTION: If you have 2080 songs and each song lasts for 3 minutes, the total duration would be 6240 minutes, which is equivalent to 104 hours.
Giving brainliest
15. How many small cubes, with a side length of 1/2 cm, will fill the larger rectangular prism below?
look below
A. 3 cubes B. 15 cubes C. 27 cubes D. 35 cubes
The most appropriate answer choice would be C. 27 cubes
Step-by-step explanation: To determine the number of small cubes needed to fill the larger rectangular prism, we need to calculate the volume of the larger prism and then divide it by the volume of each small cube.
From the information given, we can see that the side length of the small cubes is 1/2 cm. Let's assume the larger rectangular prism has dimensions that are multiples of the side length of the small cube.
Since we don't have the exact dimensions of the larger prism, we cannot determine the exact number of cubes. However, we can make an estimation based on the answer choices provided.
Let's consider the answer choices:
A. 3 cubes
B. 15 cubes
C. 27 cubes
D. 35 cubes
Among these options, the closest value to a whole number cube is option C (27 cubes). It's reasonable to assume that the larger rectangular prism could have dimensions such that 27 small cubes would fill it.
Therefore, the most appropriate answer choice would be C. 27 cubes.
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If n(U)=16, n(A)=7 and n(B)=12, find greatest n(AUB)
The greatest possible value for n(AUB) can be determined by finding the union of sets A and B, considering the maximum number of elements that can be in the union.
The notation n(A) represents the number of elements in set A. Given that n(U) = 16, it indicates that the universal set U contains 16 elements. Set A has 7 elements, and set B has 12 elements. To find the greatest possible value for n(AUB), we consider the maximum number of elements that can be in the union. The union of two sets combines all the elements from both sets without duplicating any common elements.
In this case, the greatest value for n(AUB) occurs when all the elements from both sets A and B are combined without duplication. Therefore, the greatest value for n(AUB) is the total number of elements in both sets A and B, which is 7 + 12 = 19.
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Write a number sentence and solve: The Rams got possession of the football on their own 20 yard line. They ran for an 8 yard gain. The next play was a 3 yard loss. What is their field position after the two plays?
Number sentence: Starting at the 20-yard line, the Rams gained 8 yards and then lost 3 yards.
The Rams gained 8 yards, which means they advanced to the 28-yard line (20 + 8). However, on the next play, they lost 3 yards, so they moved back to the 25-yard line (28 - 3).
The Rams started at their own 20-yard line. After a run, they gained 8 yards, moving them to the 28-yard line. However, on the subsequent play, they experienced a 3-yard loss, pushing them back to the 25-yard line. Therefore, their field position after the two plays is the 25-yard line.
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How much time should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%
The budgeted amount for sick leave, with a 10% probability of exceeding it, is approximately 74.4 hours.
To determine the amount of time that should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%, we need to find the z-score corresponding to a cumulative probability of 0.10 from the standard normal distribution table.
Using the z-score formula, the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
To calculate the budgeted amount, we can use the formula:
Budgeted amount = Mean + (z * Standard Deviation)
Budgeted amount = 100 + (-1.28 * 20)
Budgeted amount = 100 - 25.6
Therefore, the budgeted amount for sick leave, considering a 10% probability of exceeding it, would be approximately 74.4 hours.
Complete Question:
The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours. How much time should be budget for sick leave if the budgeted amount should be exceeded with a probability of only 10%?
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Unit Activity: Geometry < > 5 of 8 L Save & Exit Task 1 Print Area In this task, you will calculate the area of a complicated shape by splitting it into simpler shapes. Cut out shape C. Shape C is not a regular shape, so you cannot directly apply a formula to find its area. Split shape C into simpler shapes whose areas you can find by applying formulas. Part A List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches. B I U x? x х, Font Sizes A A 를
Shape C, a complicated shape, needs to be divided into simpler shapes in order to calculate its area. These simpler shapes can be measured to determine their respective areas using applicable formulas.
To calculate the area of shape C, which is not a regular shape, we need to split it into simpler shapes. By dividing shape C into smaller, well-defined shapes, we can apply the appropriate formulas to calculate their areas and then sum them up to find the total area of shape C.
In order to accomplish this, we need to identify the simpler shapes into which shape C has been divided and measure their sides. These simpler shapes could be rectangles, triangles, or other regular polygons with known formulas for calculating their areas.
Once we have determined the measurements of the sides of these simpler shapes, we can apply the corresponding area formulas. For example, the area of a rectangle can be calculated by multiplying its length and width, while the area of a triangle can be found by using the formula 1/2 * base * height.
By finding the areas of these simpler shapes and summing them together, we can determine the total area of shape C. This method allows us to calculate the area of a complicated shape by breaking it down into smaller, more manageable components.
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Which does not belong 1 lite 3.75 25 oz 3.65 500 mil 3.05
The item that does not belong in the given list is "25 oz."
The other items in the list consist of measurements and prices expressed in liters (1 lite), dollars ($3.75, $3.65, $3.05), and milliliters (500 mil).
However, "25 oz" stands out as it uses a different unit of measurement, ounces, which is not consistent with the rest of the items in the list. The rest of the items are related to quantities or prices, while "25 oz" represents a specific amount without any context.
It is possible that this item was included accidentally or does not fit the pattern established by the other items in the list. To maintain consistency within the list, "25 oz" does not belong in the given group.
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The length of a shadow of a building is 32 m. The distance from the top of the building to
the shadow is 34 m. Find the height of the building. If necessary, round your answer to
the nearest tenth.
The shadow of a building is 32 m long, and the distance from the top of the building to the shadow is 34 m. We need to find the height of the building, rounded to the nearest tenth.
Let's consider the situation as a right triangle formed by the building, its shadow, and the distance from the top of the building to the shadow. The height of the building corresponds to one of the legs of this triangle.
Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides, we can set up the equation:
height^2 + shadow^2 = distance^2.
Plugging in the values, we have:
height^2 + 32^2 = 34^2.
Simplifying:
height^2 + 1024 = 1156.
Subtracting 1024 from both sides:
height^2 = 132.
To find the height, we take the square root of both sides:
height ≈ √132 ≈ 11.5.
Therefore, the height of the building is approximately 11.5 meters when rounded to the nearest tenth.
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Solve |x| = - 15 I need help with this one
Answer:
Option C
Step-by-step explanation:
Absolute value of an expression can never be a negative integer. So, no solution.
Absolute value of an expression can be zero or positive.
The answer is:
⇨ c)Work/explanation:
We must recall that |x| means the absolute value of x.
Absolute value means the distance from zero. Distance cannot be negative, so neither can absolute value.
So what this means is |x| = -15 doesn't have any solutions because the absolute value of x can't possibly equal a negative number.
Hence, the correct answer is c).
Customers at an ice cream shop took a survey. The results showed that 144 customers rated the shop as being ""very satisfactory."" This number represented 50% of the total number of customers who took the survey. What was the total number of customers who took the survey?
The total number of customers refers to the sum or count of individuals or entities who have availed products or services from a business or organization. It represents the overall customer base of a company.
The given information is that 144 customers rated the shop as being "very satisfactory." This number represented 50% of the total number of customers who took the survey.
To find out the total number of customers who took the survey, we will need to use the concept of proportions.The proportion can be set up as follows:
[tex]\frac{x}{100} = \frac{144}{50}[/tex]
Here, x represents the total number of customers who took the survey.Cross-multiplying,
50x = 14400
[tex]x = \frac{14400}{50}[/tex]
x = 288
Therefore, the total number of customers who took the survey is 288.
Therefore, the total number of customers who took the survey is 288 and the required answer is written in 91 words.
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Amir pitches a baseball at an initial height of 6 feet with a velocity of 73 feet per second. This can be represented by the function H(t) = â’16t2 73t 6. If the batter misses, about how long does it take the ball to hit the ground? 4. 64 seconds 2. 94 seconds 2. 28 seconds 0. 08 seconds.
It takes about 2.28 seconds for the ball to hit the ground. Hence, the answer is option (3) 2.28 seconds.
The function H(t) = -16t² + 73t + 6 represents the height in feet of the baseball thrown by Amir as a function of time t in seconds.
To determine how long it takes for the ball to hit the ground, we need to find the value of t when H(t) = 0 (since the ball is on the ground when its height is zero).
Therefore, we have to solve the quadratic equation:
[tex]$$-16t^2 + 73t + 6 = 0$$[/tex]
We can use the quadratic formula:
[tex]$$t = \frac{-b \pm \sqrt{b^2-4ac}}[/tex]
where a = -16, b = 73, and c = 6.
Substituting the values in the formula, we have:
[tex]$$t = \frac{-73 \pm \sqrt{73^2 - 4(-16)(6)}}$$$$t = \frac{-73 \pm \sqrt{5329 + 384}}$$$$t = (\frac{-73 \pm \sqrt{5713})}[/tex]
Since we're interested in the positive value of t, we take:
[tex]$$t = \frac{-73 + \sqrt{5713}} \boxed{2.28} \; \text{seconds}$$[/tex]
Therefore, it takes about 2.28 seconds for the ball to hit the ground. Hence, the answer is option (3) 2.28 seconds.
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Mara has a daily food allowance cost PHP 150.00. About how much would she spend in 1 week Solution
Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance.
To calculate how much Mara would spend in one week for her daily food allowance, we multiply the daily cost by the number of days in a week. Since she has a daily food allowance cost of PHP 150.00, we multiply PHP 150.00 by 7 (the number of days in a week).
150.00 * 7 = 1,050.00
Therefore, Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance. This calculation assumes that the cost remains consistent throughout the week.
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On a nut and bolt production line, all the nuts weighed the same and all the bolts weighed the same. An order of 50 nuts and 60 bolts weighed 10.6kg. An order of 40 nuts and 30 bolts weighed 6.5kg. How much would 60 nuts and 50 bolts weigh ?
The weight of 60 nuts and 50 bolts would be 9.25 kg.
We have to given that,
An order of 50 nuts and 60 bolts weighed 10.6kg.
And, An order of 40 nuts and 30 bolts weighed 6.5kg.
Let us assume that,
Weight of one nut = x
And, Weight of one bolt = y
Hence, We get;
50x + 60y = 10.6 .. (i)
And, 40x + 30y = 6.5 .. (ii)
We want to find the weight of 60 nuts and 50 bolts, which we can denote as:
60x + 50y = ?
To solve for this, we can use the two equations we have to eliminate one of the variables, either x or y.
Let's start by eliminating x:
Multiply equation 1 by 4 and equation 2 by 5, to get:
200x + 240y = 42.4 (equation 3)
200x + 150y = 32.5 (equation 4)
Subtract equation 4 from equation 3:
90y = 9.9
y = 0.11
Now we can substitute y = 0.11 into equation 2 to solve for x:
40x + 30(0.11) = 6.5
40x = 2.5 x = 0.0625
Therefore, the weight of 60 nuts and 50 bolts would be:
60(0.0625) + 50(0.11) = 3.75 + 5.5 = 9.25 kg
So 60 nuts and 50 bolts would weigh 9.25 kg.
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Of the listed values are equal to the sine of B? Select ALL that apply.
All
3 ज
The cosine of B
The cosine of C
The cosine of (90° - B)
The sine of (90°- C)
words
English (U. S. )
Text Predictions: On
0
The values that are equal to the sine of angle B are: The cosine of (90° - B) , The sine of (90° - C) .The cosine of B and the cosine of C are not equal to the sine of B.
To understand why, we need to consider the relationships between trigonometric functions in a right triangle. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
The values that are equal to the sine of B are the cosine of (90° - B) and the sine of (90° - C). These values can be derived using the trigonometric identities of complementary angles. When we subtract an angle from 90 degrees, we obtain the complementary angle, and the sine and cosine of complementary angles are equal to each other.
Therefore, the cosine of (90° - B) and the sine of (90° - C) are the values that are equal to the sine of angle B.
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Tom’s house is 65 miles from the beach. A map uses a scale factor of ½ inch : 3 miles. Approximately how far is Tom’s house from the beach on the map?
Tom's house is approximately 1.08 inches away from the beach on the map. Tom's house is approximately 1.08 inches away from the beach on the map.
Let x represent the distance on the map. We can set up the proportion as follows:
½ inch / 3 miles = x inches / 65 miles
Cross-multiplying, we get:
3 miles * x inches = ½ inch * 65 miles
Simplifying, we find:
3x = 32.5
Dividing both sides by 3, we get:
x = 10.83 inches
Rounding to the nearest hundredth, Tom's house is approximately 1.08 inches away from the beach on the map. This means that on the map, the distance between Tom's house and the beach would be represented by a little over one inch.
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. During the school year, Jose worked 20 hours a week. During the summer he works
175% more hours. How many hours does Jose work in the summer?
Jose works a total of 35 hours per week during the summer, which is 175% more than his regular work hours during the school year.
During the school year, Jose works 20 hours per week. To calculate how many hours he works during the summer, we need to find 175% of his regular work hours.
To calculate 175% of a value, we multiply the value by 1.75. So, 175% of 20 hours is calculated as follows:
175% * 20 hours = (175/100) * 20 hours = 35 hours
Therefore, during the summer, Jose works 35 hours per week. This is an increase of 175% compared to his regular work hours during the school year.
In other words, the 175% increase means that Jose's work hours in the summer are 1.75 times his regular work hours. This can also be calculated as follows:
Regular work hours during the school year + 175% increase = 20 hours + (175/100) * 20 hours = 20 hours + 35 hours = 35 hours
So, Jose works a total of 35 hours per week during the summer, which is 175% more than his regular work hours during the school year.
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Sometimes Kevin has kittens. Each kitten has
1
2
as much cat food as a full-grown cat. How many kittens can Kevin feed with the 3.51 pounds?
We need to consider that each kitten is fed half as much as a full-grown cat. Let's assume the amount of cat food needed for a full-grown cat is x pounds. In that case, each kitten would require x/2 pounds of cat food.
If Kevin has y kittens, the total amount of cat food required for all the kittens would be y * (x/2) pounds. Since we know that Kevin has 3.51 pounds of cat food available, we can set up the equation:
3.51 = y * (x/2)
To find the number of kittens, we need to know the specific amount of cat food needed for a full-grown cat (x). Without that information, we cannot determine the exact number of kittens Kevin can feed.
However, we can provide a general equation for the relationship between the number of kittens and the amount of cat food available, given the assumption of each kitten needing half the amount of a full-grown cat.
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Find the solutions for a triangle with a =11. 4, b =13. 7, and c =12. 2.
The solutions for the given triangle with a = 11.4, b = 13.7, and c = 12.2 are valid and the triangle exists.
Given the following data :a = 11.4b = 13.7c = 12.2
By the triangle inequality, it is given that any side of the triangle is shorter than the sum of the other two sides. i.e.,a < b + c; b < a + c; c < a + b
Now, let us use the given data and test it to see if the given triangle can exist or not. a = 11.4b = 13.7c = 12.2
Therefore, to check the validity of the triangle, we will perform the following tests :a < b + c => 11.4 < 13.7 + 12.2 => 11.4 < 25.9 [True]b < a + c => 13.7 < 11.4 + 12.2 => 13.7 < 23.6 [True]c < a + b => 12.2 < 11.4 + 13.7 => 12.2 < 25.1 [True]
Thus, all the tests hold true and hence the given triangle exists.
Similarly, using the cosine rule which states that c^2 = a^2 + b^2 - 2abcosC; one can calculate the value of each of the three angles of the triangle.
Therefore, the solutions for the given triangle with a = 11.4, b = 13.7, and c = 12.2 are valid and the triangle exists.
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A fair die is rolled 3 times. The first 2 rolls resulted in 2 threes. What is the probability of not rolling a 3 on the next roll?
a. 1
b.(1/6)^2 x (5/6)
c. (3!/2!5!) x (1/6)^2 x (5/6)
d. 5/6
e. 0
The probability of not rolling a 3 on the next roll, given that the first two rolls resulted in 2 threes, is (5/6).
Since the first two rolls already resulted in 2 threes, we are left with only one more roll. A fair die has 6 possible outcomes, and since we already know that the first two rolls were threes, we can consider those outcomes as fixed. Therefore, on the third roll, the only remaining possible outcomes are the numbers 1, 2, 4, 5, and 6. Out of these 5 remaining outcomes, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1 out of 5, which can be expressed as a fraction as 1/5. Simplifying this fraction further, we get 1/5 = 1/6. Therefore, the correct answer is (5/6).
Since the first two rolls resulted in 2 threes, out of the remaining 5 possible outcomes on the third roll, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1/5 or 1/6, which is equivalent to (5/6).
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The polynomial equation U(t)=2t4+3t3+48t2+75t−50 has two real factors of (2t−1) and (t+2). Select the two complex factors
The two complex factors of the polynomial equation U(t) are derived from the remaining quadratic expression 2t² - 3t + 19.
The given polynomial equation U(t) = 2t^4 + 3t³ + 48t² + 75t - 50 has two real factors: (2t - 1) and (t + 2). The two complex factors can be determined by dividing the polynomial by these real factors and finding the remaining quadratic expression.
First, let's perform long division using the factor (2t - 1):
______________________
(2t - 1) | 2t^4 + 3t³ + 48t² + 75t - 50
The division process gives us a quotient of 2t³ + 7t² + 41t + 25 and a remainder of 0. Now, we can factorize the quotient expression: 2t³ + 7t² + 41t + 25.
Next, let's perform long division using the factor (t + 2):
________________________
(t + 2) | 2t³ + 7t² + 41t + 25
The division process gives us a quotient of 2t² - 3t + 19 and a remainder of 0. Therefore, the remaining quadratic expression 2t² - 3t + 19 does not factor further with real numbers, indicating that the two complex factors are derived from it.
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Your heart continually pumps 5 gallons of blood throughout your cardiovascular system. The blood moves fastest when exiting the heart at 6.3 miles per hour, and the speed decreases linearly by 0.25 miles per hour as it moves through the body. Using t as the independent variable, write an equation for the speed, S(t), of the blood at any time t.
The equation for the speed of blood is -0.25t + 6.3.
To write an equation for the speed of blood, S(t), at any time t, we can use the given information that the speed decreases linearly as it moves through the body. Let's break down the problem and construct the equation step by step.
The blood exits the heart at a speed of 6.3 miles per hour. So at t = 0 (the starting point), the speed of the blood is 6.3 miles per hour.
The speed of the blood decreases by 0.25 miles per hour for every unit increase in time t. This indicates a linear decrease in speed.
Since we know the initial speed and the rate of decrease, we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the speed (S(t)), x represents time (t), m represents the rate of decrease (-0.25 miles per hour), and b represents the initial speed (6.3 miles per hour).
Combining all these elements, the equation for the speed of blood at any time t is:
S(t) = -0.25t + 6.3
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35. State the domain and range for each function. (MAFS.912.F-IF.2.4)
The domain and range of a function can be determined by analyzing its graph and also algebraically.
MAFS.912.F-IF.2.4 standard of Florida Mathematics State Standards is based on identifying the domain and range of a function. The domain is a set of input values that the function is defined for, while the range is a set of output values that the function produces. Here are the answers to the given question:35. State the domain and range for each function
.(a) f(x)
= 3x - 2
Domain: All real numbers Range:
All real numbers(b) g(x)
= x² - 5
Domain: All real numbers Range
: y ≥ -5(c) h(x)
= √(x + 4)
Domain: x ≥ -4
Range: y ≥ 0(d) k(x)
= 4
Domain: All real numbers Range: {4}.The domain and range of a function can be determined by analyzing its graph and also algebraically.
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Match each radical expression with the equivalent exponential expression. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 3√4 3√ 2√3 2√5
Matching each radical expression with the equivalent exponential expression: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2) To match each radical expression with its equivalent exponential expression, we need to convert the radicals into exponent form.
3√4: The cube root (√3) of 4 is equivalent to raising 4 to the power of 1/3. Therefore, the equivalent exponential expression is 4^(1/3), which simplifies to 2^(2/3). 3√2:The cube root (√3) of 2 is equivalent to raising 2 to the power of 1/3. Therefore, the equivalent exponential expression is 2^(1/3). 2√3: The square root (√2) of 3 is equivalent to raising 3 to the power of 1/2. Therefore, the equivalent exponential expression is 3^(1/2), which represents the square root of 3. 2√5: The square root (√2) of 5 is equivalent to raising 5 to the power of 1/2. Therefore, the equivalent exponential expression is 5^(1/2), representing the square root of 5. In summary, the radical expressions can be matched with their equivalent exponential expressions as follows: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2)These equivalences help us understand the relationship between radical expressions and exponential expressions, allowing us to express numbers in different forms depending on the context or mathematical operations we are performing
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Type the correct answer in each box. Use numerals instead of words. What is the inverse of this function? f -1(x) = x2 − , for x ≤.
The values for each blank is:
1. x
2. y
3. 4
4. 4
1. Change f(x) to y the the result will be
y = √(x-4)
2. switch x and y, then solve for y
then, x = √y-4
x² = y-4
x² + 4 = y
3. Now change y to [tex]f^{-1}[/tex](x)
then [tex]f^{-1}[/tex](x) = x² + 4
4. Since, the original function is defined only for x - 4 ≥ 0, you solve for x and get x ≥ 4.
Hence, the final blank is 4.
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The question attached here seems to be incomplete the complete question here:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
consider the given function: f(x)= √x-4
To determine the inverse of the given function, change f(x) to y, switch______ and y, and solve for ______.
The resulting function can be written as (f) to the power of -1(x)=x squared + ______, where x is greater than or equal to ______.
W,x,y,z are the sizes of four angles of a quadrilateral. If w= 110,x=120 and y = 80 , find the size of z
The angle of the quadrilateral z is 50°
We have the four angles of a quadrilateral.
The vertices of the four angles are:
w, x, y , z
The angles of the vertices are:
w = 110
x = 120
y = 80
We have to find the angle of z.
Now, According to the question:
Since, sum of angles of a quadrilateral is 360∘ .
Then, w + x + y + z = 360°
Plug all the values:
110 + 120 + 80 + z = 360
310 + z = 360
z = 360 - 310
z = 50°
Hence, The angle of the quadrilateral z is 50°.
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If the Cable Company offers cable for $110 a month but gives a 10% discount for new customers. Find the cost for the new customers.
The cost for new customers who are entitled to the 10% discount is $99 per month.
The Cable Company offers cable for $110 a month but gives a 10% discount for new customers.
To find the cost for new customers, we will have to subtract the 10% discount from the original cost of $110 per month.
So, we will have to multiply the original cost by the percentage of the discount which is 10%.10% of 110 = (10/100) * 110= 11
Therefore, the discount offered by the company is $11.
Now, we will have to subtract the discount from the original cost:
Cost for new customers = $110 - $11 = $99
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