The statement "Volume A = Volume B" is true. The cross section of rectangular prism A measures 6 units by 4 units.
To determine the relationship between the volumes of rectangular prism A and triangular prism B, we need to calculate their volumes and compare them.
For rectangular prism A:
Cross-sectional dimensions: 6 units by 4 units
Length: 7.22 units
Volume of A = Length * Width * Height
= 7.22 units * 6 units * 4 units
= 173.28 units³
For triangular prism B:
Base dimensions: 8 units by 6 units
Height: 7.22 units
Volume of B = (Base * Height) / 2
= (8 units * 6 units * 7.22 units) / 2
= 173.28 units³
Comparing the volumes of A and B, we find that the volume of rectangular prism A is equal to the volume of triangular prism B.
Therefore, the statement "Volume A = Volume B" is true.
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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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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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ms.watson wants to join planet fitness. she paid a flat fee of $110 and $10 monthly. how much does ms.watson have to pay for her membership for the year
Ms. Watson paid a flat fee of $110 for the first year and $10 monthly for the membership. As we know, Ms. Watson has to pay for 12 months of membership. The total cost of membership for the year is $230. We can calculate the cost of membership for the year as follows:
Yearly cost = Flat fee + Monthly fee for 12 months
Yearly cost = $110 + ($10 x 12)
Yearly cost = $110 + $120
Yearly cost = $230
Therefore, Ms. Watson has to pay $230 for her membership for the year. Ms. Watson is planning to join Planet Fitness for the first time. She has to pay a flat fee for the first year and a monthly fee for the membership. The flat fee is $110, and the monthly fee is $10. Ms. Watson needs to know the total membership cost for the year. We can calculate the total cost of the membership by using simple arithmetic.
The membership for the first year is a flat fee of $110. This fee is payable only once for the first year. After that, Ms. Watson needs to pay a monthly fee of $10. The membership is valid for 12 months. Therefore, we need to calculate the total cost of 12 months of membership for Ms. Watson.
We can do this by multiplying the monthly fee of $10 by 12 months. Ms. Watson must pay a flat fee of $110 for the first year and a monthly fee of $10. She needs to pay this fee for 12 months of membership. Therefore, the total cost of membership for the year is $230.
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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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Devon bought a new suit that was discounted 40% off the original price. If the original price of the suit was $280, what was the discounted price?
The discounted price of the suit is $168.
Explanation: To calculate the discounted price, we need to subtract the discount percentage from 100% and then multiply it by the original price. In this case, the original price of the suit is $280, and it was discounted by 40%.
First, we calculate the discount amount:
Discount amount = Original price * (Discount percentage / 100)
Discount amount = $280 * (40 / 100)
Discount amount = $280 * 0.4
Discount amount = $112
Next, we will subtract the discount amount from the original price to find the discount price:
Discounted price = Original price - Discount amount.
Discounted price = $280 - $112
Discounted price = $168
Therefore, the discounted price of the suit is $168 after applying a 40% discount to the original price of $280.
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Showing results for a rectangular brick has a length of 5 centimeters a width of 9 centimeters and a height of 20 centimeters what is the surface area of that brick
The surface area of the rectangular brick can be calculated by adding up the areas of all its faces. The surface area of the rectangular brick is 650 square centimeters.
The given dimensions of the brick are:
Length = 5 centimeters
Width = 9 centimeters
Height = 20 centimeters
To find the surface area, we need to calculate the areas of the six faces of the brick. The rectangular brick has three pairs of equal faces: top and bottom, front and back, and left and right sides.
The area of each face can be found by multiplying the length by the width.
The top and bottom faces have the same dimensions, so each face has an area of 5 cm * 9 cm = 45 square centimeters.
The front and back faces also have the same dimensions, so each face has an area of 5 cm * 20 cm = 100 square centimeters.
The left and right side faces also have the same dimensions, so each face has an area of 9 cm * 20 cm = 180 square centimeters.
To find the total surface area, we add up the areas of all the faces:
Total Surface Area = 2 * (45 + 100 + 180) = 2 * 325 = 650 square centimeters.
Therefore, the surface area of the rectangular brick is 650 square centimeters.
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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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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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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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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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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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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.
Two congruent squares overlap, as shown, so that vertex A of one square lies at the intersection of the diagonals of the other square. The side of each square has length 12 inches. Find the number of square inches enclosed by the shaded region.
Thus, the number of square inches enclosed by the shaded region is 72√6 square inches.
Given, two congruent squares overlap, as shown, so that vertex A of one square lies at the intersection of the diagonals of the other square.
The side of each square has length 12 inches.
To find: The number of square inches enclosed by the shaded region.
Solution: It is given that, two squares are congruent and side of each square is 12 inches.
Let's find the shaded area.
By Pythagorean theorem, in ΔABO, we have:
OB² = AO² + AB²
We know that, side of square is 12 inches.
So, AO = BO = 6√2 inches
AB = 12 inches
Therefore,
OB² = (6√2)² + 12²
OB² = 72 + 144
OB² = 216
OB = 6√6 inches
Area of ΔABO = 1/2 × base × height= 1/2 × AB × OB= 1/2 × 12 × 6√6= 36√6 sq. inches
Area of shaded region = 2 × Area of ΔABO= 2 × 36√6= 72√6 sq. inches
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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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write this percentage as a fraction in its simplist form
To write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.
Step 1: Write the percentage as a fraction by dividing it by 100.For example, let's say we want to write 25% as a fraction in its simplest form.
25% is equivalent to 25/100 or 0.25 as a decimal.
Step 2: Simplify the fraction by finding a common factor between the numerator and denominator.
For example, let's simplify 25/100.
Both the numerator and denominator can be divided by 25, giving us 1/4.
Therefore, 25% as a fraction in its simplest form is 1/4.
Another example: let's write 60% as a fraction in its simplest form.
60% is equivalent to 60/100 or 0.6 as a decimal.
The numerator and denominator can both be divided by 20, giving us 3/5.
Therefore, 60% as a fraction in its simplest form is 3/5.
In summary, to write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.
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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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Paul had a job during his summer vacation. He earned $8.55 per hour. He worked 20 hours per week for 8 weeks. How much money did Paul earn? *
Paul earned a total of $1,368 during his summer vacation. To calculate how much money Paul earned during his summer vacation, we need to determine his hourly rate and the total number of hours he worked.
Given that Paul earned $8.55 per hour and worked 20 hours per week for 8 weeks, we can calculate his total earnings.
First, let's find the total number of hours Paul worked:
20 hours/week * 8 weeks = 160 hours.
Next, we multiply the total number of hours by his hourly rate to find his total earnings:
160 hours * $8.55/hour = $1,368.
Therefore, Paul earned a total of $1,368 during his summer vacation.
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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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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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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 ______.
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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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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The function f(x) = 467(5)x represents the growth of a ladybug population every year in a wooded area. Adrianne wants to manipulate the formula to an equivalent form that calculates every 3 months, not every year. Which function is correct for Adrianne's purposes? f(x) = 67(5)x f of x equals 467 times 5 to the 12 power to the x over 12 power f(x) = 467(5 to the one fourth power)4x f(x) = 4672(5)x.
The correct function for Adrianne's purpose, where the growth is calculated every 3 months instead of every year, is f(x) = 467(5^(x/4)).
To calculate the growth every 3 months instead of every year, we need to modify the original function by adjusting the exponent of 5.
Step 1: The original function is f(x) = 467(5)^x, where x represents the number of years.
Step 2: To calculate the growth every 3 months, we divide x by 4, as there are 12 three-month periods in a year.
Step 3: Adjust the exponent of 5 to (x/4), representing the growth over each three-month period.
Step 4: The modified function becomes f(x) = 467(5^(x/4)), which calculates the growth every 3 months.
Therefore, the correct function for Adrianne's purpose is f(x) = 467(5^(x/4)).
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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).
If the pressure exerted on a sample of gas is increased from 0. 428 atm to 0. 72338 atm what is the final volume of the gas in ml if the inital volume was 240 ml?
The final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.
The final volume of the gas in milliliters, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is unknown ml.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's Law is:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given that P1 = 0.428 atm, V1 = 240 ml, and P2 = 0.72338 atm, we can plug these values into the equation and solve for V2:
(0.428 atm) * (240 ml) = (0.72338 atm) * V2
103.2 atm * ml = 0.72338 atm * V2
V2 = (103.2 atm * ml) / 0.72338 atm
V2 ≈ 142.55 ml
Therefore, the final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.
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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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A poll of 1,000 randomly selected registered voters was taken and 584 responded that they favor candidate X for governor (p 1 = 0.5840). Just before the election, another poll of 950 registered voters was taken and 401 individuals responded that they favor candidate X (p 2 = 0.4221). A 95% two-proportion z confidence interval for the true difference between p 1 and p 2 was found to be (0.1181, 0.2057). What is the meaning of the interval in the context of the problem?
The 95% two-proportion z confidence interval (0.1181, 0.2057) in the given problem indicates that there is a 95% probability that the true difference in proportions between the two polls falls within the range of 0.1181 to 0.2057.
This means that the proportion of registered voters who favor candidate X in the first poll is estimated to be between 11.81% and 20.57% higher than the proportion in the second poll.
The confidence interval is a statistical tool that provides a range of values within which the true difference between the proportions is likely to lie. The interval is constructed based on the sample data and takes into account the variability in the estimates. In this case, it suggests that there is evidence to support the claim that candidate X was more favored by registered voters in the first poll compared to the second poll.
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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)
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English (U. S. )
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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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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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Sharon pours for different liquid ingredients into a bowl some of the liquid ingredients is 8.53 L two of her measurements are in liters and two of her measurements are in millimeters give me an example of possible measurements for Sharon’s or liquids
Here's an example of possible measurements for Sharon's liquid ingredients:
Ingredient A: 8.53 L (liters) - This could represent a larger quantity of a liquid ingredient that needs to be added in liters, such as water or broth.
Ingredient B: 1.5 L (liters) - This measurement could represent another liquid ingredient that needs to be added in liters, like oil or a sauce.
Ingredient C: 3500 mL (milliliters) - This measurement represents a smaller quantity of a liquid ingredient that is measured in milliliters, such as a flavoring extract or a concentrated ingredient.
Ingredient D: 250 mL (milliliters) - This measurement could represent another liquid ingredient measured in milliliters, like a specific sauce or a liquid seasoning.
In this example, Sharon uses a combination of liter and milliliter measurements to accurately measure different volumes of liquid ingredients for her recipe. The liter measurements (Ingredient A and Ingredient B) are used for larger quantities, while the milliliter measurements (Ingredient C and Ingredient D) are used for smaller amounts. This combination allows for precise measurement and flexibility in handling both large and small quantities of liquid ingredients.
It's important to note that the specific measurements can vary depending on the recipe and the desired quantities of each ingredient.
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