Directions: Using the digits 1 to 9 at most one time each, find the dimensions of three rectangular prisms so that their volumes are as close as possible. Note: diagram may not be drawn to scale. All the volumes are under 100 cubic units.Can you find 3 volumes that are within the range of 50 and 90?Can you find 3 volumes that are within the range of 60 and 80?The difference between all 3 volumes is less than 10.
Answers
The dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).
What is a rectangular prism?
A rectangular prism is a solid geometric shape that has three mutually perpendicular rectangular faces, and is also known as a rectangular parallelepiped or a box. It has six faces, eight vertices, and twelve edges.
The shape is defined by three dimensions: length, width and height, and is specified by the three sets of parallel and mutually perpendicular edges that form its six faces. The opposite faces of a rectangular prism are equal in area and parallel to each other. The opposite edges are also parallel and equal in length.
You can’t get a perfect match, but you can get pretty close, with dimensions of (1,8,9), (2,5,7), (3,4,6)
Hence, the dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).
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Related Questions
please answer thank you !
Answers
The volume of the squared pyramid is 9 cubic yards, so the correct option is D.
What is the volume of the ice pyramid?For a square pyramid of sidelength S (S is the sidelength of the square base), the volume is given by the formula:
V = (1/3)*S^3
Here we want to find the volume if S = 3 yards, so we just need to replace that in the formula above to get the volume of the sculpture, we will get:
V = (1/3)*(3 yd)^3
V = (1/3)*(27 yd^3)
V = 9 yd^3
The volume is 9 cubic yards, then the correct option is D.
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I need help asap, please rn
Answers
Answer:
g(f(- 5)) = - 31
Step-by-step explanation:
to calculate g(f(- 5)), evaluate f(- 5) and substitute the value obtained into g(x)
f(- 5) = (- 5)² + (- 5) - 12 = 25 - 5 - 12 = 25 - 17 = 8 , then
g(8) = - 2(8) - 15 = - 16 - 15 = - 31
Answer:
-31
Step-by-step explanation:
f(x)=x²+x-12
or,f(-5)=(-5)²+(-5)-12
=25-5-12
=25-17
=8
now, g(x)= -2x-15
= (-2)×8-15
= -16-15
=-31
kim barney pays a 290.00 annual premium for insurance plan with a 500.00 deductable. the company pays 80% of the remaining expense. if kim had 2,500.00 in medical expenses calculate the following
Answers
The amount that Kim Barney spends is $342 for medical expenses.
Given that,
Kim Barney pays a $290.00 yearly premium for a $500.00 deductible insurance plan. 80 percent of the remaining cost is covered by the business. If Kim has medical costs of $2,500.00
To find : The amount that Kim barney spends for the medical expenses.
If the business covers 80% of the remaining balance ($1710), they will be responsible for paying $1368 of it.
10% of 1710 is 171
171x8=1368
The insurance provider covers the $1368.
Kim Barney spends $342.
Consequently, Kim Barney spends the following amount on medical costs $342.
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Which statement about determining the quotient 12 ÷ 3
O Because 4 x = 12,12 divided by
O Because 18 x = 12,12 divided by
O Because 36 x
= 12,12 divided by
3
O Because 9 x = 12, 12 divided by
is 4.
is 18.
is 36.
is 9.
is true?
Answers
Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.
What is Division ?One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.
According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.
The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as
12 divided by 4 gives 3.
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Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.
What is Division ?One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.
According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.
The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as
12 divided by 4 gives 3.
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Sclect the correct option for the adjoining situation in which liquid is flowing through a pipe of variable cross-section represent presssure)
(a) if (b) values of and (c) values of and (d) valucs of and
Answers
The correct option for an adjoining situation in which liquid is flowing through a pipe of variable cross-section representing pressure is (a) V1>V2 if L1>L2.
This is because, in a pipe of variable cross-section, the velocity of the liquid (V) is directly proportional to the cross-sectional area of the pipe (L). Therefore, if the cross-sectional area of one section of the pipe (L1) is greater than that of another section (L2), then the velocity of the liquid flowing through the first section (V1) will be greater than that of the second section (V2). This is due to the fact that in the area of the pipe where the cross-sectional area is greater, the liquid will have more space to flow and thus will have a higher velocity.
The other options are incorrect because these situations are not possible.
In fluid mechanics, The pressure drop is directly proportional to the fluid velocity, as well as the density of the fluid and the length of the pipe. The pressure drop is inversely proportional to the cross-sectional area of the pipe. So if the cross-sectional area of the pipe is increasing, the pressure is decreasing. And if the cross-sectional area of the pipe is decreasing, the pressure is increasing.
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The complete question is:
Select the correct option for the adjoining situation in which liquid is flowing through a pipe of variable cross-section (P1, P2 represent pressure(a) V1>V2 if L1>L2 (b) V1<V2 for all values of L1 and L2 (c) P1<P2 for all values of L1 and L2 (d) P1>P2 values of L1 and L2
How to make a square with this equation y2+18y+
Answers
Answer: The missing value is 81.
Step-by-step explanation: In a square, the formula is [tex]y^2 + 2y + y^2[/tex],
where the first y^2 is staying there. 18/2 is 9, and 9 squared is 81.
A square has an area of 81²cm.Find its perimeter
Answers
square side ²= area
s =√81
S = 9
perimeter= 9×4 = 36
if sample size is large can we use z insteed of t distribution for given sample mean and sample standard variance
Answers
If the sample size is large (typically n > 30), then it is generally appropriate to use the standard normal distribution (z-distribution) to approximate the sampling distribution of the sample mean.
What are the standard's mean and variance?
Standard deviation is the square root of the number, while variance is equal to the average squared deviations from the mean. Additionally, the variance's square root is the standard deviation.
This is because as the sample size increases, the Central Limit Theorem states that the sample mean will become more normally distributed, regardless of the underlying distribution of the population.
This is due to the fact that the standard error of the sample mean, which is the standard deviation of the sampling distribution of the mean, decreases as the sample size increases. When the sample size is large, the sample mean will be approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
However, it is important to note that in order to use the z-distribution to approximate the sampling distribution of the sample mean, it is necessary to know the population mean and population standard deviation. If these values are not known, it is appropriate to use the t-distribution, which does not require knowledge of the population parameters.
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Help pleaseeeeeeeeeee
Answers
Answer:
m = 2/3
Step-by-step explanation:
Take two random points, I personally picked (-2, 0) and (1, 2)
Slope = rise/run = [tex]\frac{2-0}{1-(-2)} = \frac{2}{3}[/tex]
The radioactive substance cesium-137 has a half-life of 30 years. The amount A (t) (in grams) of a sample of cesium-137 remaining after t years is given by the
following exponential function.
- 647 (12)
A (t) = 64
30
Find the initial amount in the sample and the amount remaining after 100 years.
Round your answers to the nearest gram
?
Answers
The radioactive substance cesium-137 has a half-life of 30 years. For the given compound, Initial amount is 647 grams and Amount after 100 years is 64 grams.
A sample's half-life is the amount of time it takes for half of its unstable nuclei to decay, for its activity to halve, or for its count rate to decrease by half. The number of decays that a detector, like the Geiger-Muller tube, records each second is known as the count-rate.
For radioactive compounds, a general exponential function is provided by
Ao(1/2)t/t1/2 = A(t)
Where,
A(t) is the sum that is left after t years.
Ao is the radioactive substance's initial concentration.
The time it takes for a radioactive substance to degrade to A is measured in years.
The radioactive substance's half-life is represented by t1/2.
A(t) = 523(1/2)t/30 in comparison to the general exponential function
A starting point (Ao) of 523 grams
A(t) = 647(1/2)^t/30
t = 100
A(100) equals [647 × (1/2) × 100] /30
=647 × 0.53.333
=647 × 0.0992
=64.182
=64 grams (to the nearest gram)
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A bicycle has a 56 cm frame. What is this frame size equal to in inches? (1.00 in = 2.54 cm. Note
that this equivalence does not limit significant figures in the final answer.)
Answers
the bicycle has a frame size of 22.04 in.
What is unit conversion?
Units of measure are needed in order to measure these values. Sometimes the units of measurement used may not correspond to the standards required for a particular process or application, as well as the measuring choice and convenience. It's crucial to convert these units in a way that makes sense and can be used effectively. Let's use the example of someone who is only familiar with the metric system to better grasp the statement. The person finds it difficult to determine the height of a 25-foot tree. The person will comprehend the height of the tree better if they convert 25 feet to meters. Let's use a unit conversion table to learn about converting between different units.
A bicycle has a 56 cm frame.
As given 1 in = 2.54cm
so 2.54 cm =1 inc
1 cm = 1/2.54
56 cm for the frame = 56*1/2.54 = 22.04 in
Hence the bicycle has a frame size of 22.04 in.
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Find X
I’m not really sure how to do this
Answers
Answer:
x = 121°
Step-by-step explanation:
the shape is a heptagon (7 sides). the interior angles in a heptagon will always add up to 900°, so all you need to do is add all the known angles and subtract from 900.
140 + 133 + 145 + 117 + 119 + 125 = 779
900 - 779 = 121
this means that x = 121°
hope this helped, good luck!
Use the distributive property to write an equivalent expression. Then evaluate
the expression.
(15+5)
Answers
Answer:5(3+1); 20
Step-by-step explanation:
5x3 is 15 and 5x1 is 5 which is equivalent to 15+5, then add to get 20.
When Evelyn moved into a new house, she planted two trees in her backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 16 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 8 inches per year.Graph each function and determine the height of both trees at the time when they have an equal height.
Answers
The height of both trees at the time when they have an equal height will be 48 inches.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Evelyn planted two trees in her backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 16 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 8 inches per year.
We can write the functions for each tree as -Tree {A} : y {A} = 4x + 32
Tree {B} : y {B} = 8x + 16
Refer to the graph attached. The point of intersection will give the height of both trees at the time when they have an equal height.The height of both trees at the time when they have an equal height will be 48 inches.Therefore, the height of both trees at the time when they have an equal height will be 48 inches.
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A chest contains 5 balls that each have the number 3 written on them. The chest also contains 5
balls that each have the number 7 written on them, and 5 balls that each have the number 11
written on them. Octi the Octopus takes out a few balls, one at a time, and calculates the sum of
the numbers written on them. How many different sums less than 15 are possible?
Answers
There are 15 possible sums less than 15 that can be made by taking out one to three balls from the chest.
How many different sums less than 15 are possible?13 possible sums less than 15 are possible: 3, 7, 11, 6, 10, 14, 9, 13, 12, 5, 8, 4, and 2.There are a total of 15 possible sums less than 15 that Octi the Octopus can calculate.Octi can calculate the sum of 3, 7, or 11. If he takes out one ball, he could calculate 3, 7, or 11.If he takes out two balls, he could calculate 6, 14, 9, or 18.If he takes out three balls, he could calculate 9, 12, 15, 18, 21, or 24.If he takes out four balls, he could calculate 12, 15, 18, 21, 24, 27, or 30.Finally, if he takes out five balls, he could calculate 15, 18, 21, 24, 27, 30, or 33.All of these sums are less than 15 and are the only sums possible for Octi to calculate.There are fifteen possible sums less than 15 that Octi the Octopus can achieve by taking out balls one at a time from the chest. The possible sums are 3, 7, 11, 6, 9, 10, 13, 14, 12, 8, 5, 4, 2, 7 + 3 + 3, 11 + 3 + 3, and 7 + 7.All of the sums are possible because the chest contains five balls with the number three, five balls with the number seven, and five balls with the number eleven. This means that Octi can take out one, two, or three balls at a time and calculate the sum of the numbers written on them.For example, if Octi takes out one ball from the chest, the possible sums he can get are 3, 7, or 11. If he takes out two balls, the possible sums he can get are 6, 9, 10, or 13. And if he takes out three balls, the possible sums he can get are 14, 12, 8, 5, 4, 2, 7 + 3 + 3, and 11 + 3 + 3. Lastly, if he takes out four balls, the only possible sum is 7 + 7. In conclusion, Octi the Octopus can achieve fifteen different sums less than fifteen by taking out balls from the chest one at a time.To learn more about different sums less than 15 are possible refer to:
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Which mathematical sentence most accurately expresses the information in the problem below?
Christine has nine shining rings. If six of them are gold, how many are not gold?
A. n-6-9 B. 6+9 = n C. 7+9=6 D. n + 6 = 9
Answers
3 of them would not be good, 9-6= 3 non-shiny gold rings.
How many are not gold?Using two expressions, a mathematical sentence declares two things. The two expressions either employ variables, numbers, or a combination of the two. Symbols or words like equal, greater than, or less than may also be used in a mathematical sentence.
An accurate arrangement of mathematical symbols that expresses a coherent idea constitutes a mathematical sentence, which is equivalent to an English sentence in meaning. Verbs are used in sentences. The verb "=" is used in the mathematical formula "3+4=7 3 + 4 = 7".
The answer is b c 3 9-6=3
3 of them would not be good
9-6= 3 non shiny gold rings
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Square ABCD has sides of length 3. Segments CM and CN divide the square's area into three equal parts. How long is segment CM?
A √10
B √12
C √13
D√ 14
E √ 15
Answers
The length of segment CM is equal to the square root of 10. This is determined by dividing the area of the square ABCD, which has sides of length 3, into three equal parts, resulting in a segment of length √10.
The area of square ABCD can be calculated by squaring the length of one side, which is 3, to get 9. To divide this area into three equal parts, each part must have an area of 3. To find the length of segment CM, the square root of this area, 3, must be taken, resulting in a length of √10.
To find the length of segment CM in square ABCD, the area of the square must first be determined. This can be done by squaring the length of one side, which is 3, resulting in an area of 9. To divide this area into three equal parts, each part must have an area of 3. This means the length of segment CM must be the square root of 3, which is equal to √10. Therefore, the length of segment CM is equal to √10. This is the result of dividing the area of the square ABCD into three equal parts. This process can be used to determine the length of any segment dividing an area into equal parts
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Here are the weights (in pounds) of a sample of 13 male eleventh graders.
148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170
Find the median weight of these students.?
pounds
Answers
The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.
How can find the median the simplest way possible?Calculate the mean by summing the centre values and dividing them by the number. From there, you may obtain the median.
To arrange the data points in ascending order for a small data set, count the number of data points (n). To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.
148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170
140 , 141 , 146 , 148, 151 ,156, 159 ,159, 160, 167 , 170, 173, 174.
The median weight of these students is 159.
The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.
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¿A qué altura está la cometa de Ana si su cuerda mide 8 metros y tendría que moverse 6 metros para situarse debajo de ella?
Answers
The kite is 10 meters high
Solving for the height:To calculate how high Ana's kite is, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length of the string is one side of the triangle and the distance Ana needs to move to get under the kite is the other side. The height of the kite is the hypotenuse.
Therefore, the height of the kite can be calculated by:
height = [tex]\sqrt({string^{2} +distance^{2}) }[/tex]
height = [tex]\sqrt{(8^{2} + 6^{2} )[/tex]
height = √(64 + 36)
= √100
height = 10
Hence, the kite is 10 meters high.
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Given the graph for one quadratic function and the
table of values for another, determine which has a
smaller minimum.
Answers
The Minimum for quadratic function f(x) is smaller than g(x)
and it is -5.
What is a quadratic function?
Quadratic function is also a second-degree polynomial function. The graph of a quadratic function is a parabola. The parabola opens upwards if a graph is made for the quadratic formula.
The point at which the function attains maximum or minimum value is the vertex of the quadratic function. When we say second degree, then the variable is raised to the second power like x^2.
A quadratic function is of the form f(x) = ax^2 + bx + c, where a, b, and c are the numbers with a not equal to zero.
Now,
As the we find minimum value by calculating the value for f(x) or g(x)
and from given values f(x) have minimum value of -5 and g(x) have minimum value of 3.
hence,
Minimum for quadratic function f(x) is smaller than g(x)
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As the price of tickets rises from $200 to $250, the price elasticity of demand for business travelers is , and the price elasticity of demand for vacationers is , using the midpoint method. Therefore, the demand for airline tickets in this price range is elastic for vacationers because business travelers are sensitive to changes in price.
Answers
Answer:
The price elasticity of demand measures how responsive the quantity demanded is to a change in price. It can be calculated using the midpoint method, which is (change in quantity demanded / average quantity demanded) / (change in price / average price).
Using the midpoint method to calculate the price elasticity of demand for business travelers and vacationers, you would need more information such as the change in quantity demanded and the average quantity demanded for each group at different prices.
It is not possible to say if the demand is elastic or not for either group based on the information provided.
Consider the following two algorithms which both are meant to print all multiples of 11 from 1 up to a user input positive integer value - upper. Which statement correctly compares the efficiency of these two algorithms?
Algorithm 1:
for (int i = 1; i <= upper; i++)
{
if (i % 11 == 0)
{
System.out.println(i + " ");
}
}
Algorithm 2:
for (int i = 1; i <= upper / 11; i++)
{
System.out.println(i * 11 + " ");
}
Answers
Algorithm 2 is more efficient than Algorithm 1 because it only needs to loop through the numbers up to upper/11 instead of upper. This means that it will take fewer iterations to reach the result, making it more efficient than Algorithm 1.
Algorithm 1 will make upper/11 more checks than Algorithm 2, resulting in a slower runtime. Additionally, Algorithm 2 avoids the need to check the modulus of each number, further reducing the computation time. Algorithm 2 only needs to loop through the multiples of 11, which are always 11 apart from each other, so it can skip over the other numbers between them.
This makes Algorithm 2 much faster than Algorithm 1 because it is only looping through a fraction of the numbers.
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sketch an example of two different triangles, triangle `abc` and triangle `def`, that fit the given criteria (they share two sets of congruent sides and one pair of congruent angles) but are not congruent.
Answers
Congruency is said to be defined on two triangles when they have exact same length of sides and equal angles between them. The shape and size are supposed to be the same even after rotation or flipping of triangles for them to remain congruent.
There are 4 criteria to test the congruency of the triangle and they are as follows:
SAS - This proves congruency when two sides and the angle between them are the same w.r.t both trianglesSSS - Two triangles are congruent if all three sides of both of them are equal w.r.t to each otherAAS- When Two pairs of corresponding angles and one pair of corresponding sides (not between the angles) are equal then this is trueASA- When Two pairs of corresponding angles and one pair of corresponding sides between the angles are equal then this is trueIn this set of triangles, (ABC, def) AB=DE, AC=DF, and ∠ABC= ∠DEF i.e., two sides and one angle are equal but it is not congruent because according to SAS criteria, the angle should be between AB and AC (or DE and DF)
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Find the area of the figure.
Answers
The area of each of the given shapes is calculated as;
1) 143 sq.in
2) 32 sq.cm
3) 162 sq.yds
4) 150 sq.in
How to find the area of regular shapes?1) The area of a parallelogram is;
Area = base * height
Thus;
Area = 11 * 13
= 143 sq.in
2) Area of a triangle is;
Area = 1/2 * base * height
Area = 1/2 * 8 * 8
Area = 32 sq.cm
3) Area of this will be gotten by the are of the individual triangles;
Area = 2(1/2 * 7 * 8) + 2(1/2 * 12 * 8)
Area = 56 + 96
Area = 162 sq.yds
4) Area = (12 * 12) + (1/2 * 1 * 12)
= 144 + 6
= 150 sq.in
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the rectangle below has an area of x^2 8x 15x 2 8x 15x, squared, plus, 8, x, plus, 15 square meters and a width of x 3x 3x, plus, 3 meters. what expression represents the length of the rectangle? a rectangle with a width of x plus three and an unknown length. the area of the rectangle is x squared plus eight x plus fifteen.
Answers
The expression that represents the length of the rectangle is x + 5
What is meant by Area of a rectangle?Dimensions of a rectangle. A = l × b. Once a rectangle's length and breadth are known, its area may be computed. The rectangle's area can be measured in square units by multiplying the length and width. The region that a rectangle occupies in a two-dimensional space is known as a rectangle's area. Another way to describe a rectangle's area is the quantity of square units needed to fill it entirely. The whole distance around the outside of a rectangle is referred to as the rectangle's perimeter.The area of a rectangle is described as follows:
area = lw
where
l = length
w = width
Therefore,
area = x² + 8x + 15
w = x + 3
Therefore,
x² + 8x + 15 = (x + 3)l
divide both sides by x + 3
l = x² + 8x + 15 / x + 3
l = (x+3)(x+5) / (x + 3)
Finally,
length = x + 5
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one quart of water weighs about 2.1 pounds.there are 4quarts in a gallon. how much does a gallon of water weigh?
Answers
There are 4 quarts in a gallon, and a gallon weighs 8.34 pounds, so a quart weighs 2.085 pounds.
How much does a gallon of water weigh?The gallon is a volumetric unit that is used in both imperial and American customary measurements. In use right now are three different variations:
the imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries; the US gallon (US gal), defined as 3.785411784 L,[1] (231 cubic inches), which is used in the US and some Latin American and Caribbean countries; and the US dry gallon ("usdrygal"), defined as 18 US bushel (exactly 4.40488377086 L).
gallon equals 4 quarts
2.1*4 =8.4
gallon of water weigh is 8.4
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4x - 5 ≤ 6x + 3
solve
pls show work
Answers
Answer: X[tex]\geq[/tex]-4
Step-by-step explanation:
4x-5[tex]\leq[/tex] 6x + 3
-2x [tex]\leq[/tex] 3 + 5
-2x[tex]\leq[/tex] 8
X = [tex]\geq[/tex] - 8/2
independent random samples of voters from two voting districts, g and h, were selected to investigate the proportion of all voters who favor a proposal to widen a road that runs through both districts. the difference between the sample proportions (g minus h) was used to create the 95 percent confidence interval (0.13,0.47) for the population difference between districts.
Answers
The most common level of confidence is 95%, however 90% or 99% have also been used on occasion.
A series of observations that are not reliant on any other samples or data constitute an independent random sample. Random samples selected without regard to sequencing. So, choice C is the proper one.
The essential points that are highlighted below are the followings:
Because the difference between the sample proportions G minus H greater population, according to the question. Due to the interval's all-positive values, it seems expected that district G will have more supporters than district H.
Assurance interval A confidence interval (CI) is a range of estimates for an unknown parameter that is determined by a lower bound and an upper bound. At a certain level of confidence, the interval is calculated.
The most typical level of confidence is 95%, however higher levels, such 90% or 99%, are occasionally employed.
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Answers
The answers contain a. 5 b. [tex]y=-\frac{3}{4} x+\frac{1}{2}[/tex] c. 148.5 d. 1/7
a. f"(2)
f"(x) = df'(x)/dx = d(sin(πx) + x² +3)/dx = cos(πx) + 2x
f"(2)=cos(π × 2) + 2 × 2
f"(2)=cos(2π) + 4
f"(2)=1 + 4
f"(2)=5
b. Equation for the line tangent to the graph of y = 1/f(x) at x = 0
We first find f(x) by integrating f'(x)
f(x) = ∫f'(x)dx = ∫(sin(πx) + x² +3)dx = -cos(πx)/π + x³/3 +3x + C
f(0) = 2 so,
2 = -cos(π × 0)/π + 0³/3 +3 × 0 + C
2 = -cos(0)/π + 0 + 0 + C
2 = -1/π + C
C = 2 + 1/π
f(x) = -cos(πx)/π + x³/3 +3x + 2 + 1/π
f(x) = [1-cos(πx)]/π + x³/3 +3x + 2
y = 1/f(x) = 1/([1-cos(πx)]/π + x³/3 +3x + 2)
The tangent to y is thus dy/dx
dy/dx = d1/([1-cos(πx)]/π + x³/3 +3x + 2)/dx
dy/dx = -([1-cos(πx)]/π + x³/3 +3x + 2)⁻²(sin(πx) + x² +3)
at x = 0,
dy/dx = -([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)⁻²(sin(π × 0) + 0² +3)
dy/dx = -([1-cos(0)]/π + 0 + 0 + 2)⁻²(sin(0) + 0 +3)
dy/dx = -([1 - 1]/π + 0 + 0 + 2)⁻²(0 + 0 +3)
dy/dx = -(0/π + 2)⁻²(3)
dy/dx = -(0 + 2)⁻²(3)
dy/dx = -(2)⁻²(3)
dy/dx = -3/4
At x= 0,
y = 1/([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)
y = 1/([1-cos(0)]/π + 0 + 0 + 2)
y = 1/([1 - 1]/π + 2)
y = 1/(0/π + 2)
y = 1/(0 + 2)
y = 1/2
So, the equation of the tangent at (0, 1/2) is
[tex]\frac{y-\frac{1}{2} }{x-0} =-\frac{3}{4} \\\\y-\frac{1}{2} =-\frac{3}{4} x\\\\y=-\frac{3}{4} x+\frac{1}{2}[/tex]
c. If g(x) = f (√(3x² + 4). Find g'(2)
g(x) = f (√(3x² + 4) = [1-cos(π√(3x² + 4)]/π + √(3x² + 4)³/3 +3√(3x² + 4) + 2
g'(x) = [3xsinπ√(3x² + 4) + 18x(3x² + 4) + 9x]/√(3x² + 4)
g'(2) = [3(2)sinπ√(3(2)² + 4) + 18(2)(3(2)² + 4) + 9(2)]/√(3(2)² + 4)
g'(2) = [6sinπ√(12 + 4) + 36(12 + 4) + 18]/√12 + 4)
g'(2) = [6sinπ√(16) + 36(16) + 18]/√16)
g'(2) = [6sin4π + 576 + 18]/4)
g'(2) = [6 × 0 + 576 + 18]/4)
g'(2) = [0 + 576 + 18]/4)
g'(2) = 594/4
g'(2) = 148.5
d. If h is the inverse function of f. Find h' (2)
If h(x) = f⁻¹(x)
then h'(x) = 1/f'(x)
h'(x) = 1/(sin(πx) + x² +3)
h'(2) = 1/(sin(π2) + 2² +3)
h'(2) = 1/(sin(2π) + 4 +3)
h'(2) = 1/(0 + 4 +3)
h'(2) = 1/7
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Which describes 4x and −7x
in this expression?
4x−5−7x
A. constant term
B. like terms
C. multiplication
D. simplify
Answers
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Reason:
The 4x and -7x are like terms because they involve the same variable x. This allows us to combine the like terms to end up with -3x
4x-7x = -3x
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Another example of like terms is 2x and 5x.
Adding them gets us 2x+5x = 7x
We can think of it like saying "2 boxes + 5 boxes = 7 boxes". Replace each word "boxes" with the single letter "x" and we arrive at 2x+5x = 7x.
