Find the base area (B), lateral area (L) and surface area (S) of the solid. Round to the
nearest tenth, if necessary.
10.4 cm
B = 96
L =
12 cm
S=
12 cm
12 cm
8 cm
cm²
cm²
cm²
Answers
The base, lateral area and surface area is B = 96 cm², L = 499.2 cm²,S = 691.2 cm²
What is Lateral Area ?The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.
To find the lateral area (L) of this solid, we need to calculate the area of the four rectangles that make up the sides of the solid. Since each rectangle has a height of 10.4 cm and a width of 12 cm, the area of one rectangle is:
A = 10.4 cm * 12 cm = 124.8 cm²
Since there are four rectangles, the total lateral area is:
L = 4 * A = 4 * 124.8 cm² = 499.2 cm²
To find the surface area (S) of the solid, we need to add the lateral area to the area of the two circular bases. The base area is given as 96 cm², so the area of both bases is:
A = 2 * 96 cm² = 192 cm²
Therefore, the total surface area is:
S = L + A = 499.2 cm² + 192 cm² = 691.2 cm²
Rounding to the nearest tenth, we have:
B = 96 cm²
L = 499.2 cm²
S = 691.2 cm²
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Related Questions
what is the range and domain of y = 3x^2 + 2?
Answers
The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
Define range!In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).
According to question:The given function is y = 3x² + 2.
The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.
Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.
The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).
Since the minimum value of the function is 2, the range of the function is [2, ∞).
Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
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April is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her balloon payment at the end
of 7 years?
OA. $173,819.97
OB. $170,118.49
OC. $225,368.29
OD. $170,245.98
SUBMIT
Answers
The balloon payment at the end of 7 years would be $173,819.97, which is option A.
How to find the balloon payment at the end of 7 yearsA 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.
To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:
n = 23 * 12 = 276 (total number of payments)
r = 4.15% / 12 = 0.003458 (monthly interest rate)
P = (r * PV) / (1 - (1 + r)^(-n))
where
PV is the present value of the loan (the loan amount)n is the total number of paymentsr is the monthly interest ratePV = $197,000
P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)
Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.
Using the formula for the remaining balance of a loan after t payments:
B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)
Where
B is the remaining balancePV is the initial loan amount r is the monthly interest rateP is the monthly payment t is the number of payments madet = 84 (number of payments made)
B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)
B = $173,819.97
Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.
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4negative slope equations, 2undefined slope equations, and 2zero slope equations (y=mx+b)
Answers
Answer:
negative
y=-x
y=-2x+6
y=(-1/2)x+1
y=-5x+20
undefined
x=4
x=-3
zero slope
y=2
y=-100
Solve for X, please write an explanation.
Answers
Step-by-step explanation:
2x+20 and 2x-4 are supplementary angles...they form a straight line and thus = 180 degrees when added together
2x+20 + 2x-4 = 180 simplify
4x + 16 = 180 subtract 16 from both sides
4x = 164 divide both sides by 4
x = 41 degrees
Select the correct answer. Sides of three square rooms measure 14 feet each, and sides of two square rooms measure 17 feet each. Which expression shows the total area of these five rooms? A. (3 × 14^2) + (2 × 17^2) B. (2 × 14^3) + (2 × 17^2) C. (3 × 17^2) + (2 × 14^2) D. (3 × 14^2) × (2 × 17^2) Reset Next
Answers
The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.
What is expression?An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.
In the given question,
C. (3 × 17²) + (2 × 14²)
To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.
For the three rooms with sides of 14 feet each, the area of each room is:
14^2 = 196 square feet
So the total area of these three rooms is:
3 × 196 = 588 square feet
For the two rooms with sides of 17 feet each, the area of each room is:
17^2 = 289 square feet
So the total area of these two rooms is:
2 × 289 = 578 square feet
Therefore, the total area of all five rooms is:
588 + 578 = 1166 square feet
Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.
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help please without guessing ?//
Answers
Answer:
D. y ≥ x² - 4x - 5
Step-by-step explanation:
We can observe two characteristics of this graphed inequality:
1. its shading is above it, therefore the inequality sign must be greater than
2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to
From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.
____________
Note:
We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:
[tex]y \ge (x-2)^2 - 9[/tex]
Answer:
The answer is y≥ x²-4x-5
Step-by-step explanation:
x=a,x=b
where a,b are roots of the equation
a= -1 b=5
x= -1,x=5
x+1=0,x-5=0
(x+1)(x-5)=0
x²-5x+x-5=0
x²-4x-5=0
HELP MARKING BRAINLEIST
Answers
Answer:
r = 2
center: ( -7,0 )
Step-by-step explanation:
a recent survey revealed that 30% of us households own one or more cats. you visit 50 random households. what is the mean number of households that will have one or more cats? 15 what is the standard deviation of the number of households that will have one or more cats? 3.2 round your answer to 1 decimal place. suppose that 10 of the 50 random households had one or more cats. would you consider this unusual?
Answers
1. The mean number of households that will have one or more cats is 15.
2. This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.
The mean number of households that will have one or more cats can be calculated as:
Mean = (30/100) x 50 = 15
Therefore, the mean number of households that will have one or more cats is 15.
The standard deviation can be calculated using the formula:
Standard deviation = [tex]\sqrt{(npq)}[/tex]
where n is the sample size (50), p is the probability of success (30/100 = 0.3), and q is the probability of failure (1 - p = 0.7).
Standard deviation = sqrt(50 x 0.3 x 0.7) = 3.08
Rounding to 1 decimal place, the standard deviation is 3.1.
If 10 of the 50 random households had one or more cats, we can calculate the z-score as:
z = (x - μ) / σ
where x is the observed number of households with cats (10), μ is the mean (15), and σ is the standard deviation (3.1).
z = (10 - 15) / 3.1 = -1.61
Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score of -1.61 or lower is 0.053.
This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.
However, it is somewhat lower than the expected value of 15, which suggests that the sample may not be fully representative of the population.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Answers
When comparing the data from the two locations, the measure of center that should be used to determine which location typically has the cooler temperature is the median.
In Sunny Town, the histogram shows that the shaded bars are skewed to the right, indicating that the distribution is positively skewed. This means that there are a few high temperatures that pull the mean towards the higher end.
However, the median, which represents the middle value when the data is arranged in ascending order, is less affected by extreme values and is a better measure of the center for skewed distributions.In Desert Landing, the histogram shows a symmetric distribution, with the shaded bars evenly distributed around the center.
In this case, both the mean and median can be considered reliable measures of the center.Therefore, to determine which location typically has the cooler temperature, we should use the median.
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Graph Y = 1/2x - 4 on the coordinate plane
Answers
The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.
Describe Coordinate Plane?Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.
Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.
For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.
The graph is shown below when y=1.
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Graph attached below,
The coordinates of the plane is
x y
1 -3.5
2 -3
4 -2
6 -1.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].
Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]
Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]
Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]
Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]
Then coordinates of the plane is
x y
1 -3.5
2 -3
4 -2
6 -1.
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a scientist claims that the mean gestation period for a fox is more than 48.9 weeks. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g
Answers
The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.
If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.
The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.
Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.
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in the faculty lecture, dr. salon mentioned a survey that was taken in the slums in nairobi. from this survey, how long did the average person live in the slums?
Answers
Without specific data from the survey, I cannot provide the exact average length of time a person lived in the slums. I can be found by collecting data and finding average.
In general, surveys can be used to gather information on a population's characteristics and experiences, including their life expectancy. If the survey conducted in the slums of Nairobi included questions about life expectancy or mortality rates, the average lifespan of the individuals surveyed could be calculated using the data collected. It's important to note that the average lifespan in the slums may differ from that of other areas in Nairobi or other regions of the world.
Based on the information provided, Dr. Salon mentioned a survey conducted in the slums of Nairobi. To determine how long the average person lived in the slums, we would follow these steps:
1. Collect the data: The survey would gather information about the length of time people lived in the slums.
2. Calculate the average: Add up the total number of years all respondents lived in the slums and divide by the total number of respondents.
Without specific data from the survey, can't provide the exact average length of time a person lived in the slums. Please provide more information or refer back to Dr. Salon's lecture for the results of the survey.
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tell whether the ordered pair is a solution of the inequality. 2z less than 15; z =11
Answers
The ordered pair (z, 11) is not a solution of the inequality.
Explain inequality
An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.
According to the given information
To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:
2z < 15
2(11) < 15
22 < 15 (this is false)
Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.
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The equation ( x + 6)^2 + ( y + 4) ^2 = 36 models the position and range of the source of a radio signal.
1. Where is the signal located?
2. What is the range of the signal? Only enter numerical values.
Answers
1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).
What is the range of the signal?2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).
To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.
In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.
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Determine the density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm3.
Answers
The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.
What do you mean by the density of an object?Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.
Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:
Density = Mass/Volume
Substituting the given values, we get:
Density = 6 grams/12 cm³
Density = 0.5 grams/cm³
Therefore, the density of the sample is 0.5 grams/cm³.
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Can someone help me with this, please?
Learning Task 2: Try to solve the following problem. Use the block model
to help you. Write your answer in your notebook.
1) Ruben can paint square meters per hour. At the same rate, how
many square meters can he paint in an hour.
1
2 6
1
2 2
2) The lot has a length of meters and a width of meters. The
piece of lot per square unit is ₱ 850. 0. What is the total value of the lot?
Answers
Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.
Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour
what minus 1 1/2 equals 3 3/4
Answers
Answer:
5 1/4
Step-by-step explanation:
Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answers as a comma-separated list.)
(a)
3/4
Answers
The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.
What is coterminal angles ?Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).
To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).
One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:
3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π
Simplifying, we get:
3/4 + 2π = (3π + 4)/4
Therefore, one positive coterminal angle is (3π + 4)/4 radians.
One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:
3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π
Simplifying, we get:
3/4 - 2π = (-5π + 4)/4
Therefore, one negative coterminal angle is (-5π + 4)/4 radians.
Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.
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three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results. if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit? answer choices are rounded to the hundredths place.
Answers
The probability that a student selected at random is a girl who chose apple as her favorite fruit is 0.32, or 32% rounded to the nearest hundredth.
To calculate the probability that a student is a girl who chose apple as her favorite fruit, we need to use the information provided in the table. First, we need to find the total number of girls who participated in the survey, which is the sum of the number of girls who chose apples, oranges, and mangoes as their favorite fruit, i.e., 46 + 41 + 55 = 142.
Next, we need to find the number of girls who chose apples as their favorite fruit, which is 46. Therefore, the probability that a student is a girl who chose apple as her favorite fruit is given by:
Probability = Number of girls who chose apples / Total number of girls in the survey
Probability = 46 / 142
Probability = 0.32
This means that out of all the girls who participated in the survey, 32% of them chose apple as their favorite fruit.
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Complete question is:
three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results.
Boys Girls
Apple 66 46
Orange 52 41
Mango 40 55
if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit?
Chase is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2.50 per mile driven. Make a table of values and then write an equation for C,C, in terms of m,m, representing the total cost of renting the truck if Chase were to drive m miles.
Answers
The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
What is the equation?Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
The equation would be:
C is the total cost and m is the miles driven.
We know that:
Charge of the truck: $35
Charge per mile: $2.50
Then, form the equation as follows:
C = 35 + 2.50m
Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
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Convert the polar coordinates (6, -π/3) to Cartesian coordinates. Leave answers in fractional form. Use the "/" key as the fraction bar.
Answers
the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).
What is a fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:
x = r cos(θ)
y = r sin(θ)
Substituting the given values, we get:
x = 6 cos(-π/3) = 6 × (1/2) = 3
y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3
Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).
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Amy is sewing some pants for herself. This is the rule for how much fabric she needs to buy. • Measure from your waist to the finished length of thepants • Double this measurement • Add 8inches 1. Amy’s measurement from her waist to the finished length of the pants is 35inches. How many inches of fabric does sheneed?
Answers
Amy needs 78 inches of fabric for her pants if she follows the given rule.
Define inches ?
An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.
To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.
Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.
Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.
Therefore, Amy needs 78 inches of fabric for her pants.
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Find the radius of convergence, R, of the series. [infinity]
n = 2
(x + 8)n
8n ln(n)
Answers
The radius of convergence is 4.
To find the radius of convergence, R, of the collection, we can use the ratio test:
[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]
[tex]lim_n→∞ |(a_{(n+1})/[/tex]
[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]
For the series to converge, this limit need to be less than 1. therefore, we've:
[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]
For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:
|(x+8) / 4| < 1
Taking the absolute cost under consideration, we have cases:
Case 1: (x+8)/4 < 1
In this case, we have x < -4.
Case 2: (x+8)/4 > -1
In this case, we have x > -12.
Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):
R = min{8, 4} = 4
So, 4 is the radius of convergence.
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Suppose you had a bag that contained 100 Skittles! How many red Skittles would it need to have in order for you to have the same ratio of that color?, Show your work and explain your reasoning
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Answer: Let's say we want to find out how many red Skittles we need to add to the bag to have the same ratio of red Skittles as in the original bag.
Suppose the original bag contains x red Skittles. Then, the ratio of red Skittles to the total number of Skittles in the bag is x/100.
Let's say we add y red Skittles to the bag, so the total number of red Skittles in the bag becomes x + y. The total number of Skittles in the bag becomes 100 + y, since we only added red Skittles.
For the ratio of red Skittles to be the same as in the original bag, we need:
(x + y) / (100 + y) = x / 100
Cross-multiplying, we get:
100(x + y) = x(100 + y)
Simplifying and rearranging, we get:
y = 100x / (100 - x)
So, we need to add 100x / (100 - x) red Skittles to the bag to have the same ratio of red Skittles as in the original bag. For example, if the original bag has 20 red Skittles, we need to add:
y = 100(20) / (100 - 20) = 25
So, we need to add 25 red Skittles to the bag to have the same ratio of red Skittles as in the original bag.
Step-by-step explanation:
HLEP me please with math
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For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.
Explain about the scale factor:On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.
Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.
From the diagram:
coordinate of A = (1,1)
coordinate of A' = (5,5)
Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'
Same applies with the coordinates of B, C and D.
Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.
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the average car can go 25 miles on one gallon of gas. You can write an equation to show the relationship between the amount of gas you buy and how far you can travel
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Answer:
Step-by-step explanation:
the inword
Write the equation of the line that passes through the point (0, 4) and is parallel to the line with equation y=5x+3
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Sorry if my english is a bit weird, i hope that helped!
Need help ASAP
there are 600 poetry books at the library.Of the poetry books,8 1/2% are for children.How many poetry books at the library are for children
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The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.
What is number?Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.
8 1/2% is equal to 0.04.
To calculate the number of poetry books for children, multiply 0.04 by 600.
0.04 x 600 = 24
To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.
In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.
To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.
Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.
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solve for x using soh cah toa I have tried figuring it out but it says its wrong
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Answer:
13.416407865
Step-by-step explanation:
You wouldn't use soh cah toa
There is no angle given. Instead you should do 6²+12²=180
And then you would square root 180=13.416407865
Therefore the answer is 13.416407865
4.7. the time it takes a printer to print a job is an exponential random variable with the expectation of 12 seconds. you send a job to the printer at 10:00 am, and it appears to be third in line. what is the probability that your job will be ready before 10:01?
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The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.
We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.
The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.
Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.
The probability that the first job is finished before 10:01 is given by:
P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935
Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:
P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693
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