The total area of the first floor of the tiny house is 121 square feet
The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:
Total area = Area of kitchen + Area of bathroom
The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:
Area of kitchen = 11 x 7 = 77 square feet
Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:
Area of bathroom = 11 x 4 = 44 square feet
Substituting these expressions into the equation for the total area, we get:
Total area = Area of kitchen + Area of bathroom
= 77 + 44
= 121 square feet
Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.
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Ethan wrote the number below.
Lucy wrote another number in which the value of the digit 5 is 10 times larger than it is in Ethans number. Which number could be Lucy's number?
A. 4982.58
B. 4945.82
C. 4974.65
D. 4958.03
The answer would be D
Since Lucy's number has a digit of 5 which is 10x greater than Ethan's number, 5 x 10 = 50; so 50 would be in the tenth place, and option d is the only one with 5 in the tenth place.
The value of a number moves one decimal place to the left for each position it moves to the right. So, the number that Lucy could have written where the number 5 has a value 10 times larger than Ethan's number is 4974.65.
Explanation:In order for the value of the digit 5 to be 10 times larger in Lucy's number than it is in Ethan's, the '5' in Lucy's number should reside one place left compared to Ethan's. This means the 5 should be in the tens place, hundreds place, or beyond. So, we should look for a number having digit 5 at those places.
Let's examine the given options:
A. 4982.58 - '5' is in the hundredths place, which makes its value smaller, not larger.B. 4945.82 - '5' is in the ones place. No change in value.C. 4974.65 - '5' is in the tens place, making its value 10 times larger than if it were in the ones place.D. 4958.03 - '5' is in the thousands place, which makes its value even larger, but more than 10 times.Therefore, the correct answer is C. 4974.65.
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The x-value of which funtion's y-intercept is larger, f or h? justify your answer.
The function with the larger y-intercept is h, because it intersects the y-axis at a higher point than f.
How to determine larger y-intercept?To determine which function, f or h, has a larger y-intercept, we need to look at the graphs of the two functions. From the graph, we can see that function h has a larger y-intercept than function f.
The y-intercept of function h is approximately 4, while the y-intercept of function f is approximately 2. Therefore, we can conclude that the x-value of function h's y-intercept is larger than that of function f.
This is because the y-intercept of a function is the point at which it intersects with the y-axis, and the value of the x-coordinate at that point determines the x-value of the y-intercept.
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A shoe store orders shoes from the manufacturer and sells them at a mall. Storing shoes at the store costs $6 per shoe pair for a year. When reordering shoes from the manufacturer, there is a fixed cost of $14 per order as well as $7 per shoe pair. The retail store sells 1750 shoe pairs each year. Find a function that models the total inventory costs as a function of x x the number of shoe pairs in each order from the manufacturer
The total inventory costs consist of two parts: the cost of storing the shoes and the cost of reordering the shoes. The cost of storing the shoes is given by the formula:
Cost of storing = $6 per shoe pair per year x number of shoe pairs
Since the shoes are stored for a year, this cost is incurred annually. The cost of reordering the shoes is given by the formula:
Cost of reordering = $14 per order + $7 per shoe pair x number of shoe pairs
This cost is incurred each time the store places an order with the manufacturer.
Let x be the number of shoe pairs in each order from the manufacturer. The number of orders needed to sell 1750 shoe pairs each year is given by:
Number of orders = 1750 shoe pairs / x shoe pairs per order
The total inventory costs can be expressed as:
Total cost = Cost of storing + Cost of reordering
Substituting the formulas for the two costs and the expression for the number of orders, we get:
Total cost = $6 per shoe pair per year x 1750 shoe pairs + ($14 per order + $7 per shoe pair x x shoe pairs) x (1750 shoe pairs / x shoe pairs per order)
Simplifying this expression, we get:
Total cost = $10,500 + $14(1750/x) + $7(1750)
Total cost = $10,500 + $24,500/x
Therefore, the function that models the total inventory costs as a function of x is:
Total cost(x) = $10,500 + $24,500/x
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Arrange the following assets and liabilities and construct a net worth statement. Assets and Liabilities Amount Checking account $14,532 Student Loan $1,225 Retirement Savings $43,675 Credit Card Debt $3,876 Car (paid off) $12,225 Home Loan Balance $65,225 Create a table or list for assets and another for liabilities. Find the total amount for all assets and the total amount of liabilities. What is the net worth?
The net worth is about $106.
This can be calculated by the addition of liabilities and assets amount
Assets - Amount
Checking amount - $14,532
Retirement savings- $43,675
Car - $12,225
Therefore total assets equal to: $70,432
Now, for liabilities
Liabilities - Amount
Student loan $1,225
Credit card debt $3,876
Home loan balance $65,225
Therefore total liabilities equals to: $70,326
The net worth can be find out by subtracting the total liabilities from the total assets:
Hence Net worth = Total assets- Total liabilities
= $70,432- $70,326
= $106
Therefore the total net worth is about $106.
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Please I need your help!
Select each equation that the number 10 to the 3rd power makes true.
6.01 × ⬜ = 601
0.305 × ⬜ = 305
0.54 × ⬜ = 540
0.097 × ⬜ = 970
0.97 × ⬜ = 97
B. Constructing a parallel through a point (rhombus method) Steps: 1. Place the compasess on the point K and set it width to a little more than the distance to the PQ. The exact distance is not important. 2. Draw a wide arc from the right of K around so it crosses the PQ at two points. Label the left point J.
3. Without adjusting the opening of the compass, move the compass to J and draw an arc across the PQ Label this point E.
4. Without adjusting the span of the compass , move the compass to E and draw an arc across the large arc to the right of K. Label this point S.
5. Draw a straight line through points K and S.
6. Done. The KS is parallel to the PQ.
please paki sagot po.
The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential.
Constructing a parallel line through a point using the rhombus method involves the following steps:
1. Place the compass on point K and set its width slightly more than the distance to line PQ. The exact distance is not crucial.
2. Draw a wide arc from the right of K, crossing line PQ at two points. Label the left point J.
3. Without adjusting the compass opening, move the compass to point J and draw an arc across line PQ. Label this point E.
4. Keeping the compass width unchanged, move the compass to point E and draw an arc across the large arc to the right of K. Label this point S.
5. Draw a straight line through points K and S.
6. The line KS is now parallel to line PQ, as desired.
The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential. The process relies on the compass's fixed width to ensure the angles and distances remain consistent, resulting in parallel lines.
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list all the Factors. circle the GCF.
6:
9:
list 7 multiples.Circle the LCM.
5:
2:
Answer:
List all the factors
6: 3, 2, 1 (6)
9:3,(9),1
5:(5),1
2:(2),1
Step-by-step explanation:
Tell whether finding the answer requires finding a greatest common factor or a least common multiple. You do not need solve the problem. A string of holiday lights at a store have three colors that flash at different times. Red lights flash every fifth second. Blue lights flash every third seconds. Green light flashes every four seconds. The store owner turns on the lights. After how many seconds will all three lights flash at the same time for the first time?
A. ) Greatest Common Factor
B. ) Lest Common Multiple
Finding the answer requires finding the least common multiple (LCM) of 5, 3, and 4, making the correct answer B. ) Least Common Multiple.
To determine whether finding the answer requires finding a greatest common factor (GCF) or a least common multiple (LCM), we need to analyze the given information.
In this scenario, the red lights flash every fifth second, the blue lights flash every third second, and the green lights flash every fourth second. We want to find the first time when all three lights flash simultaneously.
To find this time, we need to find the smallest number that is divisible by all three given numbers (5, 3, and 4). This means we are looking for the least common multiple (LCM) of these numbers.
To calculate the LCM, we can use the formula:
LCM(a, b) = (a * b) / GCF(a, b),
where GCF(a, b) represents the greatest common factor of numbers a and b.
Therefore, in this case, finding the answer requires finding the least common multiple (LCM) of 5, 3, and 4, making the correct answer:
B. ) Least Common Multiple.
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You roll a 6-sided die.what is p(even or divisor of 3)?simplify your answer and write it as a fraction or whole number.
Answer: 5/6
Step-by-step explanation:
probabilities = possibilities/outcome
To get an even you can possible roll 2, 4, 6 with 6 total outcomes
P(even) = probability of getting an even = 3/6
To get a divisor of 3: only 3 and 6 can be divided by 3
P(divisor of 3)=2/6
Because of the or in the statement, you add the 2 probabilities
P(even or divisor of 3) = 3/6+2/6 = 5/6
Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use C for the constant of integration.)
∫9x√(-x^2 + 9dx)
The substitution is u = -x² + 9 and the evaluated value is -4.5(2/3)(-x² + 9)³/² + C.
To evaluate the given integral ∫9x√(-x² + 9dx),
we can use the substitution u = -x² + 9. This substitution will allow us to simplify the expression under the square root.
First, we can find du/dx by taking the derivative of u with respect to x: du/dx = -2x.
Next, we can solve for dx in terms of du by dividing both sides by -2x: dx = -du/(2x).
Using the substitution and the expression for dx in terms of du, we can rewrite the integral as:
∫9x√(-x² + 9dx) = -4.5∫√udu
Now, we can integrate the simplified expression √u using the power rule of integration:
-4.5∫√udu = -4.5(2/3)u³/² + C
Substituting back for u, we get:
-4.5(2/3)(-x² + 9)³/² + C
Therefore, the solution to the integral ∫9x√(-x^2 + 9dx) using the substitution u = -x^2 + 9 is:
-4.5(2/3)(-x² + 9)³/² + C
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Norma and david crawled to the barn and then hopped back to the house. they crawled at 300 centimeters per minute and hopped at 400 centimeters per minute. if round took 7 minutes, hiw long did they crawl
Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.
Find time Norma and David spent crawling to barn if the round trip took 7 minutes. They crawled at 300 cm/min hopped back at 400 cm/min.Let x be the time (in minutes) that Norma and David spent crawling to the barn, and y be the time (in minutes) they spent hopping back to the house. We know that:
x + y = 7 (the total time they spent on the round trip was 7 minutes)
300x + 400y = distance to the barn and back (since their speeds are given in centimeters per minute, the product of their speeds and the time spent crawling or hopping gives the distance in centimeters)
We want to find x, the time they spent crawling to the barn. We can solve for x by rearranging the first equation as x = 7 - y, and substituting into the second equation:
300(7 - y) + 400y = distance to the barn and back
2100 - 300y + 400y = distance to the barn and back
100y = distance to the barn and back - 2100
y = (distance to the barn and back - 2100)/100
Now we need to find the distance to the barn and back. They crawled to the barn at 300 cm/min, so the distance they crawled is 300x cm. They hopped back to the house at 400 cm/min, so the distance they hopped is 400y cm. The total distance to the barn and back is:
distance to the barn and back = 300x + 400y
= 300x + 400[(distance to the barn and back - 2100)/100] (substituting the expression we found for y)
= 300x + 4(distance to the barn and back - 2100)
Simplifying and solving for distance to the barn and back, we get:
distance to the barn and back = 5400/7 cm
Finally, we can substitute this value into the expression we found for y, and solve for x:
y = (distance to the barn and back - 2100)/100
= (5400/7 - 2100)/100
= 24/7
x = 7 - y
= 7 - 24/7
= 37/7
Therefore, Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.
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Please asap!!! will give 100 brainlest!!! (there's more than one answer)
select all the correct measures of center and variation for the following data set.
10, 20, 31, 17, 18, 5, 22, 25, 14, 43
a. first quartile = 12
b. iqr = 11
c. median = 19
d. third quartile = 25
e. mad = 7
First quartile is 14, IQR is 14, median is 19, third quartile is 28 and MAD is 7.
a. First quartile = 12 and d. Third quartile = 25 are not necessarily correct measures of quartiles for this dataset. To calculate the quartiles, we need to first order the data set and then find the value(s) that divide it into four equal parts. In this case, the sorted dataset is:
5, 10, 14, 17, 18, 20, 22, 25, 31, 43
The first quartile is the median of the lower half of the data: (5, 10, 14, 17, 18) and is 14.
b. IQR = 11 is not correct. The IQR (Interquartile Range) is the difference between the third quartile and the first quartile, which is 28-14=14 for this dataset.
c. Median = 19 is a correct measure of center.
d. The third quartile is the median of the upper half of the data: (22, 25, 31, 43) and is 28.
e. MAD = 7 is a correct measure of variation.
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Someone please help
(Composition of Transformations)
The image point of (6, 4) after the transformation R₉₀ T₁,₅ is (-3, 11).
Understanding the Composition of TransformationThe transformation R₉₀ T₁,₅ represents a rotation of 90° counterclockwise around the origin followed by a translation of 1 unit to the right and 5 units up.
To find the image point of (6, 4) under this transformation, we can apply the two transformations in order.
First, let's find the image of (6, 4) after rotating 90° counterclockwise around the origin.
Easy way to do this is by switching the x and y coordinates and negate the new x-coordinate. So, the image of (6, 4) after the rotation is (-4, 6).
Next, we apply the translation of 1 unit to the right and 5 units up. This moves the point (-4, 6) one unit to the right to get (-3, 6), and five units up to get the final image point:
Image point = (-3, 11)
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Look at picture please
Answer:
135.6 cubic centimeters
Step-by-step explanation:
To find the volume of soda in the cylindrical glass, we need to first find the volume of the glass and then multiply it by 60% to get the volume of soda. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = π(3 cm)^2(8 cm) = 72π cm^3
To find the volume of soda, we multiply the volume of the glass by 60% or 0.6:
Volume of soda = 0.6 x 72π cm^3 = 43.2π cm^3
Rounding to the nearest tenth, we get:
Volume of soda ≈ 135.6 cm^3
Therefore, there are approximately 135.7 cubic centimeters of soda in the glass
Answer: 226.3
Step-by-step explanation:
Hello! Here is how to solve this problem.
The formula for volume of a cylinder is V(c) = (B)(h)
The height is 8 cm, and the radius is 3 cm. The base is a circle, so the base area will be 22/7(r)^2. Pi is represented as 3.14 or 22/7, but 22/7 is more accurate.
V(c) = 22/7((3)^2)(8)
V(c) = 22/7(9 x 8)
V(c) = 22/7(72)
V(c) = 226.285714.
So, rounded to the nearest tenth, the volume of the soda can is 226.3 cm^3.
Tips for you:
1. Round to the nearest tenth
2. Use 22/7 for pi unless it says to use 3.14 for pi or use the symbol for pi instead of solving further.
Hope this helps, have a great day!
In ΔFGH, g = 140 inches, f = 980 inches and ∠F=170°. Find all possible values of ∠G, to the nearest degree.
The angle G from triangle FGH has a measure of approximately 1°.
How to find all missing angles of a triangle
In this problem we find the case of a triangle with two known sides and a known angle. By Euclidean geometry, the sum of all internal angles in a triangle equals 180° and we are required to find all possible values of angle G. This can be done by using sine law:
(980 in) / sin 170° = (140 in) / sin G
sin G = 0.024
G = 1.421°
The only possible value for angle G is equal to 1.421°.
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B. analyze relationships deloria says she can find the relative
frequency of nuts based on another relative frequency. what might
she be doing
nuts:3/30=15%
Deloria is analyzing the relationships between relative frequencies of nuts.
She has found that the relative frequency of a specific type of nut is 15%, which is calculated by dividing the number of that nut (3) by the total number of nuts (30).
Deloria might be comparing this relative frequency to other types of nuts to determine their prevalence or importance in a given context.
To calculate the relative frequency, we can divide the number of occurrences of the specific nut (3) by the total number of nuts (30):
Relative frequency = (Number of occurrences of specific nut) / (Total number of nuts)
Relative frequency = 3 / 30 = 0.1 = 10%
Therefore, the relative frequency of the specific type of nut is 10%, not 15%. It seems there was an error in the initial statement.
By analyzing relative frequencies, Deloria can compare the prevalence or importance of different types of nuts in a given context.
By calculating and comparing the relative frequencies of different types of nuts, Deloria can gain insights into the distribution and significance of each nut type within the dataset or sample.
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Giving away a lot of points please don't put something random, no explanation is needed only the answer.
Thank you
The theoretical probability is: 12.5%. After 100 trials, the experimental probability is of: 20%. After 400 trials, the experimental probability is of: 11%. After more trials, the experimental probability is closer to the theoretical probability.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
(eight sides, each of them is equally as likely).
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%. -> results given in the text.400 trials: 44/400 = 0.11 = 11%.The more trials, the closer the experimental probability should be to the theoretical probability.
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pls help me out on both questions !!!!
The mass of iron III sulfate is 300 g.
What is the stoichiometry?If 1 mole of iron III sulfate is produced when 3 moles of hydrogen is produced
x moles of iron III sulfate is produced when 2.25 moles of hydrogen is produced
x = 1 * 2.25/3
= 0.75 moles
Mass of the iron III sulfate = 0.75 moles * 400 g/mol
= 300 g
Number of moles of iron = 85 g/56 g/mol
= 1.5 moles
If 2 moles of iron produces 1 mole of iron III sulfate
1.5 moles of iron produces 1.5 * 1/2
= 0.75 moles
Mass of the iron III sulfate = 0.75 moles * 400 g/mol
= 300 g
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A ramp is used to go up one step.
The ramp is 3 m long. The step is 30 cm high.
How far away from the step (x) does the ramp start?
Give your answer in metres, to the nearest centimetre.
Answer:
3 meters = 300 centimeters
Using the Pythagorean Theorem:
[tex] {x}^{2} + {30}^{2} = {300}^{2} [/tex]
[tex] {x}^{2} + 900 = 90000 [/tex]
[tex] {x}^{2} = 89100[/tex]
[tex]x = 90 \sqrt{11} = 298.49[/tex]
x = about 298 centimeters
= about 2.98 meters
HELP ME PLSSSS ANYBODY OF ANY AGE I WILL LEAVE A GOOD REVIEW
Answer:
the third one
Step-by-step explanation:
Answer:
Option 3 is the correct answer
Step-by-step explanation:
The surface area of a prism is the area of the full net.
The area of the full net is the sum of the areas of each part
For the given net, there are three rectangles, and two triangles.
The area for rectangles and triangles are given by the following formulas:
[tex]A_{rectangle}=base*height[/tex]
[tex]A_{triangle}=\frac{1}{2}*base*height[/tex]
It is important to recognize that due to the fact that the 3-D shape is a prism, the two triangles are congruent, and have exactly the same dimensions and area.
Looking at the options:
Option 1 has three products added together. This would be the base time height of each of the three rectangles. It does not include the area for either of the triangles.
Option 2 does have an extra term in front with 3 numbers multiplied together. It most closely resembles 2 times the product of the base and height of the triangle, but recall the area for a triangle is one-half of the base times height (this may make more sense when looking at option 3). This over-calculates the area of the triangle, and then doubles that over-calculated area (to match the second triangle)
Option 3 has an extra term in front with the number 2 times a parenthesis with 3 terms. These three terms represent the "one-half" from the formula for the area of a triangle, and the base and height of the triangle. The 2 in front of the parentheses represents that there are two of those triangles, both with that area. This correctly calculates the area of the net, and thus, the surface area of the triangular prism.
Option 4 has an extra term in front, similar to option 3 which calculates the area of one triangle correctly, but fails to account for the area of the second triangle.
Option 3 is the correct answer.
Colton invests $1,000. He invests part of it in IBM and after one year earns 5% on his
investment. He invests the other part of the $1,000 in MacIntosh and after one year
earns 8% on his investment. If his total interest after one year is $60.80, how much did
he invest in each?
Solution:-
Here,
let, P=$1000
Money vested in IBM= x
Interest=(x×1×5)/100
=5x/100
Money invested in Macintosh=1000-x
Interest=((1000-x)1×8)/100
=(8000-8x)/100
Now,
Total Interest=5x/100 + (8000-8x)/100
or, 60.80=(5x+8000-8x)/100
or, 60.80×100=-3x+8000
or, 6080-8000=-3x
or, -1920/-3=x
x=$640
1000-x=1000-640
=360
Thus, Colton invested $640 in IBM, and $360 in Macintosh.
When you don’t replace the marble for the second draw what kind of probability is it?
If you do not replace the marble after the first draw, the probability calculation depends on whether you are dealing with a dependent or an independent event.
The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1 (inclusive), where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. The field of mathematics known as probability studies the possibility that a certain event will take place. It is a way to quantify the possibility or likelihood that something will really happen.
For an independent event, assuming that the first draw had no bearing on the outcome of the second draw, in the case of an isolated occurrence, the chance of drawing a specific marble on the second draw would be the same as the likelihood of drawing that same marble on the first draw. For a dependent event, the outcome of the first draw would determine the possibility of drawing a specific marble on the second draw.
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Hannah's favorite toy character is sold wearing one of many outfits an outfit consists of one share one pair of pants and one
cap the shirt can be striped plane or polkadotted pants may be denim or played the account may be a cowboy hat wear a baseball cap if Hannah picks a toy at random from the shelf and there are an equal number of toys wearing age outfit what is the probability that the toy is dressed in a polkadotted shirt and a cowboy hat.
A. 1/8
B. 1/6
C. 1/4
D. 1/3
E. 1/2
The probability of the toy character wearing a polka-dotted shirt and a cowboy hat is P(polka-dot shirt and cowboy hat) = 2 / 12 = 1/6.
What is the probability of the toy character wearing a polka-dotted shirt and a cowboy hat in the number of outfits?
There are 3 choices for the shirt (striped, plain, or polka-dotted), 2 choices for the pants (denim or plaid), and 2 choices for the cap (cowboy or baseball). Therefore, there are a total of 3 x 2 x 2 = 12 different outfits that the toy character could be wearing.
The probability of the toy character wearing a polka-dotted shirt and a cowboy hat is the number of outfits with a polka-dotted shirt and a cowboy hat divided by the total number of outfits:
P(polka-dot shirt and cowboy hat) = number of outfits with a polka-dot shirt and cowboy hat / total number of outfits
To find the number of outfits with a polka-dotted shirt and a cowboy hat, we need to consider each clothing item separately. There is only 1 choice for the cowboy hat and only 1 choice for the polka-dotted shirt. There are 2 choices for the pants, but we don't care which pants the toy character is wearing. Therefore, the number of outfits with a polka-dotted shirt and a cowboy hat is:
1 (cowboy hat) x 1 (polka-dotted shirt) x 2 (pants) = 2
So the probability of the toy character wearing a polka-dotted shirt and a cowboy hat is:
P(polka-dot shirt and cowboy hat) = 2 / 12 = 1/6
Therefore, the answer is (B) 1/6.
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Divide.
Simplify your answer as much as possible.
Answer:
-5z/v³ + 8 + 6v²z
Do you have to simplify it further or?
Step-by-step explanation:
[tex] \frac{ - 5z + 8v {}^{3} + 6v {}^{5} z}{v {}^{3} } = \frac{ - 5z}{v {}^{3} } + \frac{8v {}^{3} }{ {v}^{3} } + \frac{6v {}^{5} }{v {}^{3} } = \frac{ - 5z}{v {}^{3} } + 8 + 6v {}^{2}z[/tex]
The distance between san antonio and houston is 190 miles. nicholas and rose each drove 2/5 of the total distance. if charlie drove the rest of the distance, how many miles did charlie drive?
Charlie drove 90 miles between San Antonio and Houston.
Nicholas and Rose each drove 2/5 of the total distance (190 miles). To find the distance they drove together, multiply 190 miles by 2/5 twice (once for each person):
190 x (2/5) = 76 miles (Nicholas)
190 x (2/5) = 76 miles (Rose)
Together, Nicholas and Rose drove 76 + 76 = 152 miles. To find the remaining distance Charlie drove, subtract this combined distance from the total distance:
190 miles (total) - 152 miles (Nicholas and Rose) = 38 miles (Charlie).
Charlie drove 90 miles between San Antonio and Houston, as Nicholas and Rose each drove 2/5 of the total 190-mile distance, resulting in 152 miles combined, leaving 38 miles for Charlie to cover.
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Janelle has to solve this system of equations: 3x+5y=7 3x+5y=-4
She says, "I can tell just by looking that this system will have no solutions." What does she mean? How can she tell?
The system has no solution because the equations are parallel
What does she mean and How can she tell?Janelle is correct in saying that the system of equations has no solution. She can tell by looking at the coefficients of the variables in the two equations.
Both equations have the same coefficients for x and y, which means that they are parallel lines in the xy-plane.
Since parallel lines never intersect, there are no values of x and y that would satisfy both equations simultaneously, meaning that the system has no solution.
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Solve the problem The total cost, in dollars, to produce x DVD players is Cbx) 120 + 3x==2-3. Find the marginal cost when x-3 A) $228 B) $225 C) $105 D) $108
The problem involves finding the marginal cost of producing a certain number of DVD players, given the total cost function. Specifically, we are given the total cost function C(x) = 120 + 3x^2-3, where x is the number of DVD players produced, and we need to find the marginal cost when x = 3.
To find the marginal cost, we need to take the derivative of the total cost function with respect to x and evaluate it at x = 3. The marginal cost represents the cost of producing one additional unit of the product, and is an important concept in economics and business.
Understanding the relationship between marginal cost and production volume is crucial for optimizing production and pricing decisions for companies. Marginal cost analysis is used extensively in many fields, including manufacturing, finance, and marketing.
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Let D be the smaller cap cut from a solid ball of radius 6 units by a plane 3 units from the center of the sphere. Express the volume of D as an iterated triple integral in (a) spherical, (b) cylindrical
To express the volume of D as an iterated triple integral in (a) spherical, (b) cylindrical coordinates, we can use the following formulas:
(a) Spherical Coordinates:
We know that the equation of a sphere with radius 6 units is given by:
x^2 + y^2 + z^2 = 6^2
The equation of the plane 3 units from the center of the sphere is given by:
z = 3
To find the equation of the smaller cap cut from the sphere by this plane, we need to find the upper limit of the radial coordinate. This can be found by solving the equation of the sphere for z, and substituting z = 3:
z = sqrt(6^2 - x^2 - y^2)
3 = sqrt(6^2 - x^2 - y^2)
x^2 + y^2 = 27
Thus, the smaller cap D is the region of the sphere bounded by the plane z = 3 and the surface x^2 + y^2 + z^2 = 6^2, with x^2 + y^2 <= 27.
To express the volume of D as an iterated triple integral in spherical coordinates, we can use the following limits:
0 <= r <= sqrt(27)
0 <= θ <= 2π
arcsin(3/6) <= φ <= π
The volume of D can be expressed as the triple integral:
∫∫∫ D r^2 sin φ dr dφ dθ
(b) Cylindrical Coordinates:
To express the volume of D as an iterated triple integral in cylindrical coordinates, we can use the following limits:
0 <= r <= sqrt(27)
0 <= θ <= 2π
3 <= z <= sqrt(6^2 - r^2)
The volume of D can be expressed as the triple integral:
∫∫∫ D r dz dr dθ
(a) In spherical coordinates, the volume element is given by dV = ρ²sin(φ)dρdθdφ. To find the limits of integration, note that the radius of the smaller cap ranges from 0 to 3 units, the angle θ ranges from 0 to 2π, and the angle φ ranges from 0 to φ₀, where φ₀ is the angle between the plane and the line from the sphere's center to the plane's intersection with the sphere.
Using the cosine rule, we can find φ₀ as follows:
cos(φ₀) = (6² + 3² - 3²) / (2 × 6 × 3) = 1/2
φ₀ = π/3
Now, we can express the volume of D as an iterated triple integral in spherical coordinates:
∫(ρ=0 to 3) ∫(θ=0 to 2π) ∫(φ=0 to π/3) ρ²sin(φ)dρdθdφ
(b) In cylindrical coordinates, the volume element is given by dV = rdzdrdθ. To find the limits of integration, note that the height z ranges from 3 to 6 units, the radius r ranges from 0 to √((6 - z)²), and the angle θ ranges from 0 to 2π.
Now, we can express the volume of D as an iterated triple integral in cylindrical coordinates:
∫(z=3 to 6) ∫(θ=0 to 2π) ∫(r=0 to √((6 - z)²)) rdzdrdθ
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The smallest bone in the human body is the stapes bone. It is located in the ear and is about 2. 8 millimeters in length. Write this number in expanded form?
The expanded form of the smallest bone in the human body located in the ear which is about 2. 8 millimeters in length is 2 × 1 millimeter + 8 × 0.1 millimeters.
Given that the smallest bone in the human body is the stapes bone. It is located in the ear and is about 2. 8 millimeters in length.
To write 2.8 millimeters in expanded form, we need to express each digit's place value in the number.
2.8 millimeters can be written as:
2 millimeters + 0.8 millimeters
or
2 millimeters + 8/10 millimeters
In expanded form, this is:
2 millimeters + 8 tenths of a millimeter
or
2 × 1 millimeter + 8 × 0.1 millimeters
Therefore, 2.8 millimeters in expanded form is:
2 × 1 millimeter + 8 × 0.1 millimeters = 2.0 + 0.8 = 2.8 millimeters
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Two days later, Kelly surveyed the same 13 classmates and found that none of them had been given math homework since she last surveyed them.
By how much does the mean of Kelly’s second data set change in comparison with the mean of the data set in her original survey? Explain how to determine the change in the means without calculating the mean of either data set
The mean of Kelly's second data set doesn't change compared to the mean of her original survey because none of the classmates were given math homework.
To determine the change in the means without calculating the mean of either data set, you can compare the number of data points, the range, and any outliers. If the number of data points and the range are the same and there are no outliers, then the means will be the same.
In this case, since none of the classmates had math homework in both surveys, there are no changes in the data set, and the means remain the same. Therefore, there is no change in the mean of Kelly's second data set compared to her original survey.
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