The answer is (a) 0.8161.
In statistical analysis, the proportion of the variation in the response variable (selling price) explained by the predictor variables (square footage, age, number of bedrooms, number of bathrooms, and number of garages) is known as the coefficient of determination or R-squared value. The R-squared value ranges from 0 to 1, where a value closer to 1 indicates that the predictor variables explain a higher proportion of the variation in the response variable. In this case, an R-squared value of 0.8161 suggests that the predictor variables (square footage, age, number of bedrooms, number of bathrooms, and number of garages) explain about 81.61% of the variation in the selling price.
The R-squared value is an important statistic in regression analysis, as it indicates the goodness of fit of the regression model. A high R-squared value suggests that the model fits the data well and can be used to make accurate predictions. However, a high R-squared value does not necessarily mean that the regression model is the best model for the data. It is important to also consider other factors such as model complexity and statistical significance of the predictor variables.
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i need help with this
The missing values in the triangle are:
∠B = 90°
AB = 20.98
CB = 16.99
How to find the missing values?First, remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write:
51 + 39 + ∠B = 180
∠B = 180 - 51 - 39 = 90
So we have a right triangle.
Now, to find the values of AB and CB, we can use trigonometric relations, we know that teh hypotenuse is 27 units, then we can use:
cos(51°) = CB/27
27*cos(51°) = CB = 16.99
And:
cos(39°) = AB/27
27*cos(39°) = AB = 20.98
These are the missing values.
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What is the range of y=x^2-8x+12
Answer:
-infinity < x < infinity
Step-by-step explanation:
it has none.
what is the density, measured in grams per cubic centimeter, of a cube with 8-inch sides that weighs 700 grams? (1 cubic inch approximately 16.4 centimeters.) round to the nearest hundredths.
The density of the cube is 0.08343 grams per cubic centimeter
The side of cube is 8 inches
and, We know that :
The formula of Density is :
D = mass/ volume
The weight of a cube is 700 gm.
First, we convert the side inches into cm
For conversion, We have to multiply by 2.54
=> 8 × 2.54
=> 20.32cm
Now, For finding the density
We have to calculate the volume of cube :
Volume of cube = [tex](side)^3[/tex]
Volume of cube = 8390.18[tex]cm^3[/tex]
And, plug all the values in the formula of density.
Density = 700/8390.18[tex]cm^3[/tex]
Density = 0.08343 grams per cubic centimeter
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In a large city, the road system is set up like a Cartesian plane, where streets are indicated by the number of blocks they are from Street A and Street B. For example, a baseball field is located 3 blocks west of Street B and 32 blocks north of Street A. Treat the intersection of Street A and Street B as the origin of a coordinate system, with East being the positive x-axis. Answer parts (a)-(d). (a) Write the location of the baseball field using rectangular coordinates. (Type an ordered pair.) (b) Write the location of the field using polar coordinates. Use the east direction for the polar axis. Express ? in degrees. Type an ordered pair. Round to two decimal places as needed.) (c) A different ballpark is located 2 blocks west of Street B and 28 blocks south of Street A. Write the location of this ballpark using rectangular coordinates (Type an ordered pair) (d) Write the location of this ballpark using polar coordinates. Use the east direction for the polar axis. Express ? in degrees. (Type an ordered pair. Round to two decimal places as needed.)
(a) The location of the baseball field using rectangular coordinates is (-3,32).
(b) To find the location of the field using polar coordinates, we need to first find the distance r from the origin to the point (-3,32). Using the Pythagorean theorem, we have:
r = sqrt((-3)^2 + 32^2) = 32.28
Next, we need to find the angle theta between the positive x-axis and the line connecting the origin to the point (-3,32). Since the point is in the third quadrant, we know that theta is between 180 and 270 degrees. We can use the tangent function to find theta:
tan(theta) = (opposite side)/(adjacent side) = (-32)/(3)
theta = arctan(-32/3) = 276.87 degrees
Therefore, the location of the baseball field using polar coordinates is (32.28,276.87).
(c) The location of the different ballpark using rectangular coordinates is (-2,-28).
(d) To find the location of the different ballpark using polar coordinates, we need to first find the distance r from the origin to the point (-2,-28). Using the Pythagorean theorem, we have:
r = sqrt((-2)^2 + (-28)^2) = 28.06
Next, we need to find the angle theta between the positive x-axis and the line connecting the origin to the point (-2,-28). Since the point is in the fourth quadrant, we know that theta is between 270 and 360 degrees. We can use the tangent function to find theta:
tan(theta) = (opposite side)/(adjacent side) = (-28)/(-2) = 14
theta = arctan(14) = 83.66 degrees
Therefore, the location of the different ballpark using polar coordinates is (28.06,83.66).
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an air filter is rated to catch 90% of airborne particles. if the average particle diameter is 0.5 microns and the population standard deviation is 0.2 microns, what is the largest diameter particle (in microns) that will pass through the filter? assume that the diameter of particles in the air is normally distributed.
The largest diameter particle (in microns) that will pass through the filter is given as follows:
0.756 microns.
How to use the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 0.5, \sigma = 0.2[/tex]
The largest diameter is the 90th percentile, which is X when Z = 1.28, as 1.28 has a p-value of 0.9, hence:
1.28 = (X - 0.5)/0.2
X - 0.5 = 0.2 x 1.28
X = 0.756 microns.
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Twenty-five adult citizens of the U.S. were asked to estimate the average income of all U.S. households. The mean estimate was = $45,000 and s = $15,000. (Note: the actual average household income at the time of the study was about $68,000.) Assume the 25 adults in the study can be considered an SRS from the population of all adult citizens of the U.S. Which of the following would cause the most worry about the validity of a 95% confidence interval that you calculate using this information?A)A stemplot of the data shows a mild right-skew.B)You do not know the population standard deviation σ.C)You notice that there is a clear outlier in the data.
The most worrying factor for the validity of the 95% confidence interval in this case is option C) the presence of a clear outlier in the data for the average.
Let's consider each option and assess which one would cause the most worry about the validity of a 95% confidence interval calculated using the given information (mean estimate = $45,000 and standard deviation s = $15,000).
A) A mild right-skew in the stemplot indicates a slightly non-normal distribution of the data. However, since the sample size is 25, the Central Limit Theorem states that the sampling distribution of the mean should be approximately normal. So, a mild right-skew shouldn't be a significant concern for the validity of the 95% confidence interval.
B) Not knowing the population standard deviation (σ) can be a concern. However, when the sample size is large enough (which is the case here with 25 respondents), using the sample standard deviation (s) as an estimate of σ is acceptable, and the confidence interval calculation can still be valid.
C) A clear outlier in the data can greatly influence the mean estimate and the standard deviation, which may result in an inaccurate confidence interval. Outliers can cause the interval to be wider or narrower than it should be, affecting the validity of the 95% confidence interval.
Given these explanations, the most worrying factor for the validity of the 95% confidence interval in this case is option C) the presence of a clear outlier in the data. This outlier can significantly affect the accuracy and reliability of the confidence interval calculation.
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In a survey conducted among some people of a community, 650 people like meat, 550 people don't like meat, 480 don't like fish and 250 like meat but not fish. (i) How many people were surveyed? (ii) How many people like fish but not meat? (iii) How many people are vegetarians?
1. 1430 people were surveyed.
2. 150 people like fish but not meat.
3. 330 people are vegetarians.
The total number of persons surveyed1. 650 (total who like meat) - 250 (who like meat but not fish) = 400 (who like both meat and fish)
Now, we know that 550 people don't like meat, and 480 people don't like fish. Since 400 people like both meat and fish, the total number of people surveyed is:
550 (don't like meat) + 480 (don't like fish) + 400 (like both meat and fish) = 1430
So, 1430 people were surveyed.
2. 550 (don't like meat) - 400 (like both meat and fish) = 150
So, 150 people like fish but not meat.
3. 480 (don't like fish) - 150 (like fish but not meat) = 330
So, 330 people are vegetarians.
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an unpressurized aircraft with 20 occupants other than the pilots will be cruising at 14,000 feet msl for 25 minutes. for how many, if any, of these occupants must there be an oxygen supply?
There is no requirement for supplemental oxygen.
All 20 occupants can fly without oxygen supply.
Calculation of the oxygen requirements for an unpressurized aircraft flying at high altitudes:As the altitude increases, the atmospheric pressure decreases, which in turn reduces the partial pressure of oxygen in the air. This reduction in oxygen availability can cause hypoxia, which can lead to impaired judgment, vision, and coordination, and can be fatal in extreme cases.
The calculation of oxygen requirements can involve estimating the total oxygen consumption based on the number of occupants, their age, and their physical condition, and then determining the appropriate type and quantity of oxygen delivery systems to be carried on board the aircraft.
Here we have
An unpressurized aircraft with 20 occupants other than the pilots will be cruising at 14,000 feet msl for 25 minutes.
According to the Federal Aviation Regulations, if an aircraft is flying at an altitude above 12,500 feet MSL for more than 30 minutes,
then oxygen must be supplied to the occupants if:
The cabin pressure altitude exceeds 14,000 feet MSL, or
The cabin pressure altitude exceeds 15,000 feet MSL for any period of time.
In this case, the aircraft is flying at 14,000 feet MSL for 25 minutes, which is less than 30 minutes.
Therefore,
There is no requirement for supplemental oxygen.
All 20 occupants can fly without oxygen supply.
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A standard bathtub holds 60 gallons of water. A full tub drains 12 gallons per minute. Which of the following tables best represent the situation
Answer:
The correct table represents the situation is shown in Table J.
Step-by-step explanation:
Table J shows the appropriate chart that most accurately depicts the circumstance.
What is a line equation?
The line's equation in the form of a slope through the points
the formula for (x1, y1) and (x2, y2) with slope m is;
⇒ y - y₁ = m (x - x₁)
In this case, m = (y2 - y1) / (x2 - x1)
Knowing that;
60 gallons of water can be found in a typical bathtub.
12 gallons per minute are also drained from a full bathtub.
From table J, now
is the rate of change,
⇒ (24 - 12) / (2 - 1)
⇒ 12 / 1
more than 12 gallons per minute
In the given circumstance, which.
Thus, Table J is the appropriate table that most accurately depicts the situation.
8.8.PS-9
Find the surface area of
the prism.
The surface area isin.².
7 in.
15 in.
4 in.
The surface area of the given prism is 386 square inches.
To find the surface area of a prism, we need to find the area of all its faces and add them up.
The given prism has a rectangular base with dimensions of 7 inches by 15 inches, and a height of 4 inches.
The two rectangular faces (front and back) have dimensions of 7 inches by 4 inches,
so each has an area of 7 x 4 = 28 square inches.
The two rectangular faces (sides) have dimensions of 15 inches by 4 inches,
so each has an area of 15 x 4 = 60 square inches.
The top and bottom faces are both rectangles with dimensions of 7 inches by 15 inches,
so each has an area of 7 x 15 = 105 square inches.
Therefore, the total surface area of the prism is:
2(28 sq in) + 2(60 sq in) + 2(105 sq in) = 56 sq in + 120 sq in + 210 sq in
= 386 sq in.
So, the surface area of the given prism is 386 square inches.
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Suppose you have the same box with a volume of 400 i n . 3 in. 3 and a height of 5 in. You now also know that the box is 8 in. wide. What is the length of the box?
Answer:
length = 10 in.
Step-by-step explanation:
volume = 400 in.³
height = 5 in.
width = 8 in.
volume = length × width × height
V = LWH
400 = L × 8 × 5
400 = 40L
40L = 400
L = 400/40
L = 10
Answer: length = 10 in.
which of the following expressions is true
A. 4³*4 by the power of 4= 4 by the power of 12
B. 5²*5³> 5 by the power of 5
C. 3²*3 by the power of 5 < 3 by the power of 8
D. 5²* 5 by the power 4 =5 by the power 8
The correct expressions are:
B. 5² × 5³ >[tex]5^5[/tex]
C. 3² × [tex]3^5 < 3^8[/tex]
Let's evaluate each expression:
A. 4³ × [tex]4^4 = 4^{12[/tex]
Simplifying the left side: [tex]4^3 \times 4^4 = 4^{(3+4) }= 4^7[/tex]
Comparing with the right side: [tex]4^7[/tex]≠ [tex]4^{12[/tex]
Therefore, expression A is not true.
B. 5² × 5³ > [tex]5^5[/tex]
Simplifying the left side: [tex]5^2 \times 5^3 = 5^{(2+3)} = 5^5[/tex]
Comparing with the right side: [tex]5^5 = 5^5[/tex]
Therefore, expression B is true.
C. 3² × [tex]3^5 < 3^8[/tex]
Simplifying the left side: [tex]3^2 \times 3^5 = 3^{(2+5) }= 3^7[/tex]
Comparing with the right side: [tex]3^7 < 3^8[/tex]
Therefore, expression C is true.
D. 5² × [tex]5^4 = 5^8[/tex]
Simplifying the left side: [tex]5^2 \times 5^4 = 5^{(2+4) }= 5^6[/tex]
Comparing with the right side: [tex]5^6[/tex] ≠ [tex]5^8[/tex]
Therefore, expression D is not true.
In conclusion, the correct expressions are:
B. 5² × 5³ >[tex]5^5[/tex]
C. 3² × [tex]3^5 < 3^8[/tex]
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HELP PLEASESSS MAKE YOU AS BRANLESTS
Answer:
"Then I stopped the machine, and saw about me again the old familiar laboratory, my tools, my appliances just as I had left them. I got off the thing very shakily and sat down upon my bench. For several minutes I trembled violently. Then I became calmer. Around me was my old workshop again, exactly as it had been. I might have slept there, and the whole thing have been a dream.
Step-by-step explanation:
Olivia bought a new pair of shoes. The regular price was $87.50, they were having a 5% off sale and she had a $10 off coupon. (without tax) what was the total cost?
The total cost of the shoes, without tax, after the 5% off sale and the $10 off coupon, is $73.125.
To calculate the total cost of the shoes after the discount and coupon, we follow these steps:
Step 1: Calculate the discount amount.
Discount amount = Regular price * (Discount percentage / 100)
Discount amount = $87.50 * (5 / 100)
Discount amount = $87.50 * 0.05
Discount amount = $4.375
tep 2: Subtract the discount amount from the regular price.
Price after discount = Regular price - Discount amount
Price after discount = $87.50 - $4.375
Price after discount = $83.125
Step 3: Subtract the coupon amount from the price after discount.
Total cost = Price after discount - Coupon amount
Total cost = $83.125 - $10
Total cost = $73.125
Therefore, the total cost of the shoes, without tax, after the 5% off sale and the $10 off coupon, is $73.125.
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5. (16 pts) find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that has a power series expansion. also find the associated radius of convergence. f(x) = e ^ (- 6x)
The Maclaurin series for f(x) is:[tex]f(x) = 1 - 6x + 36x^2 - 216x^3 + ...[/tex]
The associated radius of convergence for this Maclaurin series is infinite, which means the series converges for all values of x.
The Maclaurin series for the function [tex]f(x) = ( {e}^{-6x} )[/tex] can be found using the definition of a Maclaurin series. The Maclaurin series represents a function as an infinite sum of terms, each term being a derivative of the function evaluated at x = 0, multiplied by a power of x divided by the factorial of the power.
To find the Maclaurin series for f(x),
we need to compute the derivatives of f(x) at x = 0.
Taking the derivatives of [tex]f(x) = ( {e}^{-6x} )[/tex]
we get:[tex]f'(x) ={ -6e}^{-6x} [/tex]
[tex]f''(x) = {36e}^{-6x} [/tex]
[tex]f'''(x) ={ -216e}^{-6x} [/tex]...
Evaluating these derivatives at x = 0,
we find:[tex]f(0) = e^0
= 1[/tex]f'(0)
= -6f''(0)
= 36f'''(0)
= -216...
Using these values,
the Maclaurin series for f(x) is:
[tex]f(x) = 1 - 6x + 36x^2 - 216x^3 + ...[/tex]
The associated radius of convergence for this Maclaurin series is infinite, which means the series converges for all values of x. This is because the exponential function [tex] {e}^{-6x} [/tex]converges for all real numbers x, and the series expansion captures the behavior of the function within that range.
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PLEASE HELP QUICK 20 POINTS
Find the exact value
Sin -5pi/6
Answer:
1/2
Step-by-step explanation:
We can use the unit circle and reference angle to find the exact value of sin(-5pi/6).
Starting from the positive x-axis (θ=0), we can rotate clockwise by 5pi/6 radians to get to the terminal side of -5pi/6.
The reference angle is pi/6 radians, which is the angle between the terminal side and the x-axis if we rotate counterclockwise instead.
At this angle, sin is negative and equal to -1/2, since the opposite side has length 1 and the hypotenuse has length 2.
Since sin is an odd function, we have sin(-5pi/6) = -sin(5pi/6) = -(-1/2) = 1/2.
Therefore, the exact value of sin(-5pi/6) is 1/2.
write the taylor series for f(x)=exf(x)=ex about x=2x=2 as ∑n=0[infinity]cn(x−2)n.
The Taylor series for f(x)=ex about x=2 is given by ∑n=0[infinity]cn(x−2)n where cn = fⁿ(2)/n! = e²/2! e²/3! ... e²/n!.
The Taylor series is a way to represent a function as an infinite sum of terms that involve the function's derivatives evaluated at a specific point.
In this case, we want to find the Taylor series for f(x)=ex about x=2. To do this, we first need to find the derivatives of f(x) at x=2.
We have fⁿ(x) = ex for all n, so fⁿ(2) = e² for all n. We can then use this to find the coefficients cn in the Taylor series.
We have cn = fⁿ(2)/n! = e²/2! e²/3! ... e²/n!.
We can then substitute these coefficients into the Taylor series to get ∑n=0[infinity]cn(x−2)n = ∑n=0[infinity] e²/2! e²/3! ... e²/n!(x−2)n, which is the Taylor series for f(x)=ex about x=2.
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7 minus the product of
3
and
x.
Answer:
7 - 3x
Step-by-step explanation:
Product would cause the 3 and x to combine.
Answer:
7 - 3x
Step-by-step explanation:
the product , multiplication of 3 and x = 3 × x = 3x
now subtract this product from 7 to obtain
7 - 3x
Find The Missing Length. The triangles in each pair are similar
The length of the side JL is 55 units.
Given that are two similar triangles, Δ LKJ and Δ TUV, we need to find the missing length,
TU = 14
TL = 22
JL = ?
KL = 35
so,
According to the definition of similar triangles,
Triangles with the same shape but different sizes are known as similar triangles.
Two triangles are said to be similar if their corresponding sides are proportionate and their corresponding angles are congruent.
In other words, two triangles are comparable if they can be changed into one another using a combination of rotations, translations, and uniform scaling (enlarging or decreasing).
TU / TV = KL / JL
14 / 22 = 35 / ?
14 x ? = 22 x 35
? = 55
Hence the length of the side JL is 55 units.
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time-use data show that married american women have cut their housework time roughly in half over the last half-century, while men have:
Over the last half-century, time-use data has shown that married American women have significantly reduced their housework time, cutting it roughly in half.
This change can be attributed to various factors such as advancements in home appliances, shifting gender roles, and increased participation of women in the workforce. On the other hand, men have gradually increased their contributions to housework during this period.
This shift in housework responsibilities can be attributed to societal changes that promote a more equitable distribution of domestic tasks between partners. As gender norms have evolved, men are increasingly taking on roles that were once predominantly associated with women, leading to a more balanced approach to housework within households. Additionally, the rise in dual-income families has necessitated a more equal division of domestic responsibilities.
In summary, over the past 50 years, married American women have seen a considerable decrease in housework time, while men have increased their contributions. This change reflects evolving gender roles and societal expectations, promoting a more equal division of labor within households.
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What is lim
x²-4?
X-2 X+2
O-4
O 0
04
ODNE
Answer:
A
Step-by-step explanation:
[tex]\lim_{x \to -2} \frac{x^{2}-4 }{x+2} \\\lim_{x \to -2} \frac{(x+2)(x-2)}{x+2}\\ \lim_{x \to -2} x-2\\= -4[/tex]
Answer:
First answer choice
[tex]- 4[/tex]
Step-by-step explanation:
[tex]\lim _{x\to \:-2}\left(\dfrac{x^2-4}{x+2}\right)\\\\\\\mathrm{Simplify}\:\dfrac{x^2-4}{x+2}\\\\\\\mathrm{Factor}\:x^2-4:\quad (x + 2)(x - 2)\\\\\lim _{x\to \:-2}\left(\dfrac{x^2-4}{x+2}\right) \\\\= \lim _{x\to \:-2}\left(\dfrac{x+2)(x-2)}{x+2}\right)[/tex]
The x+2 common factor cancels out
[tex]= \lim _{x\to \:-2}\left(x-2\right)\\\\\text{Plug in the value x= -2}\\\\= -2 - 2\\= -4[/tex]
in the long run, perfectly competitive firms produce a level of output such that multiple choice p = mc. p = minimum of ac. p = mc and p = minimum of ac. p > mc.
In the long run, perfectly competitive firms aim to produce at a level of output where their marginal cost (MC) is equal to the market price (P).
This is because in a perfectly competitive market, there are many firms competing with each other, and they cannot charge a price higher than the market price. Therefore, firms must produce at a level where their MC equals P in order to maximize profits.
Therefore, the answer to the question is that perfectly competitive firms produce a level of output such that P = MC. This is because the other options, P = minimum of AC and P > MC, do not accurately reflect the behavior of perfectly competitive firms. In a perfectly competitive market, firms cannot charge a price higher than the market price, so P will not be greater than MC. Additionally, P will not be equal to the minimum of AC because in a perfectly competitive market, there are no barriers to entry, so firms cannot earn economic profits in the long run. Therefore, they must produce at a level where P = MC to break even in the long run.
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Find the volume, and surface area. The base of the pyramid is a square. (h = 15)
type number only, no units:
V = ______in3
S.A. = ______in2
The volume of the pyramid is 1280 cubic units, and the surface area is 800 square units.
To find the volume and surface area of a pyramid, we can use the following formulas:
Volume of a pyramid = (1/3) · base area · height
Surface area of a pyramid = base area + (1/2) · perimeter · slant height
Given that the base of the pyramid is a square with a side length of 16, the base area can be calculated as:
Base area = side length² = 16² = 256 square units
The height of the pyramid is given as 15, and the slant height is given as 17.
Now, let's calculate the volume of the pyramid:
Volume = (1/3) · base area · height
Volume = (1/3) · 256 · 15
Volume = 1280 cubic units
Next, let's calculate the surface area of the pyramid:
Perimeter of the base = 4 · side length = 4 · 16 = 64 units
Surface area = base area + (1/2) · perimeter · slant height
Surface area = 256 + (1/2) · 64 · 17
Surface area = 256 + 544
Surface area = 800 square units
Therefore, the volume of the pyramid is 1280 cubic units, and the surface area is 800 square units.
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what is the length of the curve defined by the parametric equations x(t)=t2−2t and y(t)=t3−4t for 0≤t≤2 ? 4.221 4.221 6.511 6.511 10.819 10.819 28.267
The length of curve is approximately 6.511. Thus, the correct option is 6.511.
To find the length of the curve defined by the parametric equations x(t) = t^2 - 2t and y(t) = t^3 - 4t for 0 ≤ t ≤ 2, we need to use the arc length formula for parametric equations. The formula is:
Length = ∫(√((dx/dt)^2 + (dy/dt)^2)) dt, where the integral is evaluated from the lower limit to the upper limit.
First, find the derivatives dx/dt and dy/dt:
dx/dt = 2t - 2
dy/dt = 3t^2 - 4
Next, square and sum these derivatives:
(dx/dt)^2 + (dy/dt)^2 = (2t - 2)^2 + (3t^2 - 4)^2
Now, find the square root of this expression:
√((2t - 2)^2 + (3t^2 - 4)^2)
Finally, evaluate the integral of this expression from t = 0 to t = 2:
Length = ∫(√((2t - 2)^2 + (3t^2 - 4)^2)) dt, from 0 to 2
Using a calculator or numerical integration methods, the length of the curve is approximately 6.511. Therefore, the correct option is 6.511.
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Solve the system by substitution, help me
Answer: (-8, 8).
Step-by-step explanation:
Start with the first equation:y = -x Substitute this expression for y in the second equation:y = -3x - 16-x = -3x - 16Add 3x to both sides:2x = -16Divide both sides by 2:x = -8Substitute this value of x into either equation to find y:y = -x = -(-8) = 8Answer:
Step-by-step explanation:
need these both solved pls nowww
The simplified rational expressions are given as follows:
[tex]\sqrt[5]{288 \times p^5 \times p^2} = 2p\sqrt[5]{9p^2}[/tex][tex](216r^{9})^{\frac{1}{3}} = 6r^3[/tex]How to simplify the rational expressions?The first rational expression is given as follows:
[tex]\sqrt[5]{288p^7}[/tex]
The number 288 can be simplified as follows:
[tex]288 = 2^5 \times 3^2[/tex]
[tex]p^7[/tex], can be simplified as [tex]p^7 = p^5 \times p^2[/tex], hence the simplified expression is given as follows:
[tex]\sqrt[5]{2^5 \times 3^2 \times p^5 \times p^2} = 2p\sqrt[5]{9p^2}[/tex]
(as we simplify the exponents of 5 with the power)
The second expression is given as follows:
[tex](216r^{9})^{\frac{1}{3}}[/tex]
We have that 216 = 6³, hence we can apply the power of power rule to obtain the simplified expression as follows:
3 x 1/3 = 1 -> 6¹.9 x 1/3 = 3 -> r³.Hence the simplified expression is of:
[tex](216r^{9})^{\frac{1}{3}} = 6r^3[/tex]
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if nominal gdp is $7 trillion, and the money supply is $2 trillion, then what is the velocity of money? a. 7. b. 3.5. c. 2. d. 14.
Thus, the velocity of money in would be 3.5 .
The velocity of money is a measure of the rate at which money changes hands in an economy. It is calculated by dividing the nominal GDP by the money supply.
Therefore, the velocity of money in this scenario would be 3.5 (calculated as 7 trillion divided by 2 trillion). This means that on average, each dollar in the money supply is spent 3.5 times in a given year to support the production of goods and services that contribute to nominal GDP.The velocity of money can be affected by a variety of factors, including changes in interest rates, consumer and business confidence, and government policies. A higher velocity of money can be an indication of a strong and growing economy, while a lower velocity of money can signal sluggish economic growth. It is important to note that the velocity of money is a theoretical concept and may not always accurately reflect real-world economic conditions. Nonetheless, it remains a valuable tool for economists to understand and analyze the dynamics of the economy.Know more about the nominal GDP
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the frequency table shows the number of students selecting each type of food which portion of students choose nachos
A.0.5
B. 0.33
C. 0.73
D. 0.45
Please help :(
Answer:
Step-by-step explanation:
b .33
In ΔVWX, w = 600 cm,
�
m∠V=26° and
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m∠W=80°. Find the length of v, to the nearest 10th of a centimeter.
The length of v is given as follows:
v = 267.1 cm.
What is the law of sines?The law of sines is used in the context of this problem as we have two sides and two opposite angles, hence it is the most straightforward way to relate the side lengths.
Each side length is related with the sine of the opposite angle as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(26º)/v = sin(80º)/600
Hence we apply cross multiplication to obtain the length v is obtained as follows:
sin(26º)/v = sin(80º)/600
v = 600 x sine of 26 degrees/sine of 80 degrees
v = 267.1 cm.
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early tuesday a truck delivers fresh fruits to a groceries n more dad asks him justin needs to calculate the expanded total sales for 200 plums each plums weighs 80 grams and groceries n more sells of plums for $3.27
The expanded total sales for 200 plums, each weighing 80 grams, at a price of $3.27 per plum is $52.32.
How to determine expanded total sales for 200 plums each plums weighs 80 gramsWe can calculate the total weight of the plums as follows:
Total weight of plums = Weight per plum * Number of plums
Total weight of plums = 80 grams * 200 plums
we need to convert the total weight from grams to kilograms since the price is given per plum. There are 1000 grams in a kilogram, so:
Total weight of plums (in kilograms) = (Total weight of plums in grams) / 1000
Total sales = Total weight of plums (in kilograms) * Price per plum
Let's plug in the values and calculate the total sales:
Total weight of plums = 80 grams * 200 plums = 16,000 grams
Total weight of plums (in kilograms) = 16,000 grams / 1000 = 16 kilograms
Price per plum = $3.27
Total sales = 16 kilograms * $3.27 = $52.32
Therefore, the expanded total sales for 200 plums, each weighing 80 grams, at a price of $3.27 per plum is $52.32.
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