Since h is not the zero transformation, its range must be all of R1. Therefore, the rank of h is 1.
To find the null space of the linear transformation h, we need to find all vectors x = (x1, x2, x3) in R3 such that h(x) = 0. We have:
h(x) = 3x1 - x2 - x3
Setting h(x) = 0, we get:
3x1 - x2 - x3 = 0
This is a system of equations in three variables. We can solve for x3 in terms of x1 and x2 to obtain:
x3 = 3x1 - x2
So any vector x in the null space of h must have the form:
x = (x1, x2, 3x1 - x2)
We can rewrite this vector as:
x = x1(1, 0, 3) + x2(0, -1, -1)
Therefore, a basis for the null space of h is the set { (1, 0, 3), (0, -1, -1) }.
To find the rank of h, we need to determine the dimension of the range of h. Since h is a linear transformation from R3 to R1, its range is a subspace of R1. The only subspaces of R1 are {0} and R1 itself. Since h is not the zero transformation, its range must be all of R1. Therefore, the rank of h is 1.
Geometrically, the null space of h is a plane in R3. This plane contains the origin and is parallel to the vector (1, 0, 3). The vector (0, -1, -1) is perpendicular to this plane.
Visit to know more about Transformation:-
brainly.com/question/29788009
#SPJ11
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.
Learn more about total sales at https://brainly.com/question/29816337
#SPJ9
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 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.
Learn more about square pyramid click;
https://brainly.com/question/31200424
#SPJ1
Hello! Can someone explain how to do this? Due tonight hurry asap
9.172 cm² is the area of the unshaded reason.
It is given that,
From the general formula of the area of the arc of the circle,
Area of the arc = (θ/360) x πr²
where A is the area of the arc, θ is the central angle of the arc (in degrees), and r is the radius of the circle.
The area of the shaded part is given = 56.87 cm²
Angle of the shaded arc = 360-50 = 310
So,
310/360* πr² = 56.87
πr²/360 = 56.87/310
For the 50° part,
Area of the unshaded part = 50/360* πr²
From the above value of the πr²/360,
Area of the unshaded part = 50*56.87/310
Area of the unshaded part = 9.172 cm²
Therefore, the area of the unshaded reason is 9.172 cm².
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
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.
Read more on survey here:https://brainly.com/question/31121539
#SPJ1
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.
Learn more about similar triangles click;
https://brainly.com/question/29191745
#SPJ1
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
https://brainly.com/question/6348208
#SPJ11
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:
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.
Learn more about predominantly here:
https://brainly.com/question/521450
#SPJ11
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.
Learn more about marginal costs here:-brainly.com/question/7781429
#SPJ11
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.
Know more about the parametric equations
https://brainly.com/question/30451972
#SPJ11
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.
Learn more about confidence interval here:
https://brainly.com/question/16465664
#SPJ11
find f. f ′(x) = 1 3 x , f(9) = 67
To find the function f, we need to integrate f'(x) with respect to x. Thus, we have found the function f with the given derivative f'(x) and initial condition f(9) = 67.
f'(x) = (1/3)x
Integrating both sides with respect to x, we get:
f(x) = (1/3) * (x^2/2) + C
where C is the constant of integration. To find the value of C, we use the given initial condition that f(9) = 67:
f(9) = (1/3) * (9^2/2) + C = 67
Simplifying the equation, we get:
C = 67 - (1/3) * (81/2) = 67 - 13.5 = 53.5
Therefore, the function f is:
f(x) = (1/3) * (x^2/2) + 53.5
Thus, we have found the function f with the given derivative f'(x) and initial condition f(9) = 67.
Visit here to learn more about integration:
brainly.com/question/18125359
#SPJ11
The results of a question from the awesome survey are shown below.
What is the probability of selecting a student who would rather fight 100 duck sized horses, and then selecting a student who would rather fight 10 horse sized ducks (with replacement)?
Round your answer to the nearest hundredth
Answer:
0.18
Step-by-step explanation:
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.
To learn more about Taylor series : brainly.com/question/28158012
#SPJ11
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]
More can be learned about exponent rules at https://brainly.com/question/11975096
#SPJ1
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.
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).
To know more about Cordinates visit :
https://brainly.com/question/28899589
#SPJ11
Find the first five nonzero terms of the Maclaurin expansion of f(x)=−e^x-sin(x).
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
To find the Maclaurin expansion of f(x) = -e^x - sin(x), we can use the Maclaurin series of e^x and sin(x) and combine them with appropriate coefficients.
The Maclaurin series of e^x is:
e^x = 1 + x + x^2/2! + x^3/3! + ...
And the Maclaurin series of sin(x) is:
sin(x) = x - x^3/3! + x^5/5! - ...
Using these series, we can write the Maclaurin expansion of f(x) as:
f(x) = -e^x - sin(x) = -1 - x - x^2/2! - x^3/3! - ... - (x - x^3/3! + x^5/5! - ...)
Simplifying this expression, we get:
f(x) = -1 - 2x - 5x^2/2! - 19x^3/3! - 87x^4/4! - ...
Therefore, the first five nonzero terms of the Maclaurin expansion of f(x) are:
f(x) = -1 - 2x - 5x^2/2! - 19x^3/3! - 87x^4/4! + O(x^5)
This means that for small values of x, f(x) can be approximated by the polynomial -1 - 2x - 5x^2/2! - 19x^3/3! - 87x^4/4!, which becomes more accurate as more terms are added. The term O(x^5) represents the error in this approximation and means that the actual value of f(x) is within a certain range of this polynomial for values of x close to zero.
To learn more about nonzero click here: brainly.com/question/30262565
#SPJ11
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
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:
In ΔVWX, w = 600 cm,
�
m∠V=26° and
�
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.
More can be learned about the law of sines at https://brainly.com/question/4372174
#SPJ1
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.
For more such questions on tax , Visit:
https://brainly.com/question/28414951
#SPJ11
For problems 1-5, use the following information. On an end-of-year test, the scores of juniors across a large city with many high schools were normally distributed with a mean of 83 and a standard deviation of 5.2.
For random samples of 25 scores, what interval centered on the mean captures 95% of the sample means?
The 95% confidence interval centered on the mean that captures 95% of the sample means is (80.96, 85.04).
We can use the formula for the confidence interval for the mean of a normally distributed population:
CI = X ± z(α/2) * (σ/√n)
Where:
X = sample mean
z(α/2) = the z-score associated with the desired confidence level and calculated using the standard normal distribution table. For a 95% confidence level, α/2 = 0.025, and the corresponding z-score is approximately 1.96.
σ = population standard deviation
n = sample size
Substituting the given values, we get:
CI = 83 ± 1.96 * (5.2/√25)
CI = 83 ± 2.04
Therefore, the 95% confidence interval centered on the mean that captures 95% of the sample means is (80.96, 85.04).
Learn more about normal distribution here:
https://brainly.com/question/15103234
#SPJ1
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.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
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
Learn more about Density at:
https://brainly.com/question/29775886
#SPJ4
A fruit vendor bought 100 kg apples for Rs 9,000, 30 dozen bananas for Rs 1,800 and 50 kg
grapes for Rs 6,000. He spent Rs 900 on transportation and sold all the fruits as per the given
rates.
The net profit on the sale of these fruits is Rs 6,050.
To calculate the net profit on the sale of these fruits, we need to determine the total revenue generated from the sales and deduct the total expenses.
First, let's calculate the revenue from each type of fruit:
Revenue from apples: 100 kg × Rs 140/kg = Rs 14,000
Revenue from bananas: 30 dozen × Rs 75/dozen = Rs 2,250
Revenue from grapes: 50 kg × Rs 150/kg = Rs 7,500
Next, let's calculate the total revenue:
Total revenue = Revenue from apples + Revenue from bananas + Revenue from grapes
Total revenue = Rs 14,000 + Rs 2,250 + Rs 7,500
Total revenue = Rs 23,750
Now, let's calculate the total expenses:
Total expenses = Cost of apples + Cost of bananas + Cost of grapes + Transportation cost
Total expenses = Rs 9,000 + Rs 1,800 + Rs 6,000 + Rs 900
Total expenses = Rs 17,700
Finally, let's calculate the net profit:
Net profit = Total revenue - Total expenses
Net profit = Rs 23,750 - Rs 17,700
Net profit = Rs 6,050
Therefore, the net profit on the sale of these fruits is Rs 6,050.
for such more question on net profit
https://brainly.com/question/4177260
#SPJ11
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.
Learn more about right triangles at:
https://brainly.com/question/2217700
#SPJ1
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.
Learn more about Unpressurized aircraft at
https://brainly.com/question/31663341
#SPJ4
for any n ≥ 1, the factorial function, denoted by n!, is the product of all the positive integers through n: prove that for n ≥ 4, n! ≥ 2n.
For any n ≥ 1, the factorial function, denoted by n!, is the product of all the positive integers through n, it is proved that for n ≥ 4, n! ≥ 2n.
To prove this statement, we can use mathematical induction. For the base case, n = 4, we have 4! = 24 and 2^4 = 16. Since 24 > 16, the statement holds for n = 4.
Now suppose the statement holds for some integer k ≥ 4, that is, k! ≥ 2k. We need to show that the statement holds for k+1. We have:
(k+1)! = (k+1)k!
≥ (k+1)2k (by the induction hypothesis)
≥ 2·2k (since k+1 > 2 for k ≥ 4)
= 2k+1.
Therefore, the statement holds for k+1. By the principle of mathematical induction, the statement holds for all n ≥ 4. Therefore, we have proved that n! ≥ 2n for n ≥ 4.
You can learn more about factorial function at
https://brainly.com/question/9214272
#SPJ11