Answers
For the rectangle, the value x will be 14 and angle UDK will be 35°.
What exactly is a rectangle?
A rectangle is a four-sided polygon with four right angles (90-degree angles). It has opposite sides that are equal in length and parallel to each other. The rectangle is a special case of a parallelogram, where the opposite sides are also parallel. The two sides that are equal in length are called the "width" or "short side", while the other two sides are called the "length" or "long side". The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding the lengths of all four sides.
Now,
As we know all angles of a triangle are 90°.
then 5x-15+2x+7=90
7x=98
x=14
and in triangle UDK
sum of all angles = 180°
∠UDK+90+5x-15=180
∠UDK=180-145
∠UDK=35°
Hence,
the value x will be 14 and angle UDK will be 35°.
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Related Questions
eva bought 6 sponges. there were p sponges in each package. write an expression that shows how many packages eva bought. 6p
Answers
Answer: [tex]\frac{6}{p}[/tex]
Step-by-step explanation:
The number of packages Eva bought would be: 6 divided p which equals 6/p.
mobile ladder stands with a top step over 10 feet high and which is 20 inches or more in depth require:
Answers
Mobile ladder stands with a top step over 10 feet high and 20 inches or more in depth must be equipped with a safety cage or body belt and lanyard to provide protection against a fall.
The cage should be at least 30 inches tall and should be fully enclosed on all four sides. Additionally, the top step should be enclosed and provided with a grab bar. The ladder must be securely supported and stabilized. Non-skid materials should be applied to the steps and platform. Finally, the ladder must meet safety requirements outlined in the Occupational Safety and Health Administration's (OSHA) regulations.
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the variable socioeconomic status ranges from upper class to lower class and is an example of the select one: a. nominal level of measurement b. ordinal level of measurement c. interval-ratio level of measurement d. ratio level of measurement
Answers
The variable socioeconomic status ranges from upper class to lower class and is an example of the interval-ratio level of measurement. (option c)
Ordinal level of measurement is used to categorize variables that can be ranked in a specific order but do not have a uniform difference between them. For instance, a student's class rank can be categorized as first, second, or third. However, there is no uniform difference between the ranks.
Ratio level of measurement is used to categorize variables that have a meaningful zero point. For instance, height, weight, and age have a meaningful zero point.
However, in reality, it is difficult to find a person with zero income or zero education. Therefore, socioeconomic status can be considered an example of interval-ratio level of measurement but not an example of ratio level of measurement.
Hence option (c) is correct.
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A company is reviewing a batch of 22 products to determine if any are defective. On average, 3.9% of produc are defective. Does this situation describe a binomial experiment, and why? What is the probability that the company will find 2 or fewer defective products in this batch? What is the probability that 4 or more defective products are found in this batch? If the company finds 5 defective products in this batch, should the company stop production?
Answers
P(X ≤ 2) = 0.636, P(X ≥ 4) = 1 - 0.990 = 0.010
How to find probability?Use the cumulative distribution function for the binomial distribution, 2 or fewer defective products:
P(X ≤ 2) = Σ P(X = k) for k = 0, 1, 2
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = (0.961)^22 + 22(0.039)(0.961)^21 + (22!/(2!20!))(0.039)^2(0.961)^20
P(X ≤ 2) = 0.636
To find the probability of finding 4 or more defective products in this batch, we can use the complement rule:
P(X ≥ 4) = 1 - P(X ≤ 3)
Using the cumulative distribution function as before, we can calculate:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
P(X ≤ 3) = (0.961)^22 + 22(0.039)(0.961)^21 + (22!/(2!20!))(0.039)^2(0.961)^20 + (22!/(3!19!))(0.039)^3(0.961)^19
P(X ≤ 3) = 0.990
Therefore, P(X ≥ 4) = 1 - 0.990 = 0.010
If the company finds 5 defective products in this batch, they should consider stopping production, as this is much higher than the expected rate of 3.9%.
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The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis? A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries 12, 2, one-third, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries 12, 2, 0, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12.
Answers
Answer:
The correct table of values that could be used to graph g(x), a reflection of f(x) across the x-axis, is:
x f(x) g(x)
-2 1/108 12
-1 1/18 2
0 1/3 1/3
1 2 1/18
2 12 1/108
To reflect a function across the x-axis, we need to change the sign of the y-coordinate for every point on the function. Therefore, to find g(x), we take the negation of f(x) for every value of x. The second column in the third option is the negation of f(x), so it is the correct table of values for g(x).
Answer:
Its A.
Step-by-step explanation:
Other one was not clear enough lol ^
you are ordering a hamburger and can get up to 6 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 0 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
The probability of getting 0 toppings when ordering a hamburger with a choice of up to 6 toppings is 0.0154, rounded to four decimal places.
The total number of ways to choose 6 toppings out of a possible 6 is given by the combination formula:
[tex]$${ \choose 6} = \frac{6!}{6!(6-6)!} = 1$$[/tex]
This is the total number of possible outcomes.
To get 0 toppings, we need to choose 0 toppings out of 6. The number of ways to do this is:
[tex]{6_{0} =[/tex] [tex]\frac{6!}{0!(6-0)!} = 1$$[/tex]
So the probability of getting 0 toppings is:
[tex]$$P(\text{0 toppings}) =[/tex] [tex]\frac{number of ways to get 0 toppings}{total number of possible outcomes} $$[/tex] [tex]\frac{1}{1} = 1$$[/tex]
However, this is assuming that the cashier chooses the toppings randomly and without replacement. If the cashier has some bias or preference towards certain toppings, this probability may be different.
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Use que boards to do these divisions 363 divide 14
636 divide 21
908 divide 52
Answers
Using the division,
a) 363 ÷ 14 = 25 13/14
b) 636 ÷ 21 = 30 2/7
c) 908 ÷ 52 = 17 11/13
a) 363 ÷ 14, we first divide 363 by 14 to get a quotient of 25 with a remainder of 13. We then use the que board with 14 beads to represent this division. We start with the first digit of the dividend, which is 3. We count out 2 sets of 14 beads, which we move to the top of the board. We then move 1 more bead to the top, representing the remaining 13. The final result is 25 with a remainder of 13/14.
b) 636 ÷ 21, we divide 636 by 21 to get a quotient of 30 with a remainder of 6. We then use the que board with 21 beads to represent this division. We start with the first digit of the dividend, which is 6. We count out 3 sets of 21 beads, which we move to the top of the board. We then move 3 more beads to the top, representing the remaining 6. The final result is 30 with a remainder of 6/21, which can be simplified to 2/7.
c) 908 ÷ 52, we divide 908 by 52 to get a quotient of 17 with a remainder of 44. We then use the que board with 52 beads to represent this division. We start with the first digit of the dividend, which is 9. We count out 17 sets of 52 beads, which we move to the top of the board. We then move 44 more beads to the top, representing the remaining part of the dividend. The final result is 17 with a remainder of 44/52, which can be simplified to 11/13.
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The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.
Answers
Answer:
5cm (width) 18cm (height)
Step-by-step explanation:
From the text, the unknown number's value for the length of the width isn't disclosed, so we can mark it as a variable, for this case "x" as it is the most common variable to utilize in this case. We know that the length is 3 more than 3 times the width (x), so the length is 3+3x. The perimeter of the shape is 46 cm, and as we know, the perimeter is the sum of adding the length of all the sides and edges enclosing the shape, so therefore we can create a math sentence with the given information.
x+(3+3x)+x+(3+3x)=46 cm
OR
2(x+3+3x) =46 cm
Now, lets solve it.
2x+6+6x=46 (simplified)
8x+6=46 (combined variables)
8x=40 (subtracted)
x=5cm (divided)
Yay!! Now we have our answer, BUT WE ARE NOT DONE YET.
We need to replace our number in place of "3+3(x)," as well as "x." "x" is 5cm (width), and 3+3(x) is now 3+3(5), and is equal to 18cm. Hope this helped!!!!!!!!
Which recursively defined function has a first term equal to 10 and a common difference of 4?
Answers
The recursively defined function has a first term equal to 10 and a common difference of 4 is f(n) = 6 + 4n.
When a recursive procedure gets repeated, it's called recursion. A recursive is a type of function or expression stating some conception or property of one or further variables, which is specified by a procedure that yields values or cases of that function by constantly applying a given relation or routine operation to known values of the function.
We have first term = a = 10
And the common difference of d = 4
We have the formula for the t terms of a as 10 and d as 4
f(n) = a + (n - 1)d
f(n) = 10 + (n-1) x 4
f(n) = 10 + 4n - 4
f(n) = 6 + 4n
So, the defined function is f(n) = 6 + 4n.
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vital capacity is a measure of the amount of air that someone can exhales after taking a deep breath. what is the probability that we see our sample average difference or higher given there is no difference? g
Answers
a. The exit pressure is 19.76 lbf/in².
b. The ratio of the inlet area to the exit area is 3.125.
C. The exit area ratio (0.32) is less than the critical area ratio (1.89), the nozzle is converging-diverging in cross section.
To solve this problem, we need to apply the conservation equations for mass, momentum, and energy along with the isentropic relations.
a. To determine the exit pressure, we can use the isentropic relation for pressure ratio across a nozzle:
[tex]P_2/P_1 = (T_2/T_1)^{\frac{\gamma}{\gamma -1}}[/tex]
where [tex]P_1[/tex] and [tex]T_1[/tex] are the inlet pressure and temperature,
[tex]P_2[/tex] and [tex]T_2[/tex] are the exit pressure and temperature, and
γ is the specific heat ratio of air.
Using Table A-22E, we find that γ = 1.4 for air at 800°R.
Substituting the given values and solving for P2, we get:
[tex]P_2[/tex] = [tex]P_1 \times (T_2/T_1)^\frac{\gamma}{\gamma -1}[/tex] = [tex]45 \times (1500/480)^{(1.4/0.4)}[/tex]= 19.76 lbf/in²
b. To determine the ratio of the exit area to the inlet area, we can use the continuity equation:
[tex]A_1V_1 = A_2V_2[/tex]
where [tex]A_1[/tex] and [tex]A_2[/tex] are the inlet and exit areas, and
[tex]V_1[/tex] and [tex]V_2[/tex] are the inlet and exit velocities.
Substituting the given values, we get:
[tex]A_2/A_1 = V_1/V_2[/tex] = 480/1500 = 0.32
The ratio of the exit area to the inlet area is 0.32, or equivalently, the ratio of the inlet area to the exit area is 1/0.32 = 3.125.
c. To determine whether the nozzle is diverging only, converging only, or converging-diverging in cross section, we can compare the exit area ratio to the critical area ratio.
The critical area is the minimum area that allows the flow to reach sonic conditions, and it depends on the pressure and temperature of the flow.
For a converging-diverging nozzle, the exit area ratio is less than the critical area ratio, which is given by:
A* / [tex]A_1[/tex] = [tex](2/(\gamma+1))^{(\gamma+1)}/(2(\gamma-1)/(\gamma+1))^{(\gamma+1)/(\gamma-1)}[/tex]
where A* is the critical area,
[tex]A_1[/tex] is the inlet area, and
γ is the specific heat ratio.
Using the given values and γ = 1.4, we find that:
A* / [tex]A_1[/tex] = 1.89
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Question:-
Air enters a nozzle operating at steady state at 45 lbf/in.2, 800°R, with a velocity of 480 f/s, and expands isentropically to an exit velocity of 1500 ft/s. Using data from Table A-22E as needed, determine
a. the exit pressure, in lbf/in². 19.76
b. the ratio of the exit area to the inlet area. 0.577
c. whether the nozzle is diverging only, converging only, or converging-diverging in cross section. conv-div
a wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. how long ago was the artifact made?
Answers
The artifact was made about 3102.5 years ago.
An artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees, how long ago was the artifact made?
Carbon dating is used to estimate the age of organic materials, and it is used to determine the age of an artifact in this situation. The method used to estimate the age of an artifact based on its carbon-14 content is known as carbon dating. Carbon-14 has a half-life of 5,730 years. As a result, the amount of carbon-14 present in an object can be used to determine how long it has been since the object was last in contact with the atmosphere, and therefore how long it has been since it was alive.
Let C0 be the amount of carbon-14 present in living trees and C1 be the amount of carbon-14 present in the wooden artifact. After 5,730 years, C1 will have decayed to 1/2 of C0. After 2(5,730) = 11,460 years, C1 will have decayed to 1/4 of C0. After 3(5,730) = 17,190 years, C1 will have decayed to 1/8 of C0. After 4(5,730) = 22,920 years, C1 will have decayed to 1/16 of C0. After 5(5,730) = 28,650 years, C1 will have decayed to 1/32 of C0.
We'll have to solve the following equation to find the age of the artifact.
C1 = (70/100) * C0
Substitute the value of C0 into the equation and solve for t,
t = ln(0.7) / ln(1/2) = 3102.5 years
The artifact was made about 3102.5 years ago.
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Jose has 4 ants in his house and he discovers that those ants double every day. How many ants will he have after two weeks.
Answers
Answer:
In the picture is the answer
Ms. Leon opened a savings
account with an initial deposit
of $750 and will not make any more
deposits or withdrawals. The account
earns 3% simple interest.
What is the total amount that
Ms. Leon will have in her account at
the end of 4 years?
Answers
Answer: $840
Step-by-step explanation:
The formula for calculating simple interest is:
I = P * r * t
where:
I is the interest earned
P is the principal (the initial deposit)
r is the interest rate (as a decimal)
t is the time (in years)
Using this formula, we can find the interest earned on Ms. Leon's account over 4 years:
I = 750 * 0.03 * 4
I = 90
So Ms. Leon will earn $90 in interest over 4 years. To find the total amount in her account at the end of 4 years, we need to add the interest earned to the initial deposit:
Total amount = Initial deposit + Interest earned
Total amount = 750 + 90
Total amount = $840
Therefore, Ms. Leon will have a total of $840 in her savings account at the end of 4 years.
our cities recorded the temperature at midnight.
*Delway’s temperature was –8°C.
*Hickory’s temperature was –10°C.
*Midway’s temperature was –2°C.
*Ridgemonte’s temperature was 3°C.
Which list shows the cities in order from warmest to coldest?
A Delway, Hickory, Midway, Ridgemonte
B Hickory, Delway, Midway, Ridgemonte
C Midway, Ridgemonte, Hickory, Delway
D Ridgemonte, Midway, Delway, Hickory
Answers
3, -2, -8, -10, so ridge, midway, delway, and hickory
In negative numbers the lower the negative the greater the number, and the postivie goes above the negative.
So its D
describe fully the single transformation which takes shape A to shape B.
Answers
Answer:
rotation 90° anticlockwise centre 4,3.
Find the side of a square whose diagonal measures 15v2 cm
Answers
15 is area of Side of Square .
What is a square, exactly?
All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.
Length of diagonal of Square =15√2 cm-------------(1)
Let side of Square = a cm
So, Length of Diagonal
By Using Pythagorean Theorem
= √a² + a²
= a√2 ........................(2)
Equating (1) and (2)
a√2 = 15√2
a = 15
cancelling root 2 from both sides.
a = 15
Side of Square= 15 cm
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The complete question is -
Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.
X 1 2 3 4 у 0 -3 -6 -9
what is the slope intercept form?
Answers
Answer:
y = -3x + 3
Step-by-step explanation:
Knowing that;
Slope Intercept form : y = mx + b
To Find the Slope:
Used any given ordered pair given and use- m = [tex]\frac{y_2-y_1}{x_2- x_1}[/tex]
Find the slope of the lineThen Plug it in the Slope Intercept formGiven Table:
X Y
1 0
2 -3
3 -6
4 -9
Solve:
I will use the ordered pair:
(1,0)
(2, -3)
1 and 2 are "x"
0 and -3 are "y"
1 = x₁ 2 = x₂0 = y₁ -3 = y₂m [tex]=\frac{-3-0}{2- 1}[/tex]
m [tex]=\frac{-3}{1}[/tex]
m [tex]=[/tex] -3
Now putting the value of m in equation
y = -3x + b
To find the y intercept (b) in the slope intercept formula:
Choose any ordered pair and substitute it in the slope intercept.
Let's choose the first point, (1,0) for calculating y-intercept.
y = mx + b0 = -3(1) + b0 = -3 + bb = 3Now plug it in the slope intercept formula:
y = mx + b
y = -3x + 3
Hence, the slope intercept form for that table is:
y = -3x + 3.
RevyBreeze
In right triangle XYZ, ∠Y is the right angle and m∠X = 60°. If YZ = 4, what is XY?
Answers
Answer:
We can use the trigonometric ratios of a 30-60-90 triangle to find the length of XY. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
Since ∠X is 60°, we know that ∠Z is 30°, and we can set up the following equation:
XY / 4 = 2 / √3
To solve for XY, we can multiply both sides of the equation by 4√3:
XY = 4 * 2 / √3
Simplifying the right side, we get:
XY = 8 / √3
To rationalize the denominator, we can multiply the numerator and denominator by √3:
XY = (8 / √3) * (√3 / √3)
Simplifying, we get:
XY = 8√3 / 3
Therefore, the length of XY is 8√3 / 3, which is approximately 4.62 units.
there are two sets of dancers and a single pair must be randomly selected from each set. the first set consists of three men and one woman, and the second set consists of two women and one man. what is the probability that two men will be selected from the first set and two women will be selected from the second set?
Answers
The probability that two men will be selected from the first set and two women will be selected from the second set is 3/10 * 2/3, or 1/5.
The probability of selecting two men from the first set is 3/4. This is because there are 3 men in the first set and the probability of selecting one is 1/4. Since we need to select two, the probability of selecting both is 3/4 multiplied by itself, or 3/4 x 3/4. The probability of selecting two women from the second set is 2/3. This is because there are 2 women in the second set and the probability of selecting one is 1/3. Since we need to select two, the probability of selecting both is 2/3 multiplied by itself, or 2/3 x 2/3. The probability of selecting two men from the first set and two women from the second set is then 3/4 x 3/4 x 2/3 x 2/3, which is equal to 3/10 x 2/3, or 1/5.
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when on a stem and leaf plot and it does not show a number on the right side and only on the right side what would the number be on the right?
Answers
When on a stem and leaf plot and it does not show a number on the right side and only on the right side, the number on the right side would be zero.
What is a stem and leaf plot?A stem and leaf plot is a method of organizing numerical data into groups. It is a visual representation of a dataset in which each value is separated into a stem and a leaf. A stem is the left-hand digit(s) of the value, while a leaf is the right-hand digit(s).
The stem and leaf plot contains two columns, one for the stem and the other for the leaf. The stem values are arranged vertically in the left-hand column, and the leaf values are arranged horizontally in the right-hand column. The leaf column should be read from left to right to extract the values.
When a value appears multiple times, its leaves are stacked on top of one another. The stem and leaf plot is an effective method for representing data, particularly when dealing with large datasets.
Hence, If a stem and leaf plot displays a number only on the left side and not on the right side, then the number on the right side would be interpreted as zero.
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Last year, Brian and his wife earned $550,000 in
wages. How much did he pay in income taxes?
Answers
As Brian and his wife earned $550,000 in wages during 2020. The amount he pays in income taxes would be $167,700.
What do we call an income taxes?An income tax is a type of tax levied by governments on the earnings of businesses and individuals within their jurisdiction.
The amount of income tax that Brian and his wife paid in 2020 depends on several factors, such as their filing status, deductions, credits, and the tax rates that apply to their income.
Assuming that Brian and his wife filed jointly and did not have any significant deductions or credits, we can use the following tax brackets and rates for the 2020 tax year: 35% on taxable income between $414,701 and $622,050.
. Assuming that they did not have any significant deductions or credits, their taxable income would be $550,000 (their wages) minus the standard deduction for joint filers, which was $24,800 in 2020.
The income taxes will be calculated as:
= (35% * $550,000) - $24,800
= $192,500 - $24,800
= $167,700
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1. Kendra owns a restaurant. She charges $1. 50 for 2 eggs and one piece of toast, and $. 90 for one egg
and one piece of toast. Determine how much she charges for each egg and each piece of toast
Answers
Kendra cost $0.60 for each egg and $0.30 for each piece of toast.
Let's assume that the cost of one egg is x and the cost of one piece of toast is y.
From the given information, we can set up two equations:
2x + y = 1.5
x + y = 0.9
We can solve this system of equations by either substitution or elimination method.
Using the elimination method, we can multiply the second equation by -2 to eliminate y:
-2x - 2y = -1.8
2x + y = 1.5
Adding these two equations, we get:
-1y = -0.3
y = 0.3
Substituting y = 0.3 in either of the two equations, we get:
x = 0.6
Therefore, Kendra charges $0.60 for each egg and $0.30 for each piece of toast.
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i really dont understand this please help me out
Answers
Answer: D
Step-by-step explanation: It is going up in a strait trend line, making it where it has no relation ship unless very closely examined.
a project being analyzed by pert has 60 activities, 13 of which are on the critical path. if the estimated time along the critical path is 214 days with a project variance of 100, what is the probability that the project will take 224 days or more to complete? group of answer choices 0.0126 near zero 0.1587 0.14 0.8413
Answers
The probability that the project will take 224 days or more to complete is: 0.1587
The project is being analyzed by PERT, it has 60 activities, out of which 13 are on the critical path. The estimated time along the critical path is 214 days with a project variance of 100. We are required to find the probability that the project will take 224 days or more to complete.
Now, z-score = (x - μ) / σ = (224 - 214) / 10 = 1.
So, using the standard normal table, we have: P(Z > 1) = 1 - P(Z < 1) = 1 - 0.8413 = 0.1587.
Hence, the required probability that the project will take 224 days or more to complete is 0.1587.
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Find the values of x and y. Show all of your work.
Answers
x= 39
y= 123
Step by step
The angle between points EC is a vertical angle to angle DF, so they are congruent or the same = x - 11
Line AB is a straight angle with a sum equal to 180 degrees.
So (x-10) + (x-11) + (3x + 6) = 180
Combine like terms
5x -15 = 180
Add 15 to both sides to isolate variable
5x -15 + 15 = 180 + 15
Simplify
5x = 195
Divide both sides by 5 to solve for x
5/5x = 195/5
x = 39
y is a vertical angle to (3x + 6) so they are congruent or equal
We know x= 39 so substitute the value of x into the equation and equal it to y.
(3x + 6) = y
3(39) + 6 = y
123 = y
Please, I really want this pleaseeeeeeweeee
Answers
The value of ∠K is 78°
What is tangent of a circle?The tangent of a circle is a straight line that touches the circle at exactly one point, and it is perpendicular to the radius of the circle at that point.
Given that, a tangent JK is lying on the circle H whose radius are HJ and HM,
So, ∠HMJ = ∠HJM = 84°
and JK ⊥ HJ (JK is a tangent on radius HJ)
So, ∠HJK = 90°
∠HJM + ∠MJK = ∠HJK
84° + ∠MJK = 90°
∠MJK = 6°
Using exterior angle property;
∠MKJ + ∠MJK = ∠HJM
∠MKJ + 6° = 84°
∠MKJ = 84° - 6° = 78° (∠MKJ means ∠K)
Therefore, ∠K = 78°
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Please help! easy!Find the m
110⁰
x + 52
x +42
Answers
Answer: 100 < 96
Step-by-step explanation:
x+52+x+42 = 180
2x+94 = 180
2x = 180 - 94
2x = 86
x = 86/2
x = 43
110 < x + 52
110 < 43 + 52
110 < 96
A carpenter has a board that is 2 yards long He cuts it into 3 equal pieces. How many inches long is each piece?
Answers
Each piece is 24 inches long. One yard is equal to 36 inches, so two yards are equal to 72 inches.
To solve this problem, we need to convert the length of the board from yards to inches and then divide it into 3 equal parts.
First, we convert 2 yards to inches by multiplying by 36 (since there are 36 inches in a yard):
2 yards × 36 inches/yard = 72 inches
So, the board is 72 inches long.
Next, we divide 72 inches by 3 to find the length of each piece:
72 inches / 3 = 24 inches
Therefore, each piece is 24 inches long. In summary, to find the length of each piece of a board that is 2 yards long and cut into 3 equal pieces, we convert 2 yards to inches by multiplying by 36 and then divide by 3 to get each piece's length, which is 24 inches.
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the fox population iun a certain region has an annual growth rate of 9% per year. in the year 2012 there were 23900 fox counted in the area. what is the fox population predicted in the year 2020
Answers
The population of foxes in the region in 2020 is predicted to be 40,174.
The population of foxes in the region in 2020 can be calculated using the formula [tex]P = P0 (1+r)^n[/tex], where P is the population at the end of n years, P0 is the initial population, and r is the annual growth rate. The fox population iun a certain region has an annual growth rate of 9% per year. in the year 2012 there were 23900 fox counted in the area.In this case, P0 = 23900 and r = 0.09. Since the starting year is 2012, the number of years since then is n = 8. Plugging these values into the formula, P = 23900 (1.09)^8 = 40,174. Therefore, the population of foxes in the region in 2020 is predicted to be 40,174.
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in a normal distribution, 95.4% of the values fall between 5.8 and 10.6. compute the mean of the distribution.
Answers
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values are between 5.8 and 10.6, and the total number of values is 95.4%.
To calculate the mean, we must first calculate the sum of all the values. To do this, we will use the following formula:
sum of values = (lowest value + highest value) / 2
In this case, the lowest value is 5.8 and the highest value is 10.6, so the sum of values is 8.2.
We now have the sum of all the values, so we can calculate the mean by dividing the sum by the total number of values. The total number of values is 95.4%, so the mean is 8.2 / 0.954 = 8.57.
Therefore, the mean of the normal distribution is 8.57.
In conclusion, the mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%. When the sum of all the values (8.2) was divided by the total number of values (0.954), the mean was calculated to be 8.57.
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