Answer:
[tex] AC = \sqrt(26) \approx 5.1 [/tex]
Step-by-step explanation:
The diagonals are AC and BD.
Now we find the lengths of the diagonals using the distance formula.
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
AC:
[tex] AC = \sqrt{(6 - 5)^2 + (7 - 2)^2} [/tex]
[tex] AC = \sqrt{(1)^2 + (5)^2} [/tex]
[tex] AC = \sqrt{1 + 25} [/tex]
[tex] AC = \sqrt{26} [/tex]
BD:
[tex] BD = \sqrt{(9 - 2)^2 + (5 - 4)^2} [/tex]
[tex] BD = \sqrt{(7)^2 + (1)^2} [/tex]
[tex] BD = \sqrt{49 + 1} [/tex]
[tex] BD = \sqrt{50} [/tex]
Since sqrt(26) < sqrt(50), then the shorter diagonal is AC.
Answer: AC = sqrt(26) or approximately 5.1
Answer:
A = (5.2)
Step-by-step explanation:
c2= (6-5)^2 + (7-2)^2
To find AC we calculate within parenthesis (6-5) : 1
c2= 1 + (7-2)^2
calculate within parenthesis (7-2) : 5
c2 = 1^2 + 5^2
then calculate exponents 1^2:1
c^2 = 1+5^2
add and subtract left to right
c^2 = 1+25
c^2 =26
Sr of 26 = 5.09901951359
Which means the closest answer is A = 5.2
To find BD we calculate within parenthesis (9-2):7
c2= (9-2)^2 + (5 - 4)^2
calculate within parenthesis (5-4) : 1
c2 = (7)^2 + (1)^2
calculate exponents 1 ^2 : 1
c2 = 49 +1
add and subtract left to right
c2 = 50
Sr of 50 = 7.07106781187
Plz help me ASAP it’s important
Answer:
14
Step-by-step explanation:
each square is 2 you count across then up or the other way is fine too from point A to B it equals to 14
What is the range of the relation {(2, 4), (3, 4), (4,7), (5,7), (6,5)}?
Answer:
The range is {4,5,7}
Step-by-step explanation:
The range of a relation is the output values The values are 4,7,5 we normally put them in order from smallest to largest
The range is {4,5,7}
An inverted conical tank starts the day with 250 ft^3 of crayon wax in it. As the factory commences work, the tank is filled with an additional 40 ft^3 of wax per minute. The height of the wax is modeled by H(V)=3 piV/25. A. Write a function , V(t) to model the volume of wax in the tank after t minutes. B. Find an expression for the composition (HoV)(t) C. The composition in B (above) can be described as the ________ of the wax in terms of _______
Answer:
A. V(t) = 40t + 250 B. (HoV)(t) = 24πt/5 + 30π C. The composition in B (above) can be described as the height of the wax in terms of time.
Step-by-step explanation:
A. Let the rate of change of volume V with respect to time be dV/dt = 40 ft³/min
Solving this, V = 40t + C. At the start of the day, that is t = 0, V = 250 ft³
Substituting these values, we have
250 ft³ = 40(0) + C
C = 250 ft³
So, V(t) = 40t + 250
B. Since H(V) = 3πV/25
(HoV)(t) = 3π(40t + 250)/25
= 24πt/5 + 30π
C. The composition in B (above) can be described as the height of the wax in terms of time.
which equation represents a line perpendicular to the line shown on the graph
Answer:
y = 1/4x + (any number)
Step-by-step explanation:
m = -8/2 = -4, the equation shown is y = -4x + 8
perpendicular is y = 1/4x + (any number), you didn't say where the line was perpendicular.
A large western state consist of 4341 million acres of land. Approximately 83% of this land is federally owned. Find the number of acres that are not federally owned
Answer:
737.97 acres
Step-by-step explanation:
Given
Approximately 83% of a large western state land is federally owned.
Total land in percentage will be 100%
% of land not federally owned = Total land in percentage - % of land federally owned = 100% - 83% = 17%
Thus, percentage of land not federally owned = 17% of total land
Also given "A large western state consist of 4341 million acres of land"
Therefore,
number of acres that are not federally owned = 17% of total western state land
number of acres that are not federally owned = 17/100 * 4341 = 737.97
Thus, 737.97 acres of western state land are not federally owned.
ملی
A man left one-fifth of his property to his
Son , one third to his daughter
and remaining
to his wife. If his wife got 35ooo RS what was the
worth of his total property?
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
What is the solution to this equation?
3x - 7 + 4x = 28
O A. x= 35
O B. x = 21
O c. x= 5
O D. x= 3
Answer:
x = 5
Step-by-step explanation:
3x - 7 + 4x = 28
Combine like terms
7x -7 = 28
Add 7 to each side
7x - 7 +7 = 28+7
7x = 35
Divide each side by 7
7x/7 = 35/7
x = 5
Solve the equation. 4c = 3
Answer:
Brainelist~~~!!!
Step-by-step explanation:
4c=3
c=3/4
c=0.75
The solution of the linear equation 4·c = 3, obtained by solving for the variable c is; c = 3/4
What is a linear equation?A linear equation is an equation that can be expressed in the form; y = m·x + c
The equation 4·c = 3 is a linear equation
In order to solve the equation 4·c = 3 for the variable c, the variable c needs to be isolated to one side of the equation, by dividing both sides of the equation by 4 as follows;
4·c = 3
(4·c)/4 = 3/4
c = 3/4
Therefore, the solution of the equation, 4·c = 3 is; c = 3/4
Learn more on linear equations here: https://brainly.com/question/30338252
#SPJ6
The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other
number is ….
Please help meee
Which number line model represents the expression -2/5 + 4/5:
The number line model that represents the expression -2/5 + 4/5 is: Option B
How to solve Inequality on number line?
To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.
Now, in this case, the operation to solve is:
-2/5 + 4/5
Solving this gives 2/5
Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem
Read more about Inequality on number line at: https://brainly.com/question/24372553
#SPJ1
The correlation between height and weight among men age 18-74 in the U.S. is about 0.40. Say whether each conclusion below follows from the data; explain your answer. a) Taller men tend to be heavier. b) The correlation between weight and height for men age 18-74 is about 0.40. c) Heavier men tend to be taller. d) If someone eats more and puts on 10 pounds, he is likely to get somewhat taller.
Answer:
Options a, b, c are correct.
Step-by-step explanation:
First let's see the equation that governs the statement, which is the following:
[tex]r = \frac{cov (x, y)}{\sqrt{var(x) var (y)} }[/tex]
Therefore, reading options a, b, c are correct.
Since from the formula we have the correlation coefficient of two variables x and y and here it shows us the correlation between x, y and y, x is the same.
This means that the 0.4 correlation implies a moderate but positive relationship between the two variables.
that is, the highest or lowest value of one variable implies a highest or lowest value of the other variable, respectively.
whats the percentage of 56/100
Answer:
56%
Step-by-step explanation:
Percent means out of 100
56/100
56 out of 100
56%
Answer:
56%
Step-by-step explanation:
How much is 56 out of 100 written as a percentage? Convert fraction (ratio) 56 / 100 Answer: 56%
When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well.
Answer:
P(Y= 0) = 0.1
P(Y= 0) = 0.7
P(Y= 0) = 0.2
Step-by-step explanation:
Let Y be number of impurities that can be found in the well,
Let A denote the event that impurity A is randomly found in the well
Here Y can have three values i.e 0 , 1 and 2
✓It will take take the value of 0 when there is no impurity found in the well
✓It will take the value of 1 when when exactly one impurity vis found in the well
✓It will take the value of 2 when when both impurities vis found in the well
CHECK THE ATTACHMENT FOR DETAILED EXPLATION
Harasti was inspired to build his hotels after he saw seahorses living in old fishing traps. What is the volume of a fishing trap that is 2 feet wide, 5 feet long, and 3 feet tall?
HELP ME DO THIS !!!!
Answer:
volume of rectangular prism = 30 ft³
Step-by-step explanation:
The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.
volume of rectangular prism = LWH
where
L = length
W = width
H = height
volume of rectangular prism = LWH
Length = 5 ft
width = 2 ft
Height = 3 ft
volume of rectangular prism = 5 × 2 × 3
volume of rectangular prism = 10 × 3
volume of rectangular prism = 30 ft³
Given the coordinates (0,0) and (4, 1), the distance is:
Answer:
[tex]\sqrt{17}[/tex] or ≈4.12
Step-by-step explanation:
Use the distance formula
d= √(x₂ - x₁) ² + (y₂-y₁) ²
d= √(4-0)² + (1-0)²
d= √16 + 1
d= √17
Please help. I’ll mark you as brainliest if correct!
Answer:
(0. 4)
(-2, 0)
Step-by-step explanation:
The y- coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum, respectively.As per given graph,
absolute maximum is 4, point (0, 4)absolute minimum is 0, point (-2, 0)A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93, P(C) = 0.95, and P(D) = 0.92. Find the probability that the machine works properly.A) 0.8128B) 0.2441C) 0.8217D) 0.7559
Answer:
D) 0.7559
Step-by-step explanation:
Independent events:
If two events, A and B are independent:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Four independent events, A, B, C and D.
So
[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D)[/tex]
Find the probability that the machine works properly.
This is the probability that all components work properly.
[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D) = 0.93*0.93*0.95*0.92 = 0.7559[/tex]
So the correct answer is:
D) 0.7559
Amit found and labeled the areas of each of the faces of the triangle prism as shown which area calculation did Amit calculate incorrectly
Complete Question:
Amit found and labeled the areas of each of the faces of the triangular prism as shown.
Which area calculation did Amit calculate incorrectly?
Rectangular face with area 30 cm2
Rectangular face with area 40 cm2
Rectangular face with area 50 cm2
Triangular faces with areas 48 cm2
Answer:
Triangular faces with areas 48 cm2
Step-by-step Explanation:
To find out which area calculation Amit got wrong, let's calculate each faces of the given triangular prism attached below:
There area of theb5 faces should be as follows:
Area of rectangular face with L = 10 and B = 5 would be ==> 10*5= 50cm²
Area of rectangular face with L = 8 and B = 5 would be 8*5 = 40cm²
Area of rectangular face with L = 6 and B = 5 would 6*5 = 30cm²
Area of each of the triangular faces will be ½*8*6 = 48/2 = 24cm²
From our calculations, we'd observe that Amit didn't calculate the area of the triangular faces correctly. Amit got 48cm² instead of 24cm²
Answer:
Triangular faces with areas 48 cm2
Step-by-step explanation:
Find the equation for the plane through the points Upper P 0 (5 comma 4 comma 5 ), Upper Q 0 (negative 5 comma negative 1 comma negative 4 ), and Upper R 0 (negative 2 comma 1 comma negative 2 ). The equation of the plane is nothing.
Answer:
The equation of the plane is
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 7y - 5z + 13 = 0
Step-by-step explanation:
Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).
We can calculate the equation of the plane through those points as
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.
The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.
For this question,
P = (5, 4, 5)
Q = (-5, -1, -4)
R = (-2, 1, -2)
PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)
= (-10î - 5ĵ - 9ķ)
PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)
= (-7î - 3ĵ - 7ķ)
PQ × PR is then
| î ĵ ķ |
|-10 -5 -9|
|-7 -3 -7|
= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]
= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)
= 8î - 7ĵ - 5ķ
Hence, (a, b, c) = (8, -7, -5)
And using point P as (x₀, y₀, z₀) = (5, 4, 5)
The equation of the plane is
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 40 - 7y + 28 - 5z + 25 = 0
8x - 7y - 5z = 40 - 28 - 25 = -13
8x - 7y - 5z + 13 = 0
Hope this Helps!!!
normally distributed with an unknown population mean and a population standard deviation of 4.5 points. A random sample of 45 scores is taken and gives a sample mean of 84. Find a 90% confidence interval
Answer:
= ( 82.90, 85.10) points
Therefore at 90% confidence interval (a,b)= ( 82.90, 85.10) points
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 84
Standard deviation r = 4.5
Number of samples n = 45
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
84+/-1.645(4.5/√45)
84+/-1.645(0.670820393249)
84+/-1.10
= ( 82.90, 85.10) points
Therefore at 90% confidence interval (a,b)= ( 82.90, 85.10) points
If A={A,15,E,17,18, B,20} and B={ X,22, F,42, Y,62,72}, then what is n(A∪B)?
Answer:
14
Step-by-step explanation:
There are 7 elements in each set, and no elements are shared. The number of elements in the union of the sets is then ...
n(A∪B) = 7+7 = 14
What is the probability of selecting the 4 of spade or black diamond from a deck of 52 playing cards?
a) 2/52
b) 4/52
c) 3/52
d) 1/5
Answer:
b
Step-by-step explanation:
Answer:
he
Step-by-step explanation:
hi
Ms. Ironperson and Mr. Thoro are making
Avenger posters to give children when they
visit Avenger Academy. Ms. Ironperson has
completed 12 posters and will complete 6
more per day. Mr. Thoro has not started yet
but can make 12 per day. At some point Mr.
Thoro will catch up and both will have finished
the same number of posters. When this does
happen, how many posters will each Avenger
have completed?
If x denotes the number of days and y denotes
the number of posters, what are the equations
needed to solve this problem? (7 points)
Answer:
y = 12 + 6x
y = 12x
Step-by-step explanation:
From the information provided, the following equations are derived:
y = 12 + 6x ------- Eqn 1
y = 12x ------- Eqn 2
Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:
12x = 12 + 6x
Putting like terms together, we have:
12x - 6x = 12 ⇒ (12 - 6)x = 12
6x = 12 ⇒ x = 2
x = 2
Substitute x into Eqn 1 or 2
Eqn 1
y = 12 + 6x
y = 12 + 6(2) = 12 + 12
y = 24
Eqn 2
y = 12x
y = 12(2)
y = 24
It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.
2. The sum of the ages of Denise and Earl is 42
years. Earl is 8 years younger than Denise.
How old is each?
d-Denis
e-Earl
d+e=42
e+8=d
e+8+e=42
2e+8=42
2e=34
e=17
d=17+8=25
Denis is 25 and Earl is 17
Answer
Earl is 17 years old.
Denis is 25 years old.
See? Easy!
Step-by-step explanation:
What value of x is in the solution set of 2x – 3 > 11 – 5x?
Given:
2x -3 > 11 -5x
Simplify both sides:
2x - 3 > -5x + 11
Add 5x to both sides:
2x - 3 +5x > -5x + 11 +5
7x - 3 > 11
Add 3 to both sides:
7x - 3 +3 > 11 + 3
7x > 14
Divided 7 to both sides:
[tex]\frac{7x}{7}[/tex] > [tex]\frac{14}{7}[/tex]
x > 2
Answer:
Any number greater than 2 would be the answer. In Edg, choose 4! Choosing 2 would be incorrect in their system.
Step-by-step explanation:
if this net were to be folded into a cube which number would be opposite of the number 1?
Answer:
6
Step-by-step explanation:
When the cube is folded, 6 is the opposite of 1.
2 is the opposite of 4 and 5 is the opposite of 3.
When the given net is folded into a cube, the number that we will find opposite 1 is 6.
What number will be opposite 1?When the net is folded, two will be folded left and up with 3 being the base. 4 will be folded right with 5 being the top of the cube.
We will then observe the following pairs opposite each other:
5 and 3.4 and 2.1 and 6.This means that the number that we will see opposite 1 will be the number 6.
Find out more on folding nets at https://brainly.com/question/16670460.
#SPJ9
Please answer this correctly
Answer:
40 - 59 ⇒ 6
60 - 79 ⇒ 5
Answer:
40-59: 6
60-79: 5
Step-by-step explanation:
If you just added up, you can find all the values.
Probability allows one to measure effectively the risks in selecting one alternative over the others.
True
False
If f(x)=4arctan(7x), find f'(x). Find f'(4).
f'(x) = (4 arctan(7x))'
f'(x) = 4 (arctan(7x))'
By the chain rule,
f'(x) = 4/(1 + (7x)^2) * (7x)'
f'(x) = 28/(1 + 49x^2)
and hence
f'(4) = 28/(1 + 49*16) = 28/785
In case you're not sure about the derivative of arctan: If y = arctan(x), then x = tan(y). Differentiating both sides with respect to x gives
1 = sec^2y y' = (1 + tan^2y) y' = (1 + x^2) y'
==> y' = 1/(1 + x^2)
Suppose I claim that the average monthly income of all students at college is at least $2000. Express H0 and H1 using mathematical notation, and clearly identify the claim and type of testing.
Answer:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no
