Answer:
length = 8 ft
width = 5 ft
Step-by-step explanation:
width = w
length = w + 3
Area of rectangular garden = 40 square feet
length *width = 40
(w + 3) *w = 40
w*w + 3*w = 40
w² + 3w = 40
w² + 3w - 40 = 0
w² + 8w - 5w - 8*5 = 0
w(w + 8) - 5 (w +8) =0
(w + 8) (w - 5) = 0
w - 5 = 0 {Ignore w + 8 =0, as measurement will not be in -ve}
w = 5 ft
l = 5 + 3
l = 8 ft
A manufacturer puts tires on two cars (four tires each). Each tire has a 10% probability of being flat. Assume the manufacturer puts four tires on one car first and then another four on the next car second. What's the probability that there is at least one car that has no working tires?
The probability that there is at least one car that has no working tires is given as follows:
0.0002 = 0.02%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For each car, the parameters are given as follows:
p = 0.9, n = 4.
Hence the probability that a car has no working tires is given as follows:
P(X = 0) = (1 - 0.9)^4 = 0.0001.
Hence the probability that two cars have working tires is given as follows:
P(X = 2) = (1 - 0.0001)² = 0.9998.
The probability that at least one has no working tires is given as follows:
P(X < 2) = 1 - 0.9998 = 0.0002 = 0.02%.
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A librarian wants to check a sample of books from the library to get an idea of how many need replacing.
Why might simple random sampling be a good way to do this?
He will not need a list of all the books
He will take longer if he checks all the books instead of checking a few
He will have a more representative sample if he chooses randomly
He will be able to choose whichever books he likes because it is random
The reason why simple random sampling will be a good way to do the selection of bad books is; Option C: He will have a more representative sample if he chooses randomly
What is the importance of simple random sampling?A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.
The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.
Now, in this case, since the librarian wants to check a sample of books from the library to get an idea of how many need replacing, it means that a random sampling method is good because;
He will have a more representative sample if he selects randomly as the definition earlier stated makes clear.
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Everv goat has eaten a wolf: There is a wolf who has eaten every goat; Every goat is eaten by a wolf Some goat was eaten by wolf: Question 6 (1 point) Let A - { 1,2,3 and B = { 5,4,2,3 }. Select all that are true from below: A U B = {5,3,2,4] A 0 B = { 2 , 3 } A - B = { 1,3 } B - A = {4,5 }'
All of the statements are true.
Here is a breakdown of the set operations:
A U B (the union of A and B) is the set of all elements that belong to either A or B or both. In this case, the elements that belong to
A U B are {5, 3, 2, 4}, as these are the elements that belong to either A or B.A ∩ B (the intersection of A and B) is the set of all elements that belong to both A and B. In this case, the elements that belong to
A ∩ B are {2, 3}, as these are the elements that belong to both A and B.A - B (the difference between A and B) is the set of all elements that belong to A but not to B. In this case, the elements that belong to
A - B are {1}, as 1 belongs to A but not to B.B - A (the difference between B and A) is the set of all elements that belong to B but not to A. In this case, the elements that belong to
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a volunteer group decided to pick up trash along a stretch of road measuring five and one third miles. the group divided into five teams to cover an equal distance. What distance will each group have to cover?
Answer: 1 [tex]\frac{1}{15}[/tex] miles
Step-by-step explanation:
We will divide the length of the road, five and one-third miles by the number of groups, five teams, to find the answer to this question.
(5 1/3) / 5 = (16/3) / 5 = (16/3) * (1/5) = 16/15 = 1 1/15 miles
* Note: We can use "keep change flip" when multiplying with fractions. Keep the first number, change to multiplication, flip to the reciprocal of the second number
Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
Given: LM≅LK; LN≅LJ
ΔLMJ and ΔLKN are congruent by SAS congruence postulate.
What is SAS and ASA congruence rule for triangles?
SAS : If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
ASA : If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
According to the given question:
The pair of overlapping congruent triangles in the diagram are:
ΔLMJ and ΔLKN
Now,
LM ≅ LK (Given)
LN ≅ LJ (Given)
∠LJM = ∠LNK (Angles opposite to equal sides are equal)
∴ ΔLMJ ≅ ΔLKN by SAS congruence of triangles
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describe a procedure that you would use to localize the protein dynein in tissue sections of esophagus and trachea. indicate the results that you would expect from such an analysis.
Therefore, the five steps are taken to localize the protein dynein in tissue sections of the esophagus and trachea.
What is localization?Any procedure that involves moving, attaching to, or otherwise maintaining a cell, substance, or cellular entity in one place, like an organelle or protein complex. Substance localisation can also be accomplished through selective degradation.
In this case,
the steps that are done in order to localize the protein dynein in tissue sections of the esophagus and trachea are as follows:
1. Histoclear removes the medium to enable the labeling of the antibodies
2. to rehydrate the sample, add water.
3. Using BSA blocking solution after Triton X- 100, which ruptures membranes and makes antigens more accessible to antibodies
(4) Add the dynein antibody.
5. include a secondary antibody that is likewise peroxidase-active (adds specificity)
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f(x)=3x²+42-6
g(x)=62-5²-2
Find (f+g)(x).
O A. (f+g)(x) =-628+82 +42-4
O B. (f+g)(x) = 6r³-2r² +42-8
O c. (f+g)(x) = 9r³-2-8
OD. (f+g)(x) = 6x³+3x²-2-8
The composite function (f + g)(x) is (f + g)(x) = 9x² - x - 8
How to determine the composite functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=3x²+42-6
g(x)=62-5²-2
Express properly
So, we have the following representation
f(x) = 3x² + 4x -6
g(x) = 6x² - 5x - 2
The composite function is then calculated as
(f + g)(x) = f(x) + g(x)
So, we have
(f + g)(x) = 3x² + 4x -6 + 6x² - 5x - 2
Evaluate
(f + g)(x) = 9x² - x - 8
Hence, the function is (f + g)(x) = 9x² - x - 8
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someone mind helping me in the question......thank you :) ....
Answer:
NY: 4cm + 3cm = 7cm
XY: 8cm + 3cm = 11cm
Step-by-step explanation:
1. find the difference between XN and MN
2. use the difference to add to the value LN and LM
Question
There are two spinners. The first spinner has three equal sectors labeled 1, 2 and 3. The second spinner has four equal sectors labeled 3, 4, 5 and 6. The spinners are spun once.
What is the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner?
The number of possible outcomes that do not show 1 on the first spinner and 4 on the second spinner is 2.
What is sample space?It is the total number of possible outcomes from a given set.
We have,
The sample space for when both the spinners are spun once.
S = {(1, 2, 3) x (3, 4, 5, 6)}
S = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 4), (3, 5), (3, 6)}
Now,
The number of total outcomes = 12
The number of outcomes that do not show 1 on the first spinner and 4 on the second spinner.
= {(2, 4), (3, 4)}
= 2
Thus,
The number of required possible outcomes is 2.
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Suppose there are two types of tickets to a show: advance and same-day. Advance tickets cost $25, and same-day tickets cost $20. For one performance, there were 65 tickets sold in all, and the total amount paid for them was $1450. How many tickets of each type were sold?
The number of Advance tickets sold:
The number of same-day tickets sold:
By solving a system of equations we will see that they sold 35 advanced tickets and 30 same-day ones.
How to find the number of each ticket sold?Let's define the variables we will be using for this problem, these are:
x = number of same advance tickets.
y = number of same-day tickets.
With the given information we can write a system of equations:
x*$25 + y*$20 = $1,450
x + y = 65
To solve the system we can isolate x on the second equation:
x = 65 - y
Now let's replace that in the other equation:
(65 - y)*$25 + y*$20 = $1,450
$1,625 - y*$5 = $1,450
$1,625 - $1,450 = $5*y
$175/$5 = y
35 = y
Then the value of x is:
x = 65 - 35 = 30
So they sold 35 advanced tickets and 30 same-day ones.
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WHAT IS THE M(X) IN THE REGRETION EQUATION Y=20.23*X+516.1
The M(x) or the estimate slope is 20.23X
What is the regression equation?A regression equation is used in stats to find out what relationship, if any, exists between sets of data. For example, if you measure a child’s height every year you might find that they grow about 3 inches a year. That trend (growing three inches a year) can be modeled with a regression equation.
[tex]Y_i=f(X_i, \beta)+e_i[/tex] [tex]Y_i[/tex] = dependent variable
[tex]X_i[/tex] = independent variable
[tex]\beta[/tex] = unknown parameters
[tex]e_i[/tex] = error terms
Given here, Y=20.23*X+516.1
Thus comparing it with the equation above we can deduce that
M(x) = 20.23x
Hence The M(x) or the estimate slope is 20.23X
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may someone give me the answer
Answer:
x represents the number of hours.
(y) distance because the distance depends on the number of hours traveled.
H(x) = 50x
H(5) = 50(5)
H(5) - 250 miles
After 5 hours of driving at 50 miles per hour, the car has traveled 250 miles.
Step-by-step explanation:
If 3(x+1)=4x-1, then x=
Answer:
X = 4Step-by-step explanation:
To solve the equation 3(x+1) = 4x-1, we need to use the rules of algebra to isolate the variable "x" on one side of the equation and simplify the other side.
First, we can distribute the 3 on the left side of the equation to obtain 3x + 31 = 4x-1. This gives us 3x + 3 = 4x-1.
Next, we can subtract 3x from both sides of the equation to obtain 3 + 3 = 4x-1-3x. This simplifies to 3 = x-1.
Now we can add 1 to both sides of the equation to obtain 3+1 = x. This gives us the final solution x = 4.
Therefore, the solution to the equation 3(x+1) = 4x-1 is x = 4.
Answer the following questions.
1) Choose the equation of a line parallel to the given equation and passing through a point P.
x+2 y=5 ; P=(2,-5)
y=-1/2 x-1
y=2 x-4
y=-2 x-1
y=-1/2 x-4
2) Choose the equation of a line parallel to the given equation and passing through a point P.
-3 x-y=-4 ; P=(1,4)
y=-3 x+5
y=-3 x+7
$y=1/3 x-3
$y=1/3x+7
The linear functions in this problem are given as follows:
1. y = -x/2 - 4.
2. y = -3x + 7.
How to define the linear functions?Considering the options in these problems, the linear functions are defined in slope-intercept format, given as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope.b is the y-intercept.The slope-intercept definition of the two equations presented in this problem are given as follows:
y = -0.5x - 5.y = -3x + 4.When two linear functions are parallel, they have the same slope, hence the two functions will be given as follows:
y = -0.5x + b.y = -3x + b.For item 1, when x = 2, y = -5, hence the intercept b is calculated as follows:
-5 = -0.5(2) + b
b = -5 + 1
b = -4.
For item 2, when x = 1, y = 4, hence the intercept b is calculated as follows:
4 = -3(1) + b
b = 7.
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vi
18,500
-how did you divide this? 1,295 divided by 18,500
Answer:
0.07
Step-by-step explanation:
The area of a rectangle is 9/10 square meter. The width is 2/5 meter. b. How many times greater is the length than the width? Write your answer in simplest form.
Answer:
Step-by-step explanation:
a = lw
l = a/w
l = (9/10)/(2/5) = (9/4)
l/w = (9/4)/(2/5) = 5 5/8 times greater
Answer:
4.5/2 = 2.25
Dif: 2.25/0.4 = 5.625 times greater
Hope this helps
evaluate f(x)=-25x^4+3x^2+2
f(x)=-25x^4+3x^2+2 = f'(x)=-100x^3+6x
Take derivation
f'(x)=d/dx(-25x^4+3x^2+2)
Formula
d/dx(f+ g)=d/dx(f) + d/dx(g)f'(x)=d/dx(-25x^4)+d/dx(3x^2)+d/dx(2)
Formula
d/dx(x^a)=ax^(a-1)f'(x)=-25(4x^3)+3(2x)+0
f'(x)=-100x^3+6x
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What is the y-value of the solution for this system of equations:
4x - y = 10
x - 4 = y
The required value of y is obtained as -2.
What are the types of a system of equations?The given system of equation can either have a unique solution, more than one solutions or no solution.
On this basis they are divided into two parts consistent and inconsistent.
A consistent system has one or more solutions while for an inconsistent system there are no solutions.
The given system of equations is as below,
4x - y = 10 (1)
x - 4 = y (2)
Substitute the value of y from equation (2) into equation (1) to get,
4x - (x - 4) = 10
=> 3x + 4 = 10
=> 3x = 6
=> x = 2
Then, substitute x = 2 in x - 4 = y to get,
y = 2 - 4 = -2
Hence, the value of y for the given system of equations is -2.
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17. Which of the following statements about overhead expenses is true?
A. They contribute indirectly to the running of a business.
B. They contribute directly to the running of a business.
C. They're directly related to a specific department.
D. They're directly related to a specific product.
Thus ,the statement about overhead expenses which is true is option (B). .
What is overhead expenses?In the business world, an ongoing expense of operating a business is known as overhead or an overhead charge .In contrast to operating costs like raw material and labor, overheads are expenses that cannot easily be connected to or associated with any one revenue unit.
Here,
the statement about overhead expenses which is true is option (B).
Explanation :The costs of operating a firm that aren't directly connected to providing an item or service are referred to as overhead. These expenses might be either fixed, like rent, or variable, like transportation expenditures. Additionally, they may be semi-variable, like utilities. Thus contribute directly to the running of a business.
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PLEASE HELP!!!!
Jamal works as a valet and a waiter at a restaurant. As a valet, Jon made $10.25 an hour and an additional $50.10 in tips, while at the restaurant he made $6.75 an hour and an additional $125 in tips. He made the same amount of money at both jobs last week.
Part A: Select the equation that can be used to determine the number of hours Jamal worked last week.
Part B: The total amount of money that Jamal made when both paychecks were the same is $
Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9
What is equation?Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.
Here,
Part A:
Jamal works as a valet made $10.25 an hour and an additional $50.10 in tips,
Thus number of hours be x
equation : 10.25x + 50.10 =0
or
Jamal works as a waiter made $6.75 an hour and an additional $125 in tips
equation : 6.75x + 125 = 0
Part B:
The total amount he made when both paychecks are same
=> 6.75x + 125 = 10.25x + 50.10
=> 10.25x-6.75x = 125-50.10
=>3.5x = 74.9
=>x=74.9/3.5 =21.4
Thus the total amount he made
10.25(21.4) + 50.1 = 269.45
and
Total amount = 2* 269.45=538.9
Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9
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If no deposits or withdrawals
are made, money held in this
account may increase or
decrease.
This account may generate
income from a variety of
sources.
There is no risk of losing any
money put in this account.
Savings Account
Interest income is the only
way to earn money in this
type of account.
Investment Account
Answer:
Savings Account
There is no risk of losing any money put in this accountInterest income is the only way to earn money in this type of accountInvestment Account
If no deposit or withdrawals are made, money held in this account may increase or decreaseThis account may generate income from a variety of sources
what is the probability distribution that has a mean of 1 and a standard deviation of 0?
The required explanation of probability distribution that has a mean of 0 and a standard deviation of 1 is describe below.
What is probability distribution?Probability distributions help to show our reality, empowering us to get evaluations of the likelihood that a specific occasion might happen, or gauge the inconstancy of event. They are a typical method for depicting, and potentially foresee, the likelihood of an occasion
According to question:The mean of the z-scores is dependably 0. The standard deviation of the z-scores is dependably 1. The chart of the z-score dissemination generally has a similar shape as the first conveyance of test values. The amount of the squared z-scores is dependably equivalent to the quantity of z-score values.
Thus, it is dependable.
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Correct question:
A normal probability distribution can have any value of the mean or must have a standard deviation of 1 and a mean of 0?
If the 8th term of a sequence is 256, and the 5th term of the sequence is 32, the common ratio is:
The geometric sequence have a common ratio of 2
Geometric SequenceGeometric progression (GP) is a type of sequence where each next term is gotten by multiplying each previous term by a fixed number, which is called a common ratio.
In this problem, we must write out two equations to find the common ratio.
Let;
r = common ratioa = first termThe nth term of a GP is given as;
Tn = arⁿ⁻¹
T₈ = ar⁷
256 = ar⁷ ...eq(i)
T₅ = 32
32 = ar⁴ ...eq(ii)
Dividing equation (i) by equation (ii)
256 / 32 = ar⁷ / ar⁴
8 = r⁷⁻⁴
8 = r³
r = ∛8
r = 2
The common ratio of the geometric sequence is 2
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For the given probability distribution, what is P(X<4) ?
Step-by-step explanation:
5. the most significant challenge that small businesses face is financial problems.
Alexandra and Maris are playing a game where they guess how many sides the regular polygon the other is holding has. Alexandra says her regular polygon has exactly 12 lines of symmetry. Maris says her regular polygon has an angle of rotational symmetry of 24°. How many sides does each regular polygon have?
The number of sides of Alexandra's regular polygon is 12.
The number of sides of Maris's regular polygon is 15.
What is a regulars polygon?
A regular polygon is denoted a area. The area bounded by equal length of arms. The angel between any two consecutive arms will same any other pair of consecutive arms.
The number of line of symmetry of a polygon is the same is the number of arm or sides of that polygon.
Thus the number of sides of a polygon that has 12 lines of symmetry is 12.
The angle of rotational symmetry of a polygon is 360°/n, where n is the number of arms.
Therefore,
Angle of rotational symmetry = 360°/n
Putting Angle of rotational symmetry = 24°:
24° = 360°/n
Multiply both sides by n
24n = 360
Divide both sides by 24:
n = 360/24
n = 15
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one and three fifths plus three and two thirds equals blank
Answer: 5 4/15
Step-by-step explanation:
1 3/5 + 3 2/3 = 8/5 + 11/3
Find the common denominator (5 and 3) = 15
So 8/5 equals to 24/15 because if 5 x 3 = 15 , 8 must also multiply by 3.
11/3 equals to 55/15 because if 3 x 5 = 15 , 11 must also multiply by 5.
Thus 24/15 + 55/15 = 79/15
This is an improper fraction, so converting to mixed number:
79/15 = 5 4/15 because 5 x 15 + 4 = 79
A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 25%.
If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.
Calculate each sum or difference.
a) 43.78 +21.05 +52.29
Answer:
117.12
Step-by-step explanation:
43.78+21.05 = 64.83
64.83+52.29 = 117.12
Using the quadratic formula to solve 2x² = 4x-7, what are the values of x?
O2+√101
2±
O 1± 101
2± √/10/
2
O 1± √√51
Answer:
x would be equal to 5 and the other one to your right would be 3 because O1t is aka known as a linear expression so you would have the multiply by 2 and use and exponent square
Is (2, 10) a solution to this system of equations?
y = x + 8
y = 10x + 3
yes
Submit
no
Point (2,10) is not satisfying the linear function y = 10x + 3 thus it will be not the solution of the system of equations.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given point (2,10)
Put it into y = x + 8
10 = 2 + 10 = 10 (satisfy)
Put it into y = 10x + 3
10 = 10 x 2 + 3 = 23 ≠ 10 (Not satisfy)
Hence "Point (2,10) will not be the system of equations' solution since it does not fulfill the linear function y = 10x + 3".
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