The possible values for the width of rectangle are 24 and -28.
What is area of rectangle?
The area of a rectangle formula. Area of a Rectangle is A = l × b. Once the length and width of a rectangle are known, the area can be calculated. The area of the rectangle is calculated as a square unit by multiplying the length and width.
Let x is the width of rectangle.
As given a rectangle length is 4 feet longer than it is wide.
⇒ l = 4 + x
Since,
Area of rectangle = length x width
672 = (4 + x) x x
672 = 4x + x^2
x^2 + 4x - 627 = 0
To find the value of x we can use the quadratic formula.
Here a = 1, b = 4, c = -672
[tex]x = \frac{-b +-\sqrt{b^2-4ac} }{2a} \\x = \frac{-4+-\sqrt{4^2-4(1)(-672)} }{2(1)} \\x = \frac{-4+-\sqrt{2704} }{2} \\x = \frac{-4+-52}{2} \\x = -2+-26[/tex]
⇒ x = -2 + 26, x = -2 - 26
⇒ x = 24, x = -28
Hence, the possible values for the width of rectangle are 24 and -28.
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Exercise 1
Directions: Describe the end behaviors of the following functions:
1. f(x) = x5 – 19x3 + 48x
2. f(x) = - x4 - 49x2 - 5
3. f(x) = x2 - 10x + 16
4. f(x) = - x (x + 9) (x - 1)
5. f(x) = 4x2 - 2x + 1
On solving the derivatives we got - 6x5-15 , 4x² - 98x , x-5)²-9, -3x²-16x+9 , -2
What is derivative?Differentiation is the rate at which a function changes with regard to a variable in mathematics (in mathematics, the rate of change of a function with respect to a variable). The usage of derivatives is necessary while solving calculus and differential equation problems.
1. f(x) = 6x5-15 DERIVATIVE
2.f(x) = 4x² - 98x DERIVATIVE
3. f(x) = (x-5)²-9
4.f(x)= -3x²-16x+9 DERIVATIVE
5.f(x)=-2 DERIVATIVE
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If the average of 7 positive integers is 100, find the highest possible value of the largest number.
PLS ANSWER QUICKLY FOR THE SAKE OF THE GOD!!!1
Answer:
Step-by-step explanation:
3. What is the power output of an engine that does 60,000 J of work in 10 s?
the answer to the problem is 6 KILA watts
Important Formula:
[tex]p=\dfrac{w}{t}[/tex]
Where p is power(measured in watts), w is work(measured in joules), and t is time(measured in seconds).
[tex]w=60,000J[/tex]
[tex]t=10s[/tex]
[tex]p=?[/tex]
____________
[tex]p=\dfrac{w}{t}[/tex]
____________
[tex]p=\dfrac{60,000}{10}[/tex]
____________
[tex]\fbox{p = 6,000 watts}[/tex]
A bakery produces cakes, cookies, and biscuits. The raw materials for these products are all the same (eggs, flour, water and sugar). The owner of the bakery would like to determine the best mix of products to produce with the materials currently in the bakery. Which of the following are resource constraints for this problem?
-Amount of flour used <= Amount of flour available
-Amount of sugar used <= Amount of sugar available
Therefore the constraints for this problem is the amount of flour used must equal the amount of flour available and the amount of sugar used must equal the amount of sugar available.
What is constraint ?When variables are employed in equations to simulate real-world scenarios, constraints must be applied to set limits and bounds on those variables. It's possible that some answers, while theoretically proving an equation correct, may not make sense in the context of a real-world word problem.
Here,
The following resource limitations apply to this issue: -
The amount of flour used must equal the amount of flour available.
The amount of sugar used must equal the amount of sugar available.
Explanation : As the flour is limited therefore the amount of flour used will become a constraint for this problem and similarly the amount of sugar available will become a constraint to amount of sugar used.
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PLS HELP
Complex numbers are used to describe current (1), voltage (E),
and impedance (Z). Impedance is the opposition to current.
The relation between these three variables is demonstrated by
the formula for Ohm's Law:
E = (I)(Z)
Given:
I = (3 + 3i)
Z = (2+2i)
find E
E=
The relation between these three variables is demonstrated by
the formula for Ohm's Law: E = (I)(Z) is 12i.
What is Ohm's Law?
According to Ohm's law, the resistance of the circuit and the current or energy travelling through the resistance are both exactly proportional to the voltage or potential difference between two places. V=IR is the equation for Ohm's law.According to Ohm's Law, assuming the temperature and other physical parameters don't vary, the current flowing through a conductor is precisely proportional to the potential difference applied across its ends. Through a resistor, current is inversely proportional to the voltage difference.
(3+3 i)(2+2 i)
Apply complex arithmetic rule: (a+b i)(c+d i)=(a c-b d)+(a d+b c) i
=(3 .2-3. 2)+(3 .2+3 . 2) i
Simplify [tex]$(3 \cdot 2-3 \cdot 2)+(3 \cdot 2+3 \cdot 2) i: \quad 12 i$[/tex]
[tex]$=12 i$[/tex]
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A pharmacy has determined that a healthy person should receive 70 units of
proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries
the six types of health food with their ingredients as shown in the table below,
what blend of foods satisfies the requirements at minimum cost to the
pharmacy? Make a mathematical model for the given problem.
Foods Protein units Carbohydrates
units
Fat units Cost per unit
A 20 50 4 2
B 30 30 9 3
C 40 20 11 5
D 40 25 10 6
E 45 50 9 8
F 30 20 10 8
optimal solution is arrived with value of variables as :
x1=0.9091,x2=1.8182,x3=0,x4=0,x5=0,x6=0
minimize cost:
z=2x₁+3x₂+5x₃+6x₄+8x₅+8x₆=2x
subject to:
20x₁+30x₂+40x₃+40x₄+45x₅+30x₆ ≥70 : amount of protein
50x₁+30x₂+20x₃+25x₄+50x₅+20x₆ ≥100 : amount of carbohydrate
4x₁+9x₂+11x₃+10x₄+9x₅+10x₆ ≥20 : amount of fat
where x₁, x₂, x₃, x₄, x₅, x₆ are units of 6 foods
solution using Simplex method:
After introducing artificial variables:
Min Z=2x₁+3x₂+5x₃+6x₄+8x₅+8x₆+0S₁+0S₂+0S₃+MA₁+MA₂+MA₃
subject to
20x₁+30x₂+40x₃+40x₄+45x₅+30x₆-S₁+A₁ ≥ 70
50x₁+30x₂+20x₃+25x₄+50x₅+20x₆-S₂+A₂≥ 100
4x₁+9x₂+11x₃+10x₄+9x₅+10x₆-S₃+A₃=20
and x₁,x₂,x₃,x₄,x₅,x₆,A₁,A₂,A₃≥0
Refer to the image for Z
Since all Zj-Cj≤0
Hence, optimal solution is arrived with value of variables as :
x1=0.9091,x2=1.8182,x3=0,x4=0,x5=0,x6=0
Min Z=7.2727
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Use separation of variables to find the solution to the differential equation subject to the given initial condition.
dP/dt=0.07P, P(0)=30
The solution to the differential equation subject to the given initial condition is log P = 0.07t + log(30)
Differential equation in which the variables can be separated from one from one another are called separable differential equations
A general form to write a separable differential equation is
dy/dx = f(x)g(y)
where the variable x and y can be separated from each other
According to the question,
We have to solve dP/dt=0.07P by using separation of variable
=> dP/dt=0.07P
Dividing P both sides and multiplying dt
=> dP / P = 0.07 dt
Now Integrating both the sides
=> [tex]\int\limits {\frac{1}{P} \, dP = \int\limits {0.07} \, dt[/tex]
=> log P = 0.07t + c ------(1)
It is given that P(0)=30
which means at t = 0 , the value of P = 30
Substituting t = 0 and P = 30
log(30) = 0 + c
=> c = log(30)
Substituting the value of c back to equation (1)
log P = 0.07t + log(30)
=> log(P / 30) = 0.07t is our solution
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Which of the following is true when the discriminant of a quadratic equation is zero?
When an equation's discriminant is zero, the following is the given statement that is correct: There is just one viable solution.
Having the form ax2 + bx + c = 0, quadratic equations are second-degree algebraic expressions. The name "Quadratic" is derived from the word "Quad" which means square. A quadratic equation is an "equation of degree 2," to put it another way. A quadratic equation is employed in numerous situations.
There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (α, β) and are also known as the roots of quadratic equations.
Three instances of discrimination exist.The equation has two real solutions if the discriminant is strictly bigger than zero.There is just one real solution if the discriminant equals zero.Additionally, if the discriminant is strictly less than zero, there are no real solutions to the equation, meaning that both of its solutions are complex.Learn more about quadratic equations here:
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Give an example of odd function and also of even function
Therefore, the example of the polynomial function f(x)=[tex]x^{2} +x^{4} +x^{6}[/tex] is even and the polynomial function f(x)=[tex]x+x^{3} +x^{5}[/tex] is odd
Function is what?A mathematical function from one set X to another gives each element of X exactly one element of the other. The sets X and Y, respectively, represent the function's domain and codomain.
Here,
The polynomial function f(x)=[tex]x^{2} +x^{4} +x^{6}[/tex] is even.
The polynomial function f(x)=[tex]x+x^{3} +x^{5}[/tex] is odd
As we can see,
The function
f(x)=[tex]x^{2} +x^{4} +x^{6}[/tex]
when we put
f(-x)=[tex](-x)^{2} +(-x)^{4} +(-x)^{6}[/tex]
f(-x)=[tex]x^{2} +x^{4} +x^{6}[/tex]
Thus f(x)=f(-x)
Therefore it is even.
The function
f(x)=[tex]x+x^{3} +x^{5}[/tex]
f(-x)=[tex](-x)+(-x)^{3} +(-x)^{5}[/tex]
f(-x)=[tex]-x-x^{3} -x^{5}[/tex]
Thus f(x)≠f(-x)
Therefore it is odd.
Therefore, the example of the polynomial function f(x)=[tex]x^{2} +x^{4} +x^{6}[/tex] is even and the polynomial function f(x)=[tex]x+x^{3} +x^{5}[/tex] is odd
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Tanya has a collection of 52 rocks that she wants to put into display cases. Each display case can hold 8 rocks. Tanya divides to find how many cases
she needs.
52÷8=614
How many display cases will Tanya need?
A. 4
B. 6
C. 7
D. 8
E. 10
point (9,1) and (7,R) are on a line with a slope of -3/4 what is R
The value of R is 2.5 or (5/2) . We can find the answer by using concepts of slope of line.
What is the slope of a line?
Slope of a line measures its steepness . Mathematically, its calculated as "rise over run".
When two points are given,
Slope of a line = (y2 - y1)/(x2 - x1)
Here, y2 = R
y1 = 1
x2 = 7
x1 = 9
Slope of a line = (R-1)/(7-9)
In the que, its given slope = -3/4
So, (R-1)/(-2) = -3/4
R = 5/2 or 2.5
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Twenty-five samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 25 samples, a total of 135 items were found to be defective.
What is an estimate of the proportion defective when the process is in control (to 3 decimals)?
What is the standard error of the proportion if samples of size 100 will be used for statistical process control (to 4 decimals)?
Compute the upper control limit and lower control limit for the control chart (to 4 decimals, if necessary)?
a) The estimate of the proportion of defectives when the process is in control is 0.054
b) The standard error of the proportion if the sample size is 100 is 0.0226.
c) The upper control limit is 0.1218 and the lower control limit is 0 (since LCL < 0 and p > 0, we can write LCL = 0).
What are the formulas for finding the estimate of the proportion, standard variation, and control limits?1) The estimate of the proportion of success is
p = (number of success)/(total number of samples)
I.e., p = x/N
2) The standard deviation of the proportion of success is
[tex]\sigma_p = \sqrt{\frac{p(1-p)}{n} }[/tex]
3) The upper and lower control limits for a control chart are:
L.C.L = p - 3[tex]\sigma_p[/tex]
and U.C.L = p + 3[tex]\sigma_p[/tex]
Calculation:It is given that, there are 25 samples of 100 items each.
So, the total number of items i.e., the total sample size,
N = 25 × 100 = 2500
In 25 samples, a total of 135 items were found to be defective.
So, the number of defectives x = 135
a) The estimate of the proportion of defectives is p = x/N
On substituting, we get
p = 135/2500 = 0.054
b) The standard error of the proportion if the sample of size 100 is calculated by
[tex]\sigma_p = \sqrt{\frac{p(1-p)}{n} }[/tex]
On substituting p = 0.054 and n = 100, we get
[tex]\sigma_p = \sqrt{\frac{0.054(1-0.54)}{100} }[/tex]
= 0.0226
c) The control limits for the control chart are:
Upper control limit = p + 3[tex]\sigma_p[/tex]
⇒ U.C.L = 0.054 + 3(0.0226) = 0.054 + 0.0678 = 0.1218
Lower control limit = p - 3[tex]\sigma_p[/tex]
⇒ L.C.L = 0.054 - 3(0.0226) = 0.054 - 0.0678 = - 0.0138 ≈ 0
(Since we know that the lower control limit should not be a negative value, it is made equal to 0).
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construct a recursive binary search algorithm by putting the following steps in the correct order.
CASE1: If target is equal to middle, then return mid.
CASE2:If target is less than middle i.e., target<A[mid],we discard all the elements in the right search space including mid element. Now our new high would be mid-1 while 'low' remains as it is.
CASE3:If the target element is greater than middle i.e., target>A[mid],we discard all the elements in the left search space including mid element. Now our new low would be mid+1 while 'high' remains as it is.
What is Recursive Algorithm?
Recursive algorithm, a function calls itself again and again till the base condition(stopping condition) is satisfied.
Let us track the search space by using two index start and end. Initialy low=0 and high=n-1(as initialy whole array is search space).At each step, we find mid value in the search space and compare it with target value. There are three cases possible:
CASE1: If target is equal to middle, then return mid.
CASE2:If target is less than middle i.e., target<A[mid],we discard all the elements in the right search space including mid element. Now our new high would be mid-1 while 'low' remains as it is.
CASE3:If the target element is greater than middle i.e., target>A[mid],we discard all the elements in the left search space including mid element. Now our new low would be mid+1 while 'high' remains as it is.
Recursive implementation of binary search algorithm, in the method binarySearch(), follows almost the same logic as iterative version, except for a couple of differences.The first difference is that the while loop is replaced by a recursive call back to the same method with the new values of low and high passed to the next recursive invocation along with "Array" and "key" or target element.The second difference is that instead of returning false when the while loop exits in the iterative version, in case of the recursive version, the condition of low > high is checked at the beginning of the next level of recursion and acts as the boundary condition for stopping further recursive calls by returning false.Also, note that the recursive invocations of binarySearch() return back the search result up the recursive call stack so that true or false return value is passed back up the call stack without any further processing.To learn more about binarySearch:
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I don't know if "Base Angles Theorem" is correct. PLEASE ANSWER QUICKLY!!! Thank you.
The theorem use to find the base angles of the triangle ABE is base angle theorem.
How to find base angles of an isosceles triangle?An isosceles triangle is a triangle that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180 degrees.
According to the triangle ABE, the side AB and EB are congruent. This makes the triangle ABE an isosceles triangle.
AB ≅ BE
Therefore, the base angles are congruent.
The base angles theorem states that If two sides of a triangle are congruent, then the angles opposite them are congruent.
Therefore,
∠A ≅ ∠BEA by base angle theorem.
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True or False: The range of sine is...
True
False
It is false that the range of the sine function is 0 ≤ ∅ ≤ π
How to determine the true statement?From the question, we have the following parameters that can be used in our computation:
Function: sine function
Also from the question, we have
Range: 0 ≤ ∅ ≤ π
As a general rule, we have:
The minimum value of a sine function is -1The maximum value of a sine function is 1This means that the range of the sine function is from [-1, 1].
This can also be represented as -1 ≤ ∅ ≤ 1
Hence. the given statement about the sine function is false
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Answer:
The answer is false.
Step-by-step explanation:
The range of the sine function is NOT 0 ≤ ∅ ≤ π
The UGA Journalism Department is interesting in determining if there is a significant difference in the number of hours, on average per week, that UGA males and UGA female students spend reading any online or printed newspaper. Randomly selected students at UGA were asked how many hours per week they read any online or printed newspaper, their age, and gender. The 95% confidence interval for reading newspapers on μF-urn is (-1.1, 1.3). 1) Interpret this confidence interval. Because 0 is not in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males. Because 0 is not in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males. Because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males. Because 0 is in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males.
The option C, “because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males” is correct.
In the given question, the UGA Journalism Department is interesting in determining if there is a significant difference in the number of hours, on average per week, that UGA males and UGA female students spend reading any online or printed newspaper.
Randomly selected students at UGA were asked how many hours per week they read any online or printed newspaper, their age, and gender. The 95% confidence interval for reading newspapers on μ(F)-μ(M) is (-1.1, 1.3).
1) We have to interpret this confidence interval. The given options are:
• Because 0 is not in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males.
• Because 0 is not in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males.
• Because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males.
• Because 0 is in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males.
Since there interval was given.
The given interval for the 95% confidence interval for reading newspapers on μ(F)-μ(M) is (-1.1, 1.3).
Since the value of interval is between -1.1 and 1.3. So 0 is in this interval. So we cannot conclude that there is a difference in newspaper reading, on average, for females and male.
So the option C, “because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males” is correct.
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Callie took out a loan for $7000 to purchase a car. The loan must be repaod at the end of six years in one payment with interest of 5%. The total amount Callie has to pay back at the end of the loan is
A.$7350
B.$9100
C.$7900
D.$9700
The correct value of answer is B. $9100.The interest on the loan is 5% of the principal. So, the interest amount is:= $350
To calculate the total amount Callie has to pay back at the end of the loan, we need to add the principal amount (the original loan amount) and the interest accrued over the six-year period.
The interest can be calculated using the formula: Interest = Principal * Rate * TimeHere, the principal amount is $7000, the interest rate is 5% (or 0.05 as a decimal), and the time is 6 years.
Interest = $7000 * 0.05 * 6 = $2100
Adding the interest to the principal, the total amount Callie has to pay back is:
Total amount = Principal + Interest = $7000 + $2100 = $9100
Therefore, the correct answer is B. $9100.
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Among all smooth, simple closed curves in the plane, oriented counterclockwise, find one along which the work done by the following vector is greatest. 4 4 Hint: Find the region where (curl F).k>0. What is the curve along which the work is greatest?
Work done by the vector is 11π/16.
We know that,
the given closed curve in the plane is,
F(x,y) = [tex](\frac{x^{2}y }{4} + \frac{y^{3} }{3} )[/tex] i+xj
Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.
Let S be the interior of C.
Let P = [tex]\frac{x^{2}y }{4} +\frac{y^{3} }{3}[/tex] and Q = x
so the partial differentiation is,
[tex]\frac{dP}{dy} = \frac{x^{2} }{4} + y^{2}[/tex] and [tex]\frac{dQ}{dx}[/tex] = 1
By the Green's theorem work done by F is given as,
W = ∫ F dr
W = ∫∫ ( [tex]\frac{dQ}{dx} - \frac{dP}{dy}[/tex] )dxdy
W = ∫∫ [tex](1 - \frac{x^{2} }{y} -y^{2} )dxdy[/tex]
Let C = x² + y² = 1
and x = rcosθ, y = rsinθ ;
0 ≤ r ≤ 1; 0 ≤ θ ≤ 2π
Therefore
W = ∫∫ (1 - r²cos²θ/4 - r²sin²θ) [tex]|\frac{d(x,y)}{dr,0} |[/tex] dθdr
and d(x,y)/d(r,θ) = [cosθ -rsinθ; sinθ rcosθ] = r
Thus
W = ∫∫ (1 - r²cos²θ/4 - r²sin²θ)rdθdr
after solving we get,
W = 11π/16.
Hence the work done along with the vector is 11π/16.
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In how many ways can Tim draw a red or a green marble from a jar containing 20 red marbles and 4 green marbles?
The correct answer to how many different ways he can draw is 24.
Point A is the incenter of triangle DEF.
Which must be true? Select three options
A.Point A is the center of the circle that passes through points D, E, and F.
B.Point A is the center of the circle that passes through points X, Y, and Z.
C.ZA≅YA
D.EA≅FA
E.AX≅AY
The three options that describe the in-center of the given triangle are;
B. Point A is the center of the circle that passes through points X, Y, and Z.
C. ZA ≅ YA
E. AX ≅ AY
What is the in center of the triangle?The incenter of a triangle is defined as the point of intersection point of all the three interior angle bisectors of the given triangle. This means that, it can also be said to be the point where all the internal angle bisectors of the triangle cross each other.
Now, we are told that Point A is the incenter of triangle DEF. From the definition above, we can deduce that;
An inscribed circle can be drawn with center A passing through points X, Y and Z.
Similarly, since it passes through X, Y and Z, then it means that ZA≅YA, AX≅AY.
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A little girl and a little boy stop to each buy a tablet of chocolate. But the little girl is missing 10 cents to pay and the little boy is missing 1 cent. They then decide to buy a tablet together. But they are still missing 1 cent. How much does the chocolate bar cost?
The chocolate bar costs 9 cents. The little girl is missing 10 cents and the little boy is missing 1 cent, so together they are missing 11 cents.
What is cost?Cost is a monetary measure of the amount of resources, such as time or money, that must be expended to produce a product or service. It is a fundamental factor of economic production, as it is necessary to make products and services available to consumers. Cost can be determined in a variety of ways and can be linked to economic theory through the concept of opportunity cost. In business, cost is a major factor in decisions related to production, pricing, and marketing. Cost is also a factor in accounting and budgeting, as it is necessary to track and report the costs of organizational operations.
The chocolate bar costs 9 cents. The little girl is missing 10 cents and the little boy is missing 1 cent, so together they are missing 11 cents. If the chocolate bar cost 9 cents, that would leave 1 cent for them to split.
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it is possible for two sets of data to have the same regression equation but different correlations.
Yes, it is possible for two sets of data to have the same regression equation but different correlations.
What is regression and correlation?Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation.
The use of correlation analysis allows for the quantification of relationships between two continuous variables, such as those between two independent variables or between a dependent and independent variable.
Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The outcome variable is also referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".
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find the absolute maximum and absolute minimum of f (x, y) among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).
The absolute maximum and absolute minimum of f(x,y) = 3 + xy -x - 2y is f(0,0) and f(1,1) respectively.
The absolute maximum point is a point where the function obtains its greatest possible value.
And Absolute minimum is a point where the function obtains its least possible value. This is the smallest value that a mathematical function can have over its entire curve.
Given equation is, f(x,y) = 3 + xy - x - 2y
we will check absolute maximum and absolute minimum of f(x,y) at the points (0,0), (1,0), (1,1).
f(0,0) = 3 + (0)(0) - 0 - 2(0) = 3
f(1,0) = 3 + (1)(0) - 1 - 2 (0) = 2
f(1,1) = 3 + (1)(1) - 1 - 2(1) = 1
Therefore we get absolute maximum at f(0,0) and absolute minimum at f(1,1).
An absolute minimum also called a global minimum, occurs when a point of the function is lower any other point on the function within the function's domain. A local minimum also called relative minimum occurs when a point is lower than the points surrounding it.
Given question is incomplete. Complete question is:
find the absolute maximum and absolute minimum of f (x, y) = 3 + xy - x -2y among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).
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Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that P(E) = 0.24, P(B) = 0.16, and P(E and B) = 0.13. Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.0.530.130.60.27
The probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
We have to find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.
Since,
P(E or B) = P(E) + P(B) - P(E and B)
Given,
P(E) = 0.24
P(B) = 0.16
P(E and B) = 0.13
Hence,
P(E or B) = 0.24 + 0.16 - 013
P(E or B) = 0.27
Option D is correct.
Hence, the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.
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Please help, problem/picture is attached
Answer:
Step-by-step explanation:
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Select all of the algebraic expressions that could represent the phrase below.
nine more than the product of 5 times the number of tires t
9 + 5t
5 ▪ t + 9
(9 + 5)t
(5 × t) + 9
The statement nine more than the product of 5 times the number of tires t can be written as, 9 + 5t, so option A is correct.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given statement:
nine more than the product of 5 times the number of tires t
The above statement can be written as
= 9 + 5 × t
= 9 + 5t
Therefore, the statement nine more than the product of 5 times the number of tires t can be written as, 9 + 5t.
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evaluate the expression: v ⋅ w given the vectors: r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6> (2 points)
The product of the vectors v and w is gotten as; v ⋅ w = 22
What is the product of the vectors?We are given the vectors;
r = <8, 8, -6>
v = <3, -8, -3>
w = <-4, -2, -6>
We want to evaluate v.w which is a product of both vectors.
The formula will be;
v.w = (v_x * w_x) + (v_y * w_y) + (v_z * w_z)
Plugging in the values and solving gives;
v.w = (3 * -4) + (-8 * -2) + (-3 * -6)
v.w = -12 + 16 + 18
v.w = 22
We can conclude that the vector expressions has a product of 22
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A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.
The number of tiles in the bag of 10 that are yellow in colour are; 5 tiles
How to find the probability of selection?We are given;
Total number of tiles in bag = 10 tiles
Now, we are told that in the bag, the tiles are either blue, green, red, or yellow.
Now, after selecting a tile, we are told that it is put back and as such we have after 100 selections that we have 24 blue tiles, 12 green tiles and 12 red tiles. Thus;
Number that will be yellow = 100 - 24 - 12 - 12 = 52 yellow tiles
Thus, it means that the probability of selecting a yellow tile is;
52/100
Thus, number of tiles out of the 10 in the bag that are yellow =
(52/100) * 10 = 5.2
Approximately 5 yellow tiles
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Complete question is;
How many yellow tiles are most likely in the bag? Enter the answer in the box. A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.
-3x+y=2
-x+y-4=0
solving a system of linear equations by substitution
The solution to the system of linear equations by substitution is (1, 5)
How to solve the system of linear equations by substitutionFrom the question, we have the following parameters that can be used in our computation:
-3x+y=2
-x+y-4=0
Rewrite as
-3x + y = 2
-x + y - 4 = 0
Make y the subject in -x + y - 4 = 0
So, we have
y = x + 4
Substitute y = x + 4 in -3x + y = 2
-3x + x + 4 = 2
Evaluate the like terms
-2x = -2
So, we have
x = 1
Substitute x = 1 in y = x + 4
y = 1 + 4
Evaluate
y = 5
Hence, the solution is x = 1 and y = 5
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Given the equation, proof it
Answer:
Step-by-step explanation:
I forgot to add the last reason is AAS (two angles one side are congruent = triangles are congruent)
S.
1.Given
2. AE = EC
3. <AEB = <CED
4. <CDE = <ABE
5. triangles congruent
R.
1. Given
2. Segment bisector theorem
3. Vertical angles theorem
4. PAI Theorem
Hope this helps!