The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)
The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region
x+y<=2
3x+y>=3
x+3y>=3
x>=0
y>=0
Now, we would graph with the following inequalities
x+y>=2
3x+y<=3
x+3y<=3
x<=0
y<=0
Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).
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Suppose that f is differentiable for all x and that f (x)≤2 for all x. If f(1)=2 and f(4)=8 then f(2) has the value equal to a.3 b.4 c.6 d.8
The value of the function f(x) which is differentiable at all x, at x = 2
Or f(2) = b. 4.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, The function 'f' is differentiable for all x.
Now, f(1) = 2 and f(4) = 8, So, f(x) can be 2x as it is satisfying the conditions.
∴ At x = 2 or f(2) = 2(2) = 4.
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what is the solution to the system of equations x-y=-1 and x-3=- -13?
Answer:
Write in Standard Form
1. The standard form of a linear equation is
Ax + By = Cx-y=-1
2. x = 16
Ig?
I'm not sure.
Please help! It’s really hard
Houa works at an electronics store as a salesperson. Houa earns a 9% commission on the total dollar amount of all phone sales she makes, and earns a 6% commission on all computer sales. Houa made a total of $1700 in sales and earned $135 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
The required amount for phone and computer sales is $1100 and $600 respectively.
Given that,
Houa works at an electronics store as a salesperson. Houa earns a 9% commission on the total dollar amount of all phone sales she makes and earns a 6% commission on all computer sales. Houa made a total of $1700 in sales and earned $135 in commission.
What are simultaneous linear equations?
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
here,
Let the number of phone sales be x and the number of computer sales be y,
According to the question,
0.09x+0.06y=135, - - - - - (1}
x+y=1700 - - - - - - - (2)
Solving equation 1 and 2
Gives, x = $1100 and $600
Thus, the required amount for phone and computer sales is $1100 and $600 respectively.
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Find the first three nonzero terms in the Taylor polynomial approximation to the DE V" +9y + 5y3 = cos(10t), y(0) = 0, y' (0) = 1.
The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .
In the question ,
it is given that ,
the differential equation is
y'' + 9y + 5y³ = Cos(10t) ...equation(1)
y(0) = 0, y'(0) = 1
for y = 0 , the differential equation is
y''(0) + 9y(0) + 5{y(0)}³ = Cos90)
y''(0) + 9 + 5 = 1 ;
y''(0) = 1.
differentiating equation(1) with respect to "t" , we have
y''' + 9y' + 15y²y' = -10Sin(10t)
y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)
y'''(0) + 9 + 0 = 0
y'''(0) = -9
The Taylor series is given by
y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....
Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have
y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....
= t + t²/2 - 3/2.t³ + ...
Therefore , the first three terms are t , t²/2 , -3/2.t³ .
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A is a 7x7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three dimensional then it is possible that A is not diagonalizable. Select one: True False
A is a 7x7 matrix with three eigen values. One eigenspace is two-dimensional and one of the other eigenspaces is three dimensional, then it is possible that A is not diagonalizable. The given statement is true.
There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is atleast one as there is atleast one non-zero eigen vector in them.
It is given that one of the eigen space has dimension 2 and other one has dimension 3.
A 7 x 7 matrix is diagonalizable if and only if the sum of the eigenspaces' dimension is 7. The given matrix is diagonalizable if and only if the third eigen space has dimension 2.
In A, if the sum of dimensions of eigenspace is not equal to the number of columns, then A is not diagonalizable.
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thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. each student was given a choice between the macaroni and cheese and the cajun potato barrels. from the sample, 20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
Given that,
36 local middle school kids were chosen at random to take part in a taste test to choose a new menu item for a cafeteria. The Cajun potato barrels or the macaroni and cheese were the options offered to each pupil. 20 pupils chose the macaroni and cheese from the sampling, while 16 selected the Cajun potato barrels. On a scale from 1 (very dislike) to 9 (very much like), each student was asked to rank the object they selected (extremely like).
We have to find which of the following keeps this study from being an experiment with a sound design.
Each student was given the option of choosing either the macaroni and cheese or the Cajun potato barrels. Because the students' treatments were not distributed at random, those who preferred their cuisine chose it and gave it high marks. As a result, the study has selection bias.
Therefore, The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
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A potter has 9pounds of clay. He uses 3 10pound of clay for each bowl he makes.how many bowls can potter make?
Answer:
30 bowls
Step-by-step explanation:
9 lb / (3/10 lb/bowl) = 9 * 10/3 bowls = 30 bowls
What are 3 characteristics of exponential functions?
A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION [tex]f(x) = b^{x}[/tex]
-It’s a one-to-one function
-The graph passes through y-intercept of the point (0,1)
-x-intercept: none
-The domain is all real numbers: (−∞,∞)
-The range is y > 0 or (0,∞)
-The graph is increasing
-The graph is asymptotic to the x-axis as x approaches negative infinity
-Horizontal asymptote: y=0
-The graph increases without bound as x approaches positive infinity
-Increasing if b > 1
-Decreasing if b < 1
-The graph is continuous
-The graph is smooth
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A new car is purchased for 24900 dollars. The value of the car
depreciates at 11% per year. To the nearest tenth of a year, how long
will it be until the value of the car is 11800 dollars
Considering the depreciation rate of 11%, the value of car is $11800 in 4.1 years.
What is depreciation?Depreciation is the reduction in the value of an asset over time due to wear and tear, age, or obsolescence.
What is the formula of depreciation?The most basic and widely used method of calculating depreciation is Annual depreciation = (Cost of asset - Salvage value) / Useful life
To find the time it will take for the value of the car to depreciate to $11,800, we can set up the following equation:
24900 - 11800 = 11000
24900 * .11 = 2679
11000 / 2679 = 4.09 years
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1. Celia has 6 coins worth 10 cents each and 3 coins worth 25 cents each. If she chooses
two of these coins at random, what is the probability that the two coins combined will
be worth at least 35 cents?
The Total Probability of selecting two coins worth 35 cents at least is 17/36
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
There are two ways of having a sum at least 35 cents
(i) One 10 cent coin and One 25 cent coin
= 6/9 * 3/8 = 1/4
(ii) Both coins of 25 cents
= 2/9
Total Probability = 1/4 + 2/9
Total Probability = 9 + 8 / 36
Total Probability = 17 / 36
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If the domain of f(x) = x2 - 4 is limited to {-1,0,1,2} what is the greatest value of the range?
The greatest value of the range is
If the domain of f(x) = x² - 4 is limited to {-1, 0, 1, 2} the greatest value of the range is 0
How to find the greatest value of the rangeThe range represents the output values
Using the given expression to solve it can be found that the output values are
for x = -1, f(x) = x² - 4 = -1² - 4 = -3
for x = 0, f(x) = x² - 4 = 0² - 4 = -4
for x = 1, f(x) = x² - 4 = 1² - 4 = -3
for x = 2, f(x) = x² - 4 = 2² - 4 = 0
The greatest value of the range is 0
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Let U be a Universal set with subsets A and B. U={1,2,3,4,5,6,7,8,9,10} A={1,3,5,7} B={4,5,6} Find A′. Use set roster notation. If there is more than one element in the set, list in ascending order, separated by a comma.
The complement of set A is-
A' = {2, 4, 5, 6, 7, 8, 9, 10}
What is a set? What is union of sets? What is complement of a set?A set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example: {1,2,3,4} is a set of numbers.The union of two sets is a set containing all elements that are in A or in B (possibly both). For example, {1,2} ∪ {2,3} = {1,2,3}.The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.We have -
U={1,2,3,4,5,6,7,8,9,10} A={1,3,5,7} B={4,5,6}A' = U - A
A' = {1,2,3,4,5,6,7,8,9,10} - {1,3,5,7}
A' = {2, 4, 5, 6, 7, 8, 9, 10}
Therefor, the complement of set A is -
A' = {2, 4, 5, 6, 7, 8, 9, 10}
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Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.a. In every case.b. Only if n1≥30n1≥30 and n2≥30n2≥30.c. Only if n1p⎯⎯1≥5,n1(1−p⎯⎯1)≥5,n1p¯1≥5,n1(1−p¯1)≥5,n2p⎯⎯2≥5n2p¯2≥5 , and n2(1−p⎯⎯2)≥5.n2(1−p¯2)≥5.d. Only if n1p⎯⎯1≥30,n1(1−p⎯⎯1)≥30,n1p¯1≥30,n1(1−p¯1)≥30,n2p2≥30n2p2≥30 and n2(1−p⎯⎯2)≥30.n2(1−p¯2)≥30.
To conduct a hypothesis test for the difference between two population proportions under independent sampling is,
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5.
What is population proportion?
In statistics, a population proportion is a parameter that describes a percentage value connected to a population. It is typically denoted by P or the Greek letter π.
As per central limit theorem sample size needs to be greater than 30.
So required conditions are Only if n1 ≥ 30 and n2 ≥ 30.
Also for normal approximation we need the condition
[tex]np \geq 5 and[/tex] n(1 - p) ≥ 5
So one more condition is Only if
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5
Hence, to conduct a hypothesis test for the difference between two population proportions under independent sampling is
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5
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in your own words, explain what the concept of density means—without using the formula.
The concept of density explains how tightly packed together the matter in an object is
How to explain the concept of density?The density of a material is a measure of how tightly packed matter is together.
The concept of density compares the quantity of matter the material has to its volume. A material with much matter in a certain volume has a high density.
An object with high density is considered highly dense or heavy and an object with low density is considered less dense. For example, the air is about 830 times less dense than water.
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i need help with this 2 answers
(Oops forgot pic)
The angle measures in this problem are given as follows:
7 - m < ADC = 82º.
8 - m < ADC = 44º.
How to obtain the angle measures?In item 7, the angle measure is found obtained the angle addition postulate, meaning that the measures are obtained as follows:
m<ADB = m < BDC + m < ADC.
Then the equation to find the value of x is obtained as follows:
144 = 7x + 34 + 9x + 46
16x = 64
x = 64/16
x = 4.
Then the angle ADC is obtained as follows:
m < ADC = 9(4) + 46 = 82º.
In item 8, the bisection means that the two angle measures are equal, hence the value of x is obtained as follows:
7x - 19 = 9x - 37
2x = 18
x = 18/2
x = 9.
m < ADC = 9(9) - 37 = 44º.
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Mr. Freeze is a freelance ice artist who creates ice sculptures. He is paid $30 per pound of ice he uses. Last week it took him 73 hours to sculpt 5 sculptures weighing a total of 530 pounds. Based on this, what is his approximate hourly wage?
Answer:
$217.81/hr
Step-by-step explanation:
The 5 sculptures contain 530 lbs of ice, which Nr. Freeze sells at $30/lb:
His total income is: (530 lbs)*($30/lb) = $1590
The sculptures required 73 hours to create. Mr Freeze's hourly wage is therefore ($1590/73 hr) = $217.81/hr (!)
If 36 is the total number we are trying to get to how much do you add together???
To get 36 as a result, you can add different numbers, some examples that can work are 18+18, 24+12, 12+12+12, and 8+12+16.
What is addition?This is a basic mathematical operation that involves calculating the total of two, three, or more numbers. This implies in addition you combine or add numbers and in most cases you get a bigger number. Here are some examples:
5 + 6 = 11
254 + 25 = 279
0.2 + 1.2 = 1.4
How to find numbers whose total is 36?Use substraction to find possible numbers. Here is an example:
36 -18 = 18 which means 18 + 18 = 36
36 - 20 = 16 which means 20+16 = 36
Add small numbers until you get to the total. Here is an example:
2 + 4 + 8 + 6 + 3 + 7 + 5+ 1 = 36
Based on this, some numbers that you can use to get 36 are
18+18
24+12
12+12+12
8+12+16
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Determine if x and y are inversely proportional. If applicable, find the constant of variation.
The relationship between x and y is and the constant of variation is 24.
What is inversely proportional?
One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease. Building a wall would be an example of an inverse proportion in action.
Given that x and y are inversely proportion.
Assume that the relationship between x and y is
y = k/x where k is constant of variation.
Putting x = 3 and y = 8 in y = k/x :
8 = k/3
Multiply both sides by 3:
k = 8 × 3
k = 24
Putting x = 4 and y = 6 in y = k/x :
6 = k/4
Multiply both sides by 4:
k = 6 × 4
k = 24
The relationship is y = 24/x and the constant of variation is 24.
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Answer:
x and y are not inversely proportional.
Image:
y = 6x + 7, what is the slope?
Answer: m= 6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
because slope is the amount of times your changing the line
I need help with this please help me
By using the fact that segment DC bisects the angle BCA, we will see that:
m∠DCB = 67.38°
How to find the measure of angle BCD?
First, we know that the angle CDB is an angle of 90°, and the angle ACB has a measure of 134.76°.
Now, notice that the segment DC bisects that angle (bisects means that it "cuts it" right in half), then the angle BCD is half of that, we will have:
∠DCB = 134.76°/2 = 67.38°
In this way we conclude that the measure we wanted to find is 67.38°.
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factor each expression 100-5n
Answer:
5(20-n)
Step-by-step explanation:
we have to find a common factor of 100 and 5
a common factor of both is 5 so we divide both terms by 5
100/5= 20
-5n/5= -n
and now we place them together
20-n
and place 5 outside of it like this
5(20-n)
hopes this helps please mark brainliest
Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. Ŷ = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = .2683 Based on the above estimated regression equation, if advertising is $3000, then the point estimate for sales (in dollars) is?
The point estimate for sales when advertising is $3000 is $5412.
Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.
If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:
Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412
So, the required amount is $5412.
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Find the third derivative of the function y=6x-x2/x2
Statements
1. WXYZ is a
parallelogram with
diagonals
XZ and WY
intersecting at
point V.
2. WX // ZY and
XY // WZ
3. ZWXYZYZW
ZWXZ = ZYZX
4.XYZW
5. AWZVAYXV
6. WV YV
7. XZ bisects WY
Given
Reasons
Definition of a parallelogram
Opposite sides of a
parallelogram are congruent
Corresponding parts of
congruent triangles are
congruent
Definition of segment bisector
1. ZX ≅WY; WXYZ is a parallelogram. 1. Given
2. ZY≅ WX 2. The opposite sides of the
parallelogram are ≅
what is parallelogram ?There are 4 different kinds of parallelograms, including 3 unique kinds. The four types are rhombuses, squares, parallelograms, and rectangles.
There are not equal sides on a parallelogram. A parallelogram only has equal sides on its opposite sides.
what is segment bisector ?A line segment bisector splits a line segment into two equally sized pieces. It passes through the segment's halfway.
The following justifications are given for the choice made above:
The following is how the two-column proof is presented.
Statement Motive
1. ZX ≅WY; WXYZ is a parallelogram. 1. Given
2. ZY≅ WX 2. The opposite sides of the parallelogram are ≅
3. YX ≅ YX 3. The reflexive quality
4. Δ ZYX ≅ΔWXY 4. The SSS thm.
5 . ∠ZYX ≅ ∠WXY 5 . CPCTC
6 . m∠ZYX ≅m∠WXY 6. Def. of ≅
7. m∠ZYX + mWXY equal 180° 7. Parallelograms with consecutive s are additional
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Write a polynomial function f of least degree that has rational coefficients, a
leading coefficient of 1, and zeros 3 and 3 – i
Answer:
f(x) = x³ -9x² +28x -30
Step-by-step explanation:
You want a monic polynomial f of least degree with zeros 3 and 3-i.
FactorsFor zero x=a, the polynomial has a factor (x -a). Complex zeros come in conjugate pairs, so another one is 3+i. This means the factored form is ...
f(x) = (x -3)(x -3 +i)(x -3 -i)
f(x) = (x -3)(x² -6x +9 +1) . . . . . combine the two right factors
f(x) = x³ -9x² +28x -30
__
Additional comment
When multiplying polynomials mentally, it can be useful to consider the coefficients of the product terms in order of decreasing powers:
f(x) = (1)x³ +(-3 -6)x² +(10 +(-3)(-6))x +(-3)(10)
where do u get the 150 out of the answer (x+150 (x-10) in the equation x^2+140x-1500?
Answer:
See explanation.
Step-by-step explanation:
Given quadratic:
[tex]x^2+140x-1500[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], first find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
As a = 1, b = 140 and c = -1500, then:
[tex]\implies a \cdot c=1 \cdot -1500=-1500[/tex]
[tex]\implies b=140[/tex]
Therefore, the two numbers are 150 and -10 as:
[tex]\implies 150 \cdot -10 = -1500[/tex]
[tex]\implies 150+(-10)=140[/tex]
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2+(150-10)x-1500[/tex]
Distribute:
[tex]\implies x^2+150x-10x-1500[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+150)-10(x+150)[/tex]
Factor out the common term (x + 150):
[tex]\implies (x+150)(x-10)[/tex]
2. Devonne bought 3 carrots, 4 cucumbers,
6 apples, and 1 bag of crackers. How many
more vegetables does she need if she
wants to have a vegetable for dinner each
night for 2 weeks?
Please help I’m in test
1
Step-by-step explanation:
She has 3 carrots and 4 cucumbers that's a week done and 6 apples so she needs 1 more
if angle poa is a right angle and if measure of angle coa is three times as large as measure angle poc.
The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.
POA is a right angle so it is 90 degrees.
POC +COA = 90 .....(1)
Also, POC is 3 times as large as COA.
Let's take COA, "x"
POC = 3x
Substituting the values in equation (1) as follows:
x + 3x = 90
4x = 90
x= 22.5
Therefore,
COA = 22.5°
POC = 22.5*3 = 67.5°
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Please help!!
What is 9 x (46+70) 5 - 32 (40 - 219) =
9 x (46+70) 5 - 32 (40 - 219) = 11428
Using the BODMAS rule, we solve the brackets first,
9 x (46+70) 5 - 32 (40 - 219)
= 9 x 116 x 5 - 32 x -179
Next, we solve the multiplication signs
9 x 116 x 5 - 32 x -179
= 5520 - ( -5728)
Solving the subtraction sign, we get
5520 - ( -5728)
= 11428
Hence, the answer is 11428
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