When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line? A.) Picture 1 B.) Picture 2 C.) Picture 3 D.) Picture 4
Answers
Option A.) Picture 1 is correct
in the problem inequality y ≤ 2x − 4 is given
Right graph for boundary line has been asked.
Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
For the boundary line
y ≤ 2x − 4 this equation transform into
y= 2x-4
above equation is the boundary condition for the given inequality
so in picture one the the dotted line shows the information of equation
y= 2x-4.
Thus, the boundary condition for inequality y ≤ 2x − 4 is in picture 1
Learn more about inequality here:
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Related Questions
Find the vector x determined by the given coordinate vector [x]B and the given basis B.
B = {[1 -3 1], [-3 8 3],[8 -2 3]}, [x]_B = [-3 -2 3]
a. [9 -13 0]
b. [0 -6 21]
c. [13 -24 -2]
d. [3 -13 16]
Answers
I flip a fair coin 17 times. Answer the following questions:
a. What is the probability of getting 9 heads?
b. What is the probability of getting 2 heads?
c.. What is the probability of getting 1 tail?
d. What is the probability of getting 14 or more heads?
e. What is the probability of getting 17 tails?
Answers
Answer:
A) 0.1855
B) 0.0010376
C) 0.0001297
D) 0.006363
E) 0.000007629
Step-by-step explanation:
In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).
So what are the number of ways the flip of a coin 17 times can come out?
A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.
If we toss thrice, we have 2³ = 8 possible results, etc.
Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.
A) To achieve the probability of getting 9 heads, we will use combination formula;
C(n, k) = n! / (k!(n - k)!)
In this case, n = 17 and k = 9
So,
P(9 heads) = 17! / (9!(17 - 9)!) = 24310
Thus,
P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855
B) Similar to A above;
P(2 heads) = 17! / (2!(17 - 2)!) = 136
Thus,
P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376
C) Similar to A above;
P(1 tail) = 17! / (1!(17 - 1)!) = 17
Thus,
P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297
D) probability of getting 14 or more heads?
Since, there are 17 tosses, this will be;
P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)
P(14 heads) = 17! / (14!(17 - 14)!) = 680
P(15 heads) = 17! / (15!(17 - 15)!) = 136
P(16 heads) = 17! / (16!(17 - 16)!) = 17
P(17 heads) = 17! / (1!(17 - 17)!) = 1
Thus;
P(14 heads in 17 tosses) = 680/131072 = 0.005188
P(15 heads in 17 tosses) = 136/131072 = 0.0010376
P(16 heads in 17 tosses) = 17/131072 = 0.0001297
P(1 head in 17 tosses) = 1/131072 = 0.00000763
P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363
E) Similar to A above;
P(17 tails) = 17! / (17!(17 - 17)!) = 1
Thus,
P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629
Find the values of x and y in these equations. (x + yi) + (4 + 6i) = 7 − 2i (equation A) (x + yi) − (-8 + 11i) = 5 + 9i (equation B)
Answers
Answer:
Step-by-step explanation:
(x+yi)+4+6i=7-2i
x+yi=7-2i-4-6i
x+yi=3-8i
equating real and imaginary parts
x=3,y=-8
B.
x+yi=5+9i+(-8+11i)
x+yi=5+9i-8-11i
x+yi=-3-2i
equating real ,and imaginary parts
x=-3
y=-2
The value of x and y for equation A is
[tex]x=3, y=-8[/tex]
The value of x and y for equation B is
[tex]x=-3 , y=20[/tex]
Given :
[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]
find the value of x and y in the given equation
Lets open the parenthesis and combine like terms
Equate the real and imaginary part to solve for x and y
[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]
The value of x=3 and y=-8
Now we do the same with second equation
[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]
The value of x and y is x=-3 and y=20
Learn more : brainly.com/question/18552411
help with this I don't know how to solve
Answers
Answer:
86.53
Step-by-step explanation:
Area of Triangle Formula: A = 1/2bh
Pythagorean Theorem: a² + b² = c²
Step 1: Draw altitude and label numbers
If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:
3² + b² = 29²
b² = 29² - 3²
b = √832 = h
Step 2: Plug in known variables into area formula:
A = 1/2(√832)(6)
A = 3√832
A = 86.5332
A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a. Write a mathematical model representing the store's constraints.
b. Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is 0.03 and that a displayed chair will be sold is 0.05. Mathematically model each of the following objectives:
1. Maximize the total pieces of furniture displayed.
2. Maximize the total expected number of daily sales.
3. Maximize the total expected daily profit.
Answers
Answer:
a) 50S + 30C ≤ 800
b) 1) MAX = S + C
2) Max = 0.03S + 0.05C
3) Max = 6S + 5C
Step-by-step explanation:
Given:
Total space = 800 square feet
Each sofa = 50 square feet
Each chair = 30 square feet
At least 5 sofas and 5 chairs are to be displayed.
a) Write a mathematical model representing the store's constraints:
Let S denote number of sofas displayed and C denote number of chairs displayed.
The mathematical model will be:
50S + 30C ≤ 800
At least 5 sofas are to be dispayed: S ≥ 5
At least 5 chairs are to be displayed: C ≥ 5
b)
1) Maximize the total pieces of furniture displayed:
S + C = MAX
2) Maximize the total expected number of daily sales:
MAX = 0.03S + 0.05C
3) Maximize the total expected daily profit:
Given:
Profit on sofas = $200
Profit on chairs = $100
Max Expected daily profit =
Max = (200S * 0.03) + (100C * 0.05)
Max = 6S + 5C
What is coefficient of the term of degree of degree 5 in the polynomial below 3x^6+5-x^2+4x^5-9 which one is the right answer A. 3 B. 4 C. 6 D. 5
Answers
Answer:
B. 4
Step-by-step explanation:
We are looking for the coefficient of the term x⁵. When we see it in the polynomial as 4x⁵, our coefficient and answer would then be 4.
An airplane descends during the last hour of it's flight to prepare for landing. It's altitude changes at an average of -0.15 km per minute for those 60 minutes. Write an expression to represent the total change in the airplane's elevation. ( plz answer, will give brainliest )
Answers
Answer:
-.15 km/ minute * 60 minutes
-9 km
Step-by-step explanation:
The rate is -.15 km per minute
We have 60 minutes
distance = rate times time
change in elevation is the same as the distance change
change in elevation = -.15 km/ minute * 60
change in elevation =-9 km
Answer:
(0.15 km/min) * (60 min)
Step-by-step explanation:
We see that the plane descends 0.15 kilometres every minute over the span of 60 minutes.
Use the distance-rate-time formula: d = rt, where d is the distance, r is the rate, and t is the time.
Here, our rate is r = 0.15 km/min and our time is t = 60 minutes. Then the total change in elevation is:
d = rt
d = 0.15 * 60 = 9 km
Note that we disregard the negative sign from -0.15 km/min because the question is asking for the change in elevation. Change is never a negative value.
Hence, the expression will be: 0.15 * 60, which simplifies to 9 km.
~ an aesthetics lover
3
Select the correct answer.
What are the solutions to this equation?
16x² + 9 = 25
Answers
Answer:
Step-by-step explanation:
16x^2 + 9 = 25
16x^2 = 16
x^2 = 1
x = 1, -1
The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree
Answers
Answer:
[tex]\frac{6}{5} =\frac{x}{12}[/tex]
Step-by-step explanation:
Write a proportion in the form:
Height/side= height/side
The side lengths are 5 and 12.
The height (of the 5 side) is 6.
The proportion can be written as:
[tex]\frac{6}{5} =\frac{x}{12}[/tex]
Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X
c) P(X
d) P(X ->a)= 0.89
e) P(X >a)= 0.31
Answers
Answer:
a) 4.8
b) 2.96
c) 4.4
d) 1.44
e) 3.76
Step-by-step explanation:
What we will do is solve point by point, knowing the following:
Fx (x) = P (X <= x) = (x - 1) / 4
a) P (X <-a) = 0.95
Fx (a) = 0.95
(a -1) / 4 = 0.95
a = 1 + 0.95 * 4
a = 4.8
b) P (X <a) = 0.49
Fx (a) = 0.49
(a -1) / 4 = 0.49
a = 1 + 0.49 * 4
a = 2.96
c) P (X <a) = 0.85
Fx (a) = 0.85
(a -1) / 4 = 0.55
a = 1 + 0.85 * 4
a = 4.4
d) P (X> a) = 0.89
P (X <a) = 1 - 0.89 = 0.11
Fx (a) = 0.11
(a -1) / 4 = 0.11
a = 1 + 0.11 * 4
a = 1.44
e) P (X> a) = 0.31
P (X <a) = 1 - 0.31 = 0.69
Fx (a) = 0.69
(a -1) / 4 = 0.69
a = 1 + 0.69 * 4
a = 3.76
Please help! Need Geometry help!!!!!
Answers
Answer:
938 feet
Step-by-step explanation:
b/c every angle of a rectangle is 90° u can u Pythagorean theroem to solve the question
a*a+ b*b=c*c
900*900+264*264=c*c
c=√879,696
c=938feet
Answer:
938 feet
Step-by-step explanation:
Well to solve this we need to use the Pythagorean Theorem,
[tex]a^2 + b^2 = c^2[/tex].
So we have a and b which are 900 and 264,
and we need to find c or the walking distance.
So we plug in 900 and 264 for a and b.
[tex](900)^2 + (264)^2 = c^2[/tex]
So, 900*900 = 810,000
264 * 264 = 69696
810000 + 69696 = 879696
So now we have,
879696 = c^2
To get the c by itself we do,
[tex]\sqrt{879696} = \sqrt{c}[/tex]
= c = 937.921105424
c = 938 rounded to the nearest foot
Thus,
the solution is 938.
Hope this helps :)
Beginning three months from now, you want to be able to withdraw $2,300 each quarter from your back account to cover college expenses over the next four years. If the account pays .45 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years?
Answers
Answer:
$36,450.46
Step-by-step explanation:
The amortization formula can be used to figure this. For quarterly payment A, the principal invested must be P for interest rate r and compounding n times per year for t years.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
2300 = P(0.0045/4)/(1 -(1 +0.0045/4)^(-4·4))
2300 = P·0.06309934
P = 2300/0.06309934 = 36450.46
You need $36,450.46 in your account today so that you can withdraw $2300 quarterly for 4 years.
whats 1/2 + 2/4 - 5/8?
Answers
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Answer:
3/8
Step-by-step explanation:
Look at the denominator:
2, 4, 8. The LCM (Lowest Common Multiple) is 8.
So this equation becomes
4/8+4/8-5/8=3/8
y=x2+3x+1 has how many real roots?
Answers
Answer:
2
Step-by-step explanation:
we will find the discriminant of the equation
d = b^2 - 4ac (here, a = 1 , b = 3 , c = 1. from the general formula: ax^2 + bx + c)
d = 9 - 4
d = 5
since d > 0, the roots are real and different
hence, the both the roots of this equation are equal
help help help help pls
Answers
Hi !!
For f(x) = 3/x + 4 , B is correct.
• f(-3) = 3/(-3) + 4
f(-3) = - 1 + 4
f(-3) = 3
• f(-2) = 3/(-2) + 4
f(-2) = -1,5 + 4
f(-2) = 2,5
• f(1) = 3/(1) + 4
f(1) = 3 + 4
f(1) = 7
• f(2) = 3/(2) + 4
f(2) = 1,5 + 4
f(2) = 5,5
• f(3) = 3/(3) + 4
f(3) = 1 + 4
f(3) = 5
Find the critical value z Subscript alpha divided by 2 that corresponds to the confidence level 90%.
Answers
Answer:
,.........................................................
What is a quadrilateral and give ten examples
Answers
Answer:
A quadralateral is any shape that has 4 sides ...
Step-by-step explanation:
rectangle
square
rhombus
Answer: A quadrilateral is a two dimensional shape(closed) with four sides.
Step-by-step explanation: The sides do not have to be equal.
Square
Rectange
Trapazoid
Diamond
Any four sided shape. They will classify as a quadrilateral as long as two of the shapes are not the same.
calculate find the area f a rectangle measuring 25 feet long by 8 feet wide
Answers
Answer: 200 ft²
Step-by-step explanation:
The area of a rectangle is length times width
So, simply do 25 * 8 = 200
Hey there! :)
Answer:
A = 200 ft².
Step-by-step explanation:
Use the formula A = l × w to determine the area of a rectangle:
A = 25 × 8
Multiply:
A = 200 ft².
An adult has a total of about 22.5 square feet (ft2) of skin. Use the fact that 1 m is approximately equal to 3.281 feet to convert this measurement to square meters (m2). Round your answer to the nearest hundredth. Do not type the units in the space below.
Answers
Answer:
There are about 3.281 * 3.281 = 10.764 square feet in one square meter. Therefore, 22.5 square feet is 22.5 / 10.764 = 2.09 square meters.
During a 5 5 -day period, a florist served a different number of customers at a flower shop each day. The mean number of daily customers served during this period was 17 17 . In the following month, during another 5 5 -day period, the florist served 16 16 customers per day for four of the days, but served 25 25 customers on the fifth day. What is the difference between the mean number of customers the florist served during each of the two five-day periods?
Answers
Answer:
0.8
Step-by-step explanation:
Mean for the first 5 day period = 17
Mean for the second 5 day period = 17.8
Difference 17.8 - 17 = 0.8
The difference between the mean number of customers the florist served during each of the two five-day periods is of 0.8.
-------------------------------
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
-------------------------------
First period:
5 days, mean of 17.
-------------------------------
Second period:
First four days, mean of 16, thus total of [tex]4 \times 16 = 64[/tex]Fifth day, 25 customers.Thus, 64 + 25 = 89 customers in 5 days, and the mean is:
[tex]M = \frac{89}{5} = 17.8[/tex]
-------------------------------
Difference:
17.8 - 17 = 0.8
The difference between the mean number of customers the florist served during each of the two five-day periods is of 0.8.
A similar question is given at https://brainly.com/question/10235056
Arrange in ascending order. 8/13, 2/9,28/29
Answers
Step-by-step explanation:
he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19
Which equation, when solved, gives 8 for the value of x?
A: 5/2x+7/2x=3/4x+14
B: 5/4x-9=3/2x-12
C: 5/4x-2=3/2x-4
D: 5/2x-7=3/4x+14
Answers
Answer:
Step-by-step explanation:
C. 5x/4-2=3x/2-4
5x/4 -2=6x/4-4
+4 +4
5x/4+2=6x/4
-5x/4
2=x/4
*4
x=8
Answer:
your answer is C
Step-by-step explanation:
Construct a confidence interval of the population proportion at the given level of confidence.
x equals =860
n equals =1200
94% confidence
The lower bound of the confidence interval is __?
Answers
Answer:
The lower bound of the confidence interval is 0.6922.
Step-by-step explanation:
We have to calculate a 94% confidence interval for the proportion.
The sample proportion is p=0.7167.
[tex]p=X/n=860/1200=0.7167[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.7167*0.2833}{1200}}\\\\\\ \sigma_p=\sqrt{0.000169}=0.013[/tex]
The critical z-value for a 94% confidence interval is z=1.8808.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.8808 \cdot 0.013=0.0245[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.7167-0.0245=0.6922\\\\UL=p+z \cdot \sigma_p = 0.7167+0.0245=0.7412[/tex]
The 94% confidence interval for the population proportion is (0.6922, 0.7412).
Please Help! Select the correct answer. Simon used these steps to solve an equation:
Answers
Answer:
A.
Step-by-step explanation:
From Step 3 to Step 4, Simon added -42 to both sides.
This is the addition property of equality: as long as you add the same thing to both sides, the equation remains equal.
A.
Is (0,-2) a solution of 3x - y = 2?
Answers
Answer:
yes, (0,-2) is the answer when graphing this equation.
Step-by-step explanation:
Answer:
yes.
Step-by-step explanation:
A company has developed a new type of light bulb, and wants to estimate its mean
lifetime. A simple random sample of 12 bulbs had a sample mean lifetime of 665
hours with a sample standard deviation of 59 hours. It is reasonable to believe that
the population is approximately normal. Find the lower bound of the 95% confidence
interval for the population mean lifetime of all bulbs manufactured by this new
process.
Round to the nearest integer. Write only a number as your answer. Do not write any
units.
Answers
Answer:
628
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 12 - 1 = 11
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.2\frac{59}{\sqrt{12}} = 37[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 665 - 37 = 628 hours.
The answer is 628
Box A contains 5green and 7 red balls. Box B contains 3green, 3 red and 6 yellow balls. A box is sleeted at random and a ball is drawn at random from it. What is the probability that the drawn ball is green?
Answers
Answer:
5/48Step-by-step explanation:
Given
the sample space for box A
green balls = 5
red balls= 7
sample size= 5+7= 12
the sample space for box B
green balls = 3
red balls= 3
yellow balls= 6
sample size= 3+3+6= 12
The probability of drawing a green ball from box A= 5/12
The probability of drawing a green ball from box B= 3/12= 1/4
Therefore the probability of picking a green ball from either of the boxes at random is =[tex]=\frac{5}{12} *\frac{1}{4}[/tex][tex]=\frac{5}{48}[/tex]
Which inequality is represented by the graph?
Answers
Answer:
y ≤ 2/5x - .5
Step-by-step explanation:
Well it is a solid line with it shaded down meaning the inequality starts with
y ≤,
And by look at the y axis we can tell that the line crosses the y axis at -.5 which is the y intercept.
And by looking at the line we can tell the slope is 2/5.
Hence, the inequality is y ≤ 2/5x - .5
HELP PLEASE!!!! I NEED HELP ASAP Which statement best describes the expression 3 + y ÷ 2? The quotient of 2 and the sum of 3 and y The quotient of the sum of 3 and y, and 2 The sum of 3 and the quotient of 2 and y The sum of 3 and the quotient of y and 2
Answers
Answer:
I believe it is D
Answer:
The sum of 3 and the quotient of y and 2.
Step-by-step explanation:
The order of operations requires that you evaluate the expression ...
3 + y ÷ 2
by first performing the division, then the addition. So, the addition gives you the sum of 3 and a quotient, because the quotient must be evaluated first.
The quotient is of y and 2 (not 2 and y), because the wording "the quotient of a and b" is always interpreted to mean a÷b.
So, the expression can be described as ...
the sum of 3 and the quotient of y and 2.
I NEED HELP ASAP,THANKS! :)
Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour? Show work.
Answers
Answer:
$1170
Step-by-step explanation:
Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...
x ≥ 1y ≥ 6x +y ≤ 30And the objective function we want to maximize is ...
p = 40x +35y
__
I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.
Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...
24 economy seats and 6 deluxe seats
The corresponding profit will be ...
24(40) +6(35) = 1170
The maximum profit from one tour is $1170.