Answer:
[tex]66\dfrac{2}{3}\%[/tex]
Step-by-step explanation:
Given,
The number of cartons = k,
Time taken by machine a = 8 hours,
So, the number of cartons made by machine a in one hour
= [tex]\frac{\text{Cartons in 8 hours}}{8}[/tex]
= [tex]\frac{k}{8}[/tex]
Time taken by machine b = 4 hours ,
So, the number of cartons made by machine b in one hour
= [tex]\frac{k}{4}[/tex]
Total cartons made in 1 hour = [tex]\frac{k}{8}+\frac{k}{4}[/tex]
[tex]=\frac{k+2k}{8}[/tex]
[tex]=\frac{3k}{8}[/tex]
∵ for the whole number value of k,
[tex]\frac{k}{4}>\frac{k}{8}[/tex]
i.e. machine b is faster,
Also, the percent of the cartons were sealed by the machine b
[tex]=\frac{\text{Cartons made in 1 hour by machine b}}{\text{Total cartons}}\times 100[/tex]
[tex]=\frac{\frac{k}{4}}{\frac{3k}{8}}\times 100[/tex]
[tex]=\frac{2}{3}\times 100[/tex]
[tex]=\frac{200}{3}[/tex]
[tex]=66\dfrac{2}{3}\%[/tex]
Hence, OPTION D is correct.
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
a 3
b 4
c 6
d 7
Answer: A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
a 3
b 4
c 6
d 7
Step-by-step explanation:
3lbs of Cashews
Answer:
Step-by-step explanation:
4x+(10-x)*6.5 =4.75*10
4x+65-6.5x=47.5
6.5 x-4 x=65-47.5
2.5 x=17.5
x=7
peanuts=7 -pound
cashews=10-7=3 -pound
Given the functions f(x)=x-7 and g(x)=x^2+1, evaluate (f*g)(-1).
I keep getting -16, but that's not an answer choice...?
For this case we have the following functions:
[tex]f (x) = x-7\\g (x) = x ^ 2 + 1[/tex]
We must find [tex](f * g) (x)[/tex]. By definition we have to:
[tex](f * g) (x) = f (x) * g (x)[/tex]
So:
[tex](f*g)(x)=(x-7)(x^2+1)[/tex]
We apply distributive property:
[tex](f * g) (x) = x ^ 3 + x-7x ^ 2-7\\(f * g) (x) = x ^ 3-7x ^ 2 + x-7[/tex]
We evaluate at [tex]x = -1:[/tex]
[tex](f * g) (- 1) = (- 1) ^ 3-7 (-1) ^ 2 + (- 1) -7\\(f * g) (- 1) = - 1-7 (1) -1-7\\(f * g) (- 1) = - 1-7-1-7[/tex]
Equal signs are added and the same sign is placed:
[tex](f * g) (- 1) = - 16[/tex]
Answer:
[tex](f * g) (- 1) = - 16[/tex]
Need help asap thanks y'all
Answer:
what do you need help with?
Step-by-step explanation:
Answer:
It would be 15 cm. because if the triangles are similar then BC = EF
Please mark me the brainliest!!!An investment of $25,000 pays 7% (simple) annual interest. What will be the total value of the investment in 10 years? Give your answer in dollars to the nearest dollar.
Answer: the total value of the investment in 10 years is $42500
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T =10 years
P = $25000
R = 7%
Therefore
I = (25000 × 7 × 10)/100
I = 1750000/100
I = $17500
Therefore, the total value of the investment in 10 years would be
25000 + 17500 = $42500
James Smith and Bill Ross purchased a property together for their business venture with stated proportionate interest of 1/3 and 2/3 respectively without the right of survivorship. Each of them wants his share to be inherited by his wife. They are a partnership and not a corporation. James and Bill most likely took title as:_________
A) joint tenants.
B) tenants in common.
C) in severalty.
D) a general partnership.
Answer:
B) tenants in common.
Explanation:
There were two men, first was James Smith, and second was Bill Ross who bought a property mutually for their business venture by declared proportionate interest of 1/3 as well as 2/3 sequentially without the right regarding survivorship. Both of them want their shares to be acquired by their spouses'. Both hold a partnership but not a company. James, as well as Bill, most likely took the title as tenants in common. Because tenants in common possess versatility in whence they divide control as well as assign the rights concerning survivorship. Joint tenants, on the different hand, keep the property in similar shares while a common partnership is a business unit serving separate sharers. Severalty, as asserted beforehand, is individual ownership.
I need help, I don’t understand how to do this
Answer:
x = 45.
Step-by-step explanation:
As the triangles are similar the corresponding sides are in the same proportion. Therefore:
18 / 2 = x / 5
x / 5 = 9
x = 5*9
x = 45.
PLZZ HELP Factor 75t2 + 12.
3(25t 2 + 4)
3(25t 2 - 4)
3(5t + 2) 2
Answer:
The answer to your question is 3(25t² - 4)
Step-by-step explanation:
To factor this binomial, just look for the common factor between both terms.
75t² + 12
75 12 2
75 6 2
75 3 3
25 3 3
25 1 5
5 1 5
1
The greatest common factor is 3, that is the common factor.
Now, factor the polynomial
3(25t² - 4)
Answer: 3(25t 2 + 4)
Step-by-step explanation:
In an analysis of the environmental impact of a community's motor vehicle use, which of the following is best represented by "a" in the I = P x A x T equation?
a) energy efficiency of motor vehicles.
b) the number of cars owned by each household.
c) average family size.
d) the average daily commute by motor vehicles.
Answer:
The answer is B.
Step-by-step explanation:
The variable A in the I=PAT equation stands for affluence. It represents the average consumption of each person in the population. As the consumption of each person increases, the total environmental impact increases as well. The choice B is the best choice that represents average consumption of each person in the population.
If you are dealt 5 cards at random from a standard deck of playing cards, what is the probability that at most 4 of them are spades?
Answer:
Step-by-step explanation:
No of ways in which 5 cards are chosen is [tex]N=^{52}C_5[/tex]
No of ways in which at most 4 cards are spades [tex]N_0=[/tex]Total ways-5 spades
[tex]=^{52}C_5-^{13}C_5[/tex]
Probability that at most 4 cards are spade [tex]P=\frac{N_0}{N}[/tex]
[tex]P=\frac{^{52}C_5-^{13}C_5}{^{52}C_5}[/tex]
[tex]P=\frac{2598960-1287}{2598960}[/tex]
[tex]P=\frac{2597673}{2598960}=0.9995[/tex]
The probability of being dealt 5 cards with at most 4 of them being spades from a standard deck is approximately 0.9995.
To determine the probability of being dealt 5 random cards with at most 4 of them being spades from a standard deck of 52 cards, follow these steps:
1. Understanding the total number of possible hands
The total number of ways to choose 5 cards from a deck of 52 is given by the combination formula C(52, 5):⇒ C(52, 5) = 2,598,960
2. Calculating the number of desired outcomes
We need to find the number of ways to get hands with 0, 1, 2, 3, or 4 spades.0 Spades: C(13, 0) × C(39, 5)
1 Spade: C(13, 1) × C(39, 4)
2 Spades: C(13, 2) × C(39, 3)
3 Spades: C(13, 3) × C(39, 2)
4 Spades: C(13, 4) × C(39, 1)
Using the combination formula C(n, k) = n! ÷ (k!(n - k)!), we calculate each:0 Spades:
⇒ 1 × 575,757 = 575,757
1 Spade:
⇒ 13 × 82,251 = 1,069,263
2 Spades:
⇒ 78 × 9,139 = 712,842
3 Spades:
⇒ 286 × 741 = 211,926
4 Spades:
⇒ 715 × 39 = 27,885
The total number of favorable outcomes is the sum of these values:⇒ 575,757 + 1,069,263 + 712,842 + 211,926 + 27,885 = 2,597,673
3. Calculating the probability
The probability is found by dividing the number of favorable outcomes by the total number of possible hands:⇒ P(at most 4 spades) = 2,597,673 ÷ 2,598,960
≈ 0.9995
(50 pts!) Help pls
Find the value of x
Answer:
x = 3.5.
Step-by-step explanation:
This is an equilateral triangle ( as all angles = 60 degrees) so all 3 sides are of equal length.
Thus 2x - 3 = 4
2x = 7
x = 3.5.
Answer:
hi its me
Step-by-step explanation:
Lie detectors Refer to Exercise 82. Let Y = the number of people who the lie detector says are telling the truth.
(a) Find P(Y ≥ 10). How is this related to P(X ≤ 2)? Explain.
(b) Calculate μX and σY. How do they compare with μX and σY? Explain why this makes sense.
Answer:
a) [tex] P(Y\geq 10) = PX \leq 2) = 0.558[/tex]
b) [tex] E(X) = \mu_X = np = 12*0.2 = 2.4[/tex]
[tex] \sigma_X = \sqrt{np(1-p)}=\sqrt{12*0.2*(1-0.2)}=1.386[/tex]
[tex] E(Y) = \mu_Y = np = 12*0.8 = 9.6[/tex]
[tex] \sigma_Y = \sqrt{np(1-p)}=\sqrt{12*0.8*(1-0.8)}=1.386[/tex]
For this case the expected value of people lying is 2.4 and the complement is 9.6 and that makes sense since we have a total of 12 poeple.
And the deviation for both variables are the same.
Step-by-step explanation:
Assuming this previous info : "A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X = the number of people who the lie detector says are being deceptive"
For this case the distribution of X is binomial [tex] X \sim N(n=12, p=0.2)
And we define the new random variable Y="the number of people who the lie detector says are telling the truth" so as we can see y is the oppose of the random variable X, and the distribution for Y would be given by:
[tex] Y \sim Bin (n=12,p=1-0.2=0.8)[/tex]
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
For this case we want to find this probability:
[tex] P(Y \geq 10) = P(Y=10)+P(Y=11) +P(Y=12)[/tex]
And if we find the individual probabilites we got:
[tex]P(Y=10)=(12C10)(0.8)^{10} (1-0.8)^{12-10}=0.283[/tex]
[tex]P(Y=11)=(12C11)(0.8)^{11} (1-0.8)^{12-11}=0.206[/tex]
[tex]P(Y=12)=(12C12)(0.8)^{12} (1-0.8)^{12-12}=0.069[/tex]
And if we replace we got:
[tex] P(Y \geq 10) =0.283+0.206+0.069=0.558[/tex]
And for this case if we find [tex] P(X\leq 2)=P(X=0) +P(X=1)+P(X=2)[/tex] for the individual probabilites we got:
[tex]P(X=0)=(12C0)(0.2)^0 (1-0.2)^{12-0}=0.069[/tex]
[tex]P(X=1)=(12C1)(0.2)^1 (1-0.2)^{12-1}=0.206[/tex]
[tex]P(X=2)=(12C2)(0.2)^2 (1-0.2)^{12-2}=0.283[/tex]
[tex] P(X\leq 2)=0.283+0.206+0.069=0.558[/tex]
So as we can see we have [tex] P(Y\geq 10) = P(X \leq 2) = 0.558[/tex]
Part b
Random variable X
For this case the expected value is given by:
[tex] E(X) = \mu_X = np = 12*0.2 = 2.4[/tex]
And the deviation is given by:
[tex] \sigma_X = \sqrt{np(1-p)}=\sqrt{12*0.2*(1-0.2)}=1.386[/tex]
Random variable Y
For this case the expected value is given by:
[tex] E(Y) = \mu_Y = np = 12*0.8 = 9.6[/tex]
And the deviation is given by:
[tex] \sigma_Y = \sqrt{np(1-p)}=\sqrt{12*0.8*(1-0.8)}=1.386[/tex]
For this case the expected value of people lying is 2.4 and the complement is 9.6 and that makes sense since we have a total of 12 poeple.
And the deviation for both variables are the same.
Answer:
dfbustos is correct! But I wanted to add a bit more to part b, specifically why the standard deviation makes sense.
Step-by-step explanation:
Y = # of people who the lie detector says are telling the truth.
X = # of people who the lie detector says are telling being deceptive.
This leads to the following conclusion:
Y = 12 - X
(We are given that 12 people answered.)
Because the standard deviation is not affected by adding or subtracting a constant, it makes sense for the σY = σX.
In a collection of toys, 1/2 are red, 1/2 are waterproof, and 1/3 are cool. 1/4 are red and waterproof. 1/6 are red and cool. 1/6 are waterproof and cool. 1/6 are neither red, waterproof, nor cool. Each toy has an equal chance of being selected.Draw an area diagram to represent these events.
Answer:
only red = 1/12, only water proof = 1/12 , only cool = nil we assume nil for toys with three collections( cool, red, waterproof) as it was not stated.
11/6 are neither red, water proof and cool.
Step-by-step explanation:
outside the circles contain probability of neither red, cool and water proof. where the circles intersect shows probability of both either red and cool, water proof and cool and water proof and red etc. where all the circles intersect if for the three combinations which is nill. Attached is the diagram
Answer:
The answer representation is attached below
Step-by-step explanation:
This is a representation on a diagram.
n(R) = Number of red toys
n(WP) Number of water proof toys
n(C) = Number of cool toys
n(R∩WP) = Number of red and waterproof
n(R∩C) = Number of red and cool
n(WP∩C) = Number of waterproof and cool
n(R'∩WP∩C) = Neither red, waterproof nor cool
From the image as depicted on a venn diagram, each part is represented and filled ont the diagram, the small circle space filled represent the information given in the question.
First, use the "completing the square" process to write this equation in the form (x + D)² = E. x² - 8 x + 12 = 0 is equivalent to:
Answer:
D = -4
E = 2
Step-by-step explanation:
The procedure for completing the square method is given as:
x2 + bx + c = 0
x2 + bx = -c
x2 + bx + (b/2)2 = -c + (b/2)2
Aolving the LHS simultaneously,
(x + b)2 = -c + (b/2)2
Find the square root of both sides,
(x + b) = sqrt(-c + (b/2)2)
So for the equation, x2 - 8x + 12
x2 - 8x = -12
x2 - 8x + 16 = -12 + 16
(x - 4)2 = 4
So square root both sides,
(x - 4) = 2
Comparing this to the equation given,
(x - D) = E;
D = -4
E = 2
The cup on the 9th hole of a golf course is located dead center in the middle of a circular green that is 70 feet in diameter. Your ball is located as in the picture below: The ball follows a straight line path and exits the green at the right-most edge. Assume the ball travels a constant rate of 10 ft/sec.
(a) Where does the ball enter the green?(b) When does the ball enter the green?(c) How long does the ball spend inside the green?(d) Where is the ball located when it is closest to the cup and when does this occur.The ball follows a straight
Answer:
a. The ball enters the green at Q (-13.46, -32.31)
b. 3.189s
c. 5.824s
d. Closest point = (10.77, -16.15), it occurs 6.102s after the ball starts its journey
Step-by-step explanation:
he rightmost edge is taken as the right end of the horizontal diameter
Coordinates of the hole at H:(0,0)
Coordinates of the ball B:(-40,-50)
Coordinates of the point the ball exits green P:(35,0)
So, the line joining B and P is given by
Looking for the gradient of the line B P we have
(x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50))
= 75/50=3/2
The line equation therefore = (y-(-50))/(x-(-50)) = 2/3
(y + 50)/(x+40) =2/3
y+50 = 2/3 (x+40)
The equation of a circle is given by
x^2+y^2 = 35^2
solving the two equations we have
x = ((3y+150)/2)-40 = 1.5y-35
Substituting the value of x into the above equations we have (1.5y-35)2 + y2 = 352
3.25×y2+105×y = 0
From where we have y×(3.25×y + 105) = 0
From where y = 0 or y = -105/3.25 = -32.31m
Also x = 35 or x = -13.46
The line intersects the circle at
Q:(-13.46,-32.31) and P:(35,0)
a. The ball enters the green at Q (-13.46, -32.31)
b. The ball enters the green after (length BQ)/Velocity
Where length BQ is given as
√((-13.46-(-40))2+(-32.31-(-50))2) = √(26.532+17.692) = 31.89ft
The ball enters after 31.89ft/10ft/s or 3.189s
c. To find out how long the ball spends inside the green we have
Q:(-13.46,-32.31) and P:(35,0)
Length QP2 = (-13.46-(35))2 + (-32.31- 0)2 = 3392.31 = 58.24m
Time spent in the green = 58.24/10 = 5.824s
d. The ball is closest to the cup at the point when the perpendicular from the cup intersects the line PQ
and this is at the center of the line PQ hence the locus of the point is
((-13.46 + (35-(-13.46))/2), (-32.31+(0-(-32.31))/2) = (10.77, -16.15)
This occurs at (√( (10.77-(-40))2 + (-16.15(-50))2))/10 = 61.02ft/10ft/s = 6.102s after the ball starts its journey
As the cup of the 9th hole in the golf course is located as the dead in the center of the milled green circular shape that is 70 feet. A ball follows the straight-line path and exists at the fright most edge.
The rightmost edge is taken as per the right end of horizontal diameter. The coordinates of the hole at H: (0,0) B:(-40,-50) ball exits green P:(35,0) The line joining B and P is given by (x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50)) = 75/50=3/2. Similarly, The ball enters the green at Q (-13.46, -32.31) , b. 3.189s , c. 5.824s, d. Closest point = (10.77, -16.15), it occurs 6.102s after the ball starts its journey.Learn more about the hole of a golf course is located dead center in the middle.
brainly.com/question/2553954.
Which graph represents the system of equations?
y=2x
y=x^2+1
Option D is the correct answer.
Step-by-step explanation:
The given system of equations are [tex]y=2x[/tex] and [tex]y=x^{2} +1[/tex]
To plot the equations in the graph, if we know the values of x and y coordinates.
To plot the equation [tex]y=2x[/tex] in the graph, let us substitute the value for x to find the value of y-coordinate.
For, [tex]x=0[/tex] ⇒ [tex]y=0[/tex]
For, [tex]x=1[/tex] ⇒ [tex]y=2[/tex]
For, [tex]x=2[/tex] ⇒ [tex]y=4[/tex]
Similarly, to plot the equation [tex]y=x^{2} +1[/tex], let us substitute the value for x,
For, [tex]x=0[/tex] ⇒ [tex]y=1[/tex]
For, [tex]x=1[/tex] ⇒ [tex]y=2[/tex]
For, [tex]x=2[/tex] ⇒ [tex]y=5[/tex]
These values are plotted in the graph. The graph that represents the system of equations is attached below.
Thus, the correct answer is option D.
Answer:
d
Step-by-step explanation:
what is the midpoint of the line segment
Answer:
The answer to your question is (-1, -1)
Step-by-step explanation:
Data
A (1, -6)
B (-3, 4)
Formula
Xm = [tex]\frac{x1 + x2}{2}[/tex]
Ym = [tex]\frac{y1 + y2}{2}[/tex]
Process
1.- Substitute the values in the formula
x1 = 1 x2 = -3
Xm = [tex]\frac{1 - 3}{2} = \frac{-2}{2} = -1[/tex]
y1 = -6 y2 = 4
Ym = [tex]\frac{-6 + 4}{2} = \frac{-2}{2} = -1[/tex]
2.- The midpoint is (-1, -1)
Think of each segment in the diagram as part of a line. Which line or plane appears to fit in the description? (This is a rectangular prism - all angles in the corner are right angles.
Part A
Answer: Line FGThis line contains point G (as an endpoint) and it runs perpendicular to line FE. This line is in the bottom face of the rectangular prism. This line is also in the front face as well.
===================================================
Part B
Answer: Line ABAB is parallel to CD, GH and FE.
===================================================
Part C
Answers: line AB and line AGSkew lines are lines that aren't parallel nor perpendicular nor intersecting. Skew lines can only be found in 3D space (not 2D space). Think of a line on the ground running from north to south. If we had a straight wire that did not bend at all run from north to south, then we would have two parallel lines. However, if we aim the wire to go from east to west, then the line on the ground and the wire will be skew lines. The line on the ground and the wire line do not intersect. The same story happens with AB and FE, along with AB and AG.
===================================================
Part D
Answer: Plane GCHThe front face is plane AGF. We simply locate the three points A, G, F and note this is the front face. The back face is parallel to the front face. This face is plane GCH, and it contains point C.
note: we could say "plane AGFD" but we only need 3 points at minimum to uniquely determine a plane.
Any flat surface (plane) of a rectangular prism fits the description as they each have corners making right angles. Each edge of these faces can be seen as a line segment that would form a straight line if extended.
Explanation:
In a rectangular prism, each segment can be thought of as a part of a line. The plane that fits this description could be any of the flat surfaces of the prism, as they have each corner making a right angle. For example, consider you have a box (a rectangular prism). The front face of the box forms a plane, and each edge of this face can be seen as a line segment. Similarly, the top face of the box also forms a plane with all right angles. The edges of each face are line segments that are part of a straight line if extended. Therefore, all faces (planes) and edges (line segments) of the rectangular prism fit the description.
Learn more about Rectangular Prism here:https://brainly.com/question/18124581
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Important Characteristics Quiz The probability of success in each of the 58 identical engine tests is p = 0.92. What is the mean of this binomial distribution?
Answer: The mean of this binomial distribution is 53.36.
Step-by-step explanation:
We know that , the mean of this binomial distribution is given by :_
[tex]\mu = np[/tex]
, where n = sample size or the number of possible trials .
p = probability of getting success in each trial.
We are given that , the probability of success in each of the 58 identical engine tests is p = 0.92.
i.e. n= 58
p=0.92
Then, the mean of this binomial distribution = [tex]58\times0.92=53.36[/tex]
Hence , the mean of this binomial distribution is 53.36.
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 25002500 grams and a standard deviation of 800800 grams while babies born after a gestation period of 40 weeks have a mean weight of 27002700 grams and a standard deviation of 375375 grams. If a 3232-week gestation period baby weighs 20252025 grams and a 4040-week gestation period baby weighs 22252225 grams, find the corresponding z-scores. Which baby weighs lessless relative to the gestation period?
Answer:
32-35 Week case
[tex]z = \frac{2025-2500}{800}=-0.594[/tex]
40 week case
[tex]z = \frac{2225-2700}{375}=-1.27[/tex]
For this case since the z score is lower (-1.27<-0.574) for the baby of 40 week this one would be the baby that weighs less relative to the gestation period
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
32-35 Week case
Let X the random variable that represent the weight, and for this case we know the distribution for X is given by:
[tex]X \sim N(2500,800)[/tex]
Where [tex]\mu=2500[/tex] and [tex]\sigma=800[/tex]
The z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And if w replace for the value of x=2025 we got:
[tex]z = \frac{2025-2500}{800}=-0.594[/tex]
40 week case
Let X the random variable that represent the weight, and for this case we know the distribution for X is given by:
[tex]X \sim N(2700,375)[/tex]
Where [tex]\mu=2700[/tex] and [tex]\sigma=375[/tex]
The z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And if w replace for the value of x=2225 we got:
[tex]z = \frac{2225-2700}{375}=-1.27[/tex]
For this case since the z score is lower (-1.27<-0.574) for the baby of 40 week this one would be the baby that weighs less relative to the gestation period
Which linear inequality is represented by the graph?
A. y ≤ 1/2x + 2
B. y ≥ 1/2x + 2
C. y ≤ 1/3x + 2
D. y ≥ 1/3x + 2
Answer:
c i did the test
Step-by-step explanation:
Travis lives 195 miles from Dallas on a normal trip it takes and 180 minutes to make the drive what is Travis's average rate of speed in miles per hour
Answer:
Step-by-step explanation:
Distance covered= 195miles
Time = 180min = 3hours
Speed = distance/time
Speed = 195/3
Speed = 65miles/hour
Travis is driving at an average rate of speed of 65 miles per hour.
What is Speed?Speed in mathematics is one of the measurable quantity which is defined as the ratio of the distance covered by an object to the time taken to cover that distance.
Or in other words, speed of an object can be defined as the rate of change of the position of that object in any direction.
Speed is a scalar quantity, as it only has magnitude and no direction.
Speed can be calculated by the formula,
Speed = Distance / Time
Distance Travis travelled = 195 miles
Time taken to travel that distance = 180 minutes
= 180 / 60 hours
= 3 hours.
Speed = 195 / 3
= 65 miles per hour
Hence the average rate of speed of Travis in the drive is 65 miles per hour.
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(35 Points)
Evaluate ƒ(x) when x = 6.
The value of the function is 6
Step-by-step explanation:
The function that we have in this problem is
[tex]f(x)=\left \{ {{3x^2+1}, -4<x<6 \atop {6}, 6\leq x <9} \right.[/tex]
This means that:
when x is between -4 (excluded) and 6 (excluded), the value of the function is [tex]3x^1+2[/tex]
when x is between 6 (included) and 9 (excluded), the value of the function is 6
In this problem, we are asked to evaluate f(x) when x = 6. Therefore, we are in the second case: therefore, the value of the function is 6,
[tex]f(x)=6[/tex]
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Answer:
the value is 6
Step-by-step explanation:
Which of the following is a polynomial function in factored form with zeros at –6, –2, and 3? a.f(x) = (x + 6)(x + 2)(x – 3) b.f(x) = x3 + 5x2 – 12x – 36 c.f(x) = (x – 6)(x – 2)(x + 3) d.f(x) = x3 – 5x2 – 12x + 36
Answer:
a) f(x) = (x + 6)(x + 2)(x – 3)
b) [tex]f(x) = x^3 + 5x^2 - 12x - 36[/tex]
Step-by-step explanation:
We have to find the polynomial with zeroes as -6, -2, and 3.
Roots are those values of x for which the polynomial is zero.
a) f(x) = (x + 6)(x + 2)(x – 3)
[tex]f(x) = (x + 6)(x + 2)(x -3)=0\\\Rightarrow x+6 = 0, x+2 = 0, x-3 = 0\\\Rightarrow x = -6,x = -2, x = 3[/tex]
b)
[tex]f(x) = x^3 + 5x^2 - 12x - 36 \\\text{It can be factored as}\\f(x) = (x+6)(x-3)(x+2) = 0\\\Rightarrow (x+6)=0,(x-3)=0,(x+2)=0\\\Rightarrow x = -6, x = 3, x = -2[/tex]
c) f(x) = (x – 6)(x – 2)(x + 3)
[tex]f(x) = (x - 6)(x - 2)(x + 3) =0\\\Rightarrow (x -6)(x -2)(x + 3) = 0\\\Rightarrow (x -6)=0,(x -2)=0,(x + 3)=0\\\Rightarrow x = 6, x = 2, x = -3[/tex]
d)
[tex]f(x) = x^3 - 5x^2 - 12x + 36\\f(x) = (x-2)(x+3)(x-6)=0\\\Rightarrow (x-2) = 0, (x+3)=0,(x-6)=0\\\Rightarrow x =2, x = -3, x = 6[/tex]
If a tadalafil 10mg/tab has a typical half life of 17.5 hours, how long will it take until the blood concentration of this dosage falls to 25% of its initial strength?
A. 70 Hours.B. 52.5 Hours.C. 35 Hours.D. 17.5 Hours.
Answer:
Step-by-step explanation:
Final answer:
It takes 35 hours for the blood concentration of tadalafil to fall to 25% of its initial strength, given a half-life of 17.5 hours.
Explanation:
We can determine how long it takes for the blood concentration of a drug to fall to a certain percentage of its initial strength by knowing the drug's half-life. In this case, a half-life is the time required for the concentration of the drug to reduce to half its original value. For tadalafil 10mg/tab with a half-life of 17.5 hours, we want to calculate when the concentration falls to 25% of its initial strength.
To reach 25% of the original concentration, the drug needs to go through two half-lives (each half-life reduces the concentration by half):
After 1 half-life (17.5 hours), the concentration will be at 50%.After 2 half-lives (17.5 hours × 2 = 35 hours), the concentration will be at 25%.Therefore, it will take 35 hours for the blood concentration of tadalafil to fall to 25% of its initial dosage, which corresponds to Option C.
A small business owner has created a linear regression model to predict the number of new customers who will visit a shop based on the number of times the owner has an advertisement played on the radio. What is the explanatory variable and what is the response variable?
Answer: Explanatory variable = " number of times the owner has an advertisement played on the radio"
Response variable = "number of new customers who will visit a shop"
Step-by-step explanation:
An explanatory variable is a kind of independent variable that can be manipulated by researcher in a study to check the response of the response variable.In the given situation , the business owner is predicting the number of new customers who will visit a shop based on the number of times the owner has an advertisement played on the radio.
Here , He is controlling the advertisement played on the radio to see the response of customers.
Therefore ,
Explanatory variable = " number of times the owner has an advertisement played on the radio"
Response variable = "number of new customers who will visit a shop"
In the given linear regression model, the 'number of times an advertisement is played on the radio' is the explanatory variable, and the 'number of new customers who will visit the shop' is the response variable.
Explanation:In a linear regression model, there are two types of variables: the explanatory variable and the response variable. In this particular context of predicting the number of new customers who will visit a shop based on the number of times an advertisement is played on the radio, the explanatory variable is the 'number of times the advertisement is played on the radio'. This is because it is the variable that we are changing in hopes of influencing the outcome.
The response variable, on the other hand, is the 'number of new customers who will visit the shop'. This is the outcome we are interested in predicting or explaining.
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When planning his crops, Farmer Joe knows that his 5 acres can support corn and strawberries. He wants to make $5,500 from his crops. He can make $1,000 per acre of corn (the variable c) and $1,500 per acre of strawberries (the variable s). Which equation below would be a constraint in his system of equations?a. c + s = 5.
b. c − s = 5.c. 1,500c + 1,000s = 5,500.d. 1,500s − 1,000c = 5,500.
Answer:
Option a) c + s = 5.
Step-by-step explanation:
Let variable c represent acre of corn crop and variable s represent acre of strawberries crop.
5 acres can support corn and strawberries.
Thus, this can be expressed with the help of equation.
[tex]c + s = 5[/tex]
Farmer wants to make $5,500 from his crops.
He can make $1,000 per acre of corn and $1,500 per acre of strawberries.
This can be written as:
[tex]1000c + 1500s = 5500[/tex]
We have to find the constraint for the given system.
A constraint is something that limits or controls what we want to do. Here, the amount of land is limited and act as a constraint for the given situation.
Thus, the constraint for the given system is
Option a) c + s = 5.
Let the independent and dependent variables of a line be x and y, respectively. Find the equation of the line with the given description.
Answer:
[tex]y = mx+b[/tex]
[tex] m =\frac{y_2 -y_2}{x_2 -x_1}[/tex]
[tex] b = y_1 -m x_1[/tex]
Or equivalently:
[tex] b = y_2 - m x_2[/tex]
Step-by-step explanation:
If we are assuming that we have:
x independent variable
y dependent variable
And we want to find an equation of the line, we have the following general expression:
[tex]y = mx+b[/tex]
Where m represent the slope and b the y intercept. The general formula for the slope is given by:
[tex] m =\frac{y_2 -y_2}{x_2 -x_1}[/tex]
Where [tex] (x_1,y_1) , (x_2,y_2)[/tex] are the minimum required points in order to estimate the slope.
In order to find the y intercept we just need to use one of the points selected [tex] (x_1,y_1) , (x_2,y_2)[/tex] and we can solve for b like this:
[tex] b = y_1 -m x_1[/tex]
Or equivalently:
[tex] b = y_2 - m x_2[/tex]
An oak tree is 1.5×103 centimeters tall. Which unit of measurement is most appropriate to measure this height? kilometers feet inches millimeters
Answer:
I think the correct answer is feet
Answer:
Feet
Step-by-step explanation:
On a box of cookie mix, the instructions say that it will take no longer than 30 minutes to make the cookies. It takes t minutes to make the cookies. What inequality represents the scenario
Answer:
The inequality represents the scenario is [tex]t\leq 30[/tex].
Step-by-step explanation:
Given:
Number of minutes used to make cookie written on box = 30 minutes.
Number of minutes used to make cookies = [tex]t \ minutes[/tex]
We need to write inequality represents the scenario
Solution:
We can say that;
Number of minutes used to make cookies should be less than or equal to Number of minutes used to make cookie written on box.
framing in equation form we get;
[tex]t\leq 30[/tex]
Hence The inequality represents the scenario is [tex]t\leq 30[/tex].
The inequality representing the scenario where cookie mix instructions indicate a maximum of 30 minutes to make cookies is t ≤ 30.
The inequality that represents the scenario where the cookie mix instructions say it will take no longer than 30 minutes to make cookies is t ≤ 30. This inequality means that the time taken to make the cookies, represented by t, is less than or equal to 30 minutes. If we consider that one option is to bake the cookies for 10 minutes, that fits well within the constraint given by the inequality since 10 is less than 30.
The graph of f passes through left parenthesis negative 4 comma 3 right parenthesis(−4,3) and is perpendicular to the line that has an x-intercept of 22 and a y-intercept of negative 4−4.
Answer:
The answer to your question is y = -11/2x - 19
Step-by-step explanation:
Data
Point (-4, 3)
⊥ to the line x- intercept of 22 and y-intercept of -4.
Process
1.- Find the equation of the perpendicular line
This line has passes through the points (22, 0) and (0, -4)
Slope = [tex]\frac{-4 - 0}{0 - 22} = \frac{-4}{-22} = \frac{2}{11}[/tex]
2.- Find the slope of the new equation
Slope = [tex]\frac{-11}{2}[/tex] because the lines are perpendicular
3.- Find the equation of the new line
y - 3 = -11/2 (x + 4)
y - 3 = -11/2x - 44/2
y - 3 = -11/2 x - 22
y = -11/2 x - 22 + 3
y = -11/2x - 19
See the graph below