The chance that a hypothesis test will incorrectly reject the null hypothesis when the p-value cutoff is 1%. The correct option is A.
What is a hypothesis test?A hypothesis test is used to test the validity of a hypothesis by calculating the probability that a sample statistic occurred by chance.
The null hypothesis is the hypothesis that is being tested, and it is usually assumed to be true unless there is evidence to the contrary.
The p-value is the probability of obtaining a sample statistic at least as extreme as the one observed, assuming the null hypothesis is true. If the p-value is less than the significance level, which is the p-value cutoff chosen by the researcher, then the null hypothesis is rejected.
If the p-value is greater than or equal to the significance level, then the null hypothesis is not rejected. The p-value cutoff is the significance level chosen by the researcher, and it represents the maximum probability of rejecting the null hypothesis when it is actually true.
In this case, the p-value cutoff is 1%, which means that the maximum probability of rejecting the null hypothesis when it is actually true is 1%. Therefore, the chance that a hypothesis test will incorrectly reject the null hypothesis when the p-value cutoff is 1%.
Therefore, the correct option is A.
Learn more about hypothesis test here:
https://brainly.com/question/30588452
#SPJ11
the national center for heatlh has found that there is a 0.41% chance that an american citizen will die from falling. what is the probability that you will not die from a fall?
If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.
Answer: 99.59%.
Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1,5) y P₂=(-2,-6)
Cómo resolver este ejercicio de ecuaciones lineales de dos puntos
The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)
In mathematics, how do you find coordinates?To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.
It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.
We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)
Using the values provided:
P1 = (-1.5, Y1) (-1.5, Y1)
P2 = (-2, -6) (-2, -6)
These values can be used as substitutes in the formula:
m = (-6 - Y1) / (-2 - (-1.5))
Making the denominator simpler:
m = (-6 - Y1) / (-2 + 1.5)
m = (-6 - Y1) / (-0.5)
m = 12 + 2Y1
To know more about equation visit:-
https://brainly.com/question/29657988
#SPJ1
Question:
Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1.5) and P₂=(-2,-6)
How to solve this exercise of linear equations of two points.
Landon buys cookies and lemons at the store he pays a total of $29.12 He pays $2.66 for the cookies he by seven bags of lemons that each cost the same amount Which tape diagram could be used to represent the contacts if X represents how much each bag of lemons cost
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
what is unitary method ?A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.
given
The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.
The first segment on the left, which is $2.66, represents the price of the cookies.
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
A sector subtends an angle of 42° at the centre of a circle of radius 2.8 cm. Calculate the perimeter of the sector.
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]
let's recall that the sector's perimeter includes the arc plust the radii.
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
The expected probability distribution is $4.35
We must multiply each supplied chance by the respective payout value in order to determine the expected value.
As a result, we have the payout probability distribution shown below:
0.35(1) + 2(0.2) + 5(0.1) + 8(0.2) + 10(0.15) (0.15)
= 0.35 + 0.4 + 0.5 + 1.6 + 1.5
= $4.35
When the set of possible outcomes is discrete in nature, the distribution is referred to as a discrete probability distribution. When a dice is rolled, all conceivable results, for instance, are discrete and result in a large number of outcomes. A different name for it is the probability mass function.
statistical distributions that can be used
Uniform discrete distribution The chances of each outcome are equal.
Single-trial distribution with two potential results.
A series of Bernoulli events are called the binomial distribution.
Poisson Distribution: The likelihood that a particular occurrence may or may not occur.
To know more about probability distribution, click the below link
https://brainly.com/question/14210034
#SPJ4
how many four digit positive integers x are there with the property that x and 3x have only even digits?
16 four digit positive integers x are there with the property that x and 3x have only even digits.
There are 16 such four-digit positive integers x.
At first we have to find the four-digit positive integers x with the property that both x and 3x have only even digits, we need to consider the possible digits that x can have.
Since both x and 3x must have only even digits, the digits of x can only be 0, 2, 4, 6, or 8.
Let, the possible cases for the first digit of x:
If the first digit of x is 0:
In this case, x would be a three-digit number (e.g., 012, 024, 036, etc.). Now, if we multiply any three-digit number by 3, the resulting number will always have at least one odd digit.
we get, this case does not satisfy the condition.
If the first digit of x is 2 or 8:
In this case, the last digit of 3x will be 6 or 4, respectively. But since 6 is not an even digit and 4 is not a valid digit for x, this case is not possible either.
If the first digit of x is 4 or 6:
In this case, the last digit of 3x will be 2 or 8, respectively.
These are valid digits for x.
Now, we need to make sure that the second digit of x and 3x are also even.
The only even digits that can be used as the second digit are 0 and 8 (because 2 and 6 are already used as the first digit).
So, there are two possible cases for the first digit of x: 4 or 6.
Now, we have two choices for the second digit of x (0 or 8).
For each of these combinations, we have two choices for the third digit of x (0 or 8).
Finally, we have two choices for the fourth digit of x (0 or 8).
So, we get the total number of four-digit positive integers x with the property that both x and 3x have only even digits is:
Number of choices = 2 (choices for the first digit) * 2 (choices for the second digit) * 2 (choices for the third digit) * 2 (choices for the fourth digit) = 2⁴ = 16.
Therefore, there are 16 such four-digit positive integers x.
To learn more on combination click:
brainly.com/question/10699405
#SPJ12
I WILL AWARD YOU THE BRAINLIEST!!!!!!!!!
whats 1+1-1
Answer:
1
Step-by-step explanation:
LOL
Answer:
1+1-1=1
Step-by-step explanation:
1+1=2
2-1=1
your answer is 1
a particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. twenty fish are placed in a tank containing this concentration of chemical in water. a find the probability that exactly 14 survive. b find the probability that at least 10 survive.
A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore
a. The probability that exactly 14 fish survive is 0.263b. The probability that at least 10 fish survive is 0.983How do we calculate the probability?a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263
b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.
See more about binomial distribution at: https://brainly.com/question/29163389
#SPJ11
Sharon’s brother has saved a total of $450 for a phone. He has earned $90 from his parents plus $60 each week from his job. How many weeks has he been saving?
Answer:
6 weeks
Step-by-step explanation:
$450 - $90(from parents) = $360
$360 ÷ $60(from job) = 6
He's been saving money for "6 weeks".
I need help please
Answer:
64 sq cm
Step-by-step explanation:
triangle area = 1/2*b*h (×4 because 4 triangles)
square area = lw
I keep getting stuck on these questions.. (Middle school btw)
15 points.
Answer:
Let's say "x" is the number we're trying to find.
According to the problem, we know that 54 is 60% of that number.
So we can set up an equation:
54 = 0.6x
To solve for x, we need to isolate it on one side of the equation.
Divide both sides by 0.6:
54/0.6 = x
Simplify:
90 = x
Therefore, 54 is 60% of 90.
Step-by-step explanation:
Answer: 90
Step-by-step explanation:
Step 1. 54 = 60% × Y
Step 2. 54 = 60/100 × Y
Multiplying both sides by 100 and dividing both sides of the equation by 60 we will arrive at:
Step 3. Y = 54 × 100/60
Step 4. Y = 54 × 100 ÷ 60
Step 5. Y= 5400 ÷ 60
Step 6. Y = 90
Suppose a large candy machine has 45% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion
pof orange candies. Find the standard deviation of the sampling distribution of
pCheck to see if the 10% condition is met.
The standard deviation of the sampling distribution of pCheck to see if the 10% condition is 0.44.
If a large candy machine has 45% orange candies, and an SRS of 25 candies is taken from it, then the 10% condition can be checked to see if it is met. To do this, it is necessary to calculate the sample proportion p. To calculate p, the number of orange candies in the sample (let's call it x) is divided by the total number of candies in the sample (25). Thus, p = x/25. The 10% condition is met if the value of p is less than or equal to 0.1 (10%).
Since the value of p is unknown, the number of orange candies in the sample must first be determined. To find this number, the proportion of orange candies in the entire candy machine must be used. The proportion of orange candies is 45%, or 0.45.
This means that for every 100 candies in the candy machine, 45 are orange. Since there are 25 candies in the sample, 0.45*25 = 11.25 orange candies are expected in the sample. Since this is a sample proportion, the exact value of x must be rounded to the nearest whole number. This gives a value of 11 orange candies in the sample.
Now that the value of x is known, the value of p can be calculated. This gives p = 11/25 = 0.44.
Since 0.44 is greater than 0.1 (10%), the 10% condition is not met in this case.
for such more questions on proportion
brainly.com/question/870035
#SPJ11
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
a. using only volunteers from the basketball team in the experiment.
b. using ἁ =0.05 instead of ἁ =0.05
c. using ἁ =0.05 instead of ἁ =0.01
d. giving the drug to 25 randomly selected students instead of 50.
e. using a two-sided test instead of a one-sided test.
The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.
The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.
To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.
However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.
To know more about the "null hypothesis": https://brainly.com/question/15980493
#SPJ11
Are the following statements equivalent? a>b and there is the number c ,so that a=b+c
No, the statements are not equivalent as the statement "a > b" simply means that "a" is greater than "b" and there exists a number "c" such that when added to "b", it equals "a". This does not necessarily mean that "a" is greater than "b".
The statements "a>b" and "there is the number c, so that a=b+c" are not equivalent. The statement "a>b" simply means that "a" is greater than "b," while the statement "there is the number c, so that a=b+c" means that "a" can be expressed as the sum of "b" and another number "c."
These statements are not equivalent because even if "a" is greater than "b," it may not be possible to express "a" as the sum of "b" and another number "c."
Additionally, even if "a" can be expressed as the sum of "b" and another number "c," it may not necessarily be true that "a" is greater than "b."
Learn more about equivalent equation at
https://brainly.com/question/12211497
#SPJ4
3. The population of bees has been increasing by 5% each year since 2010. There were 1,000 bees counted in 2010. a. Create an explicit formula that models the bee population for n years since 2010. (Hint: What function have we studied that can be represented by this situation?)
Answer: 1000 x 1.05^n
Step-by-step explanation:
1.05 is the increase experienced each year and n is the number of years.
Answer:
The population of bees is increasing by 5% each year since 2010. Let P(n) be the population of bees in the nth year since 2010.
The explicit formula for the bee population can be found using the formula for compound interest:
P(n) = P(0) * (1 + r)^n
where P(0) is the initial population in 2010, r is the annual growth rate, and n is the number of years since 2010.
Substituting the given values, we have:
P(n) = 1000 * (1 + 0.05)^n
Simplifying the expression, we get:
P(n) = 1000 * 1.05^n
Therefore, the explicit formula that models the bee population for n years since 2010 is P(n) = 1000 * 1.05^n.
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
w = 28 miles
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
The sum of the lengths of the sides is w + 28 + 28.
The perimeter is 84.
w + 28 + 28 must equal 84.
w + 28 + 28 = 84
Now we solve for w.
Add 28 and 28.
w + 56 = 84
Subtract 56 from both sides.
w = 28
Answer: w = 28 miles
GEOMETRY
determine whether each pair of triangles is similar. give details about each set of sides or angles. give the theory used. write a similarity statement.
The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.
What is the Angle Side Angle Congruence Theorem?The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:
m < W = m < Z.m < V = m < Y.The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.
More can be learned about the Angle-Side-Angle congruence theorem at https://brainly.com/question/3168048
#SPJ1
Cindy rides her bike with a constant speed of 8 miles per hour how long will she take to a travel a distance of 2 miles
Cindy will take 0.25 hours or 15 minutes to travel a distance of 2 miles at a constant speed of 8 miles per hour.
What is the formula for Time?The formula for time is: time = distance / speed where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.
What is the formula for Speed?The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel.This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.
In the given question,
We can use the formula:
time = distance / speed
where "distance" is the distance traveled and "speed" is the speed at which Cindy is riding her bike.
Substituting the given values, we get:
time = 2 miles / 8 miles per hour
Simplifying, we get:time = 0.25 hours.
To know more about speed,distance and time , visit:
https://brainly.com/question/10504780
#SPJ1
W(–1, 4), X(4, 0), Y(–5, 1), and Z(0, –3) are vertices of quadrilateral WXZY. What is true of wx and yz?
The length of WX is greater than the length of YZ, and that the sides are neither parallel nor perpendicular.
Quadrilateral WXZY has four vertices: W(-1,4), X(4,0), Y(-5,1), and Z(0,-3). We are asked what is true about the sides WX and YZ.
To determine the length of WX, we can use the distance formula: d = √((x2-x1)² + (y2-y1)²). So, d(W,X) = √((4-(-1))² + (0-4)²) = √(5² + 4²) = √41. Similarly, d(X,Z) = √((0-4)² + (-3-0)²) = √16 + 9 = √25 = 5.
To determine the length of YZ, we can use the same formula: d(Y,Z) = √((-3-(-5))²+ (0-1)²) = √4 + 1 = √5.
Now, we need to compare the lengths of WX and YZ to determine what is true about them. √41 is greater than √5, so we know that WX is longer than YZ.
However, this does not tell us whether WX and YZ are parallel, perpendicular, or neither. To determine this, we need to examine the slopes of the sides.
The slope of WX is (0-4)/(4-(-1)) = -4/5. The slope of YZ is (0-(-3))/(-5-0) = 3/5. Since the slopes are not equal, we know that the sides are not parallel.
To determine if the sides are perpendicular, we can multiply their slopes. If the product is -1, then the sides are perpendicular. So, (-4/5) * (3/5) = -12/25, which is not equal to -1. Therefore, we can conclude that the sides WX and YZ are neither parallel nor perpendicular.
Learn more about quadrilateral here: brainly.com/question/29934440
#SPJ4
A function is shown.
f(x) = x² + 2x - 3
Use the Add Point tool to show the x-intercepts and maximum or minimum of the function.
the x-intercepts are (-3, 0) and (1, 0), and the minimum occurs at the vertex (-1, -4).
What is a function?
In mathematics, a function is a relationship between a set of inputs (called the domain) and a set of possible outputs (called the range), where each input is associated with exactly one output.
To find the x-intercepts, we set the function equal to zero and solve for x:
x² + 2x - 3 = 0
Using the quadratic formula, we get:
x = (-b ± sqrt(b² - 4ac)) / 2a
Where a = 1, b = 2, and c = -3.
Plugging in the values, we get:
x = (-2 ± sqrt(2² - 4(1)(-3))) / 2(1)
Simplifying, we get:
x = (-2 ± sqrt(16)) / 2
x = (-2 ± 4) / 2
x1 = -3, x2 = 1
Therefore, the x-intercepts are (-3, 0) and (1, 0).
To find the maximum or minimum, we can use the vertex form of the equation:
f(x) = a(x - h)² + k
where (h, k) is the vertex.
To get the vertex, we complete the square:
f(x) = x² + 2x - 3
f(x) = (x + 1)² - 4
The vertex is (-1, -4), which is a minimum since the coefficient of the squared term is positive.
Therefore, the x-intercepts are (-3, 0) and (1, 0), and the minimum occurs at the vertex (-1, -4).
To learn more about function from the given link:
https://brainly.com/question/21145944
#SPJ1
What is the y-intercept of the line with the equation y = 4 x + 2?
a. -2
b. 4
c. 2
d. -1/2
Answer:
C. 2-----------------------------------
The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.
To find the y-intercept, substitute 0 for x in the equation y = 4x + 2:
y = 4*0 + 2 y = 2The y-intercept is 2 and matching choice is C.
Answer:
2
Step-by-step explanation:
We need to find out the y intercept of the given equation which is y = 4x + 2 .
y intercept is a point where the graph of the equation cuts the y axis. So at y intercept x coordinate will be 0 , so plug in x = 0 , in the given equation as ;
y = 4x + 2
y = 4(0) + 2
y = 0 + 2
y = 2
Therefore the y intercept of the line is 2 . ( option C )
Ngozi is twice older than Ada and agens is one third as old as Ada if the sum of their age is 30 what is ngozi age
Answer:
Ngozi is 45 years old
Step-by-step explanation:
N = 2A
AG = 1/3A
A + AG = 30
Subsitute AG with 1/3A.
A + 1/3A = 30
1 1/3 A = 30
A = 22.5
AG = 7.5
Ngozi = 45
Solve for x and graph the solution on the number line below
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
please help i need to hurry
Answer:
( 9, 1/7 )
Step-by-step explanation:
I/9x- y=6/7 equation (1)
1/18x-2y=3/14 equation (2)
9x(1)-18x(2) multiply equation (1 ) by 9 and (2 ) by 18 and subtract
them
we get y=1/7
then put the value of y=1/7 in ( 1 ) or (2)
1/9x-1/7=6/7 ⇒x=9
therefore the right answer is ( 9, 1/7 )
At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−18x2+4x
represents the path of a T-shirt. The function 3y=2x−14
represents the height of the bleachers. In both functions, y
represents vertical height (in feet) and x
represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?
The height that the T-short lands on the bleachers is x = 0.65.
What is quadratic formula?The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.
Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.
The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3
To find the height of the T-shirt landing we find the intersection of the two equations as follows:
-18x² + 4x = (2x - 14)/3
-54x² + 12x = 2x - 14
54x² - 10x - 14 = 0
27x² - 5x - 7 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Substitute the values;
x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)
x = (5 ± √(925)) / 54
x = (5 ± 5√37) / 54
x = (5 + 5√37) / 54 = 0.65 and
x = (5 - 5√37) / 54 = -0.47
Hence, the height that the T-short lands on the bleachers is x = 0.65.
Learn more about quadratic formula here:
https://brainly.com/question/2615966
#SPJ1
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The second figure.
Step-by-step explanation:
The first figure's perimeter is:
70 in + 42 in + 56 in = 168 inches.
And the second figure's perimeter is:
42 in + 33 in + 33 in + 64 in = 172 inches.
Therefore, Figure 1 < Figure 2.
I NEED HELP ON THIS ASAP!!
a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380
b) The maximum profit of $5200 achieved.
Define the term selling profit?Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.
a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:
x ≥ 0 (non-negative constraint)
y ≥ 0 (non-negative constraint)
x ≤ 260 (maximum number of mahogany boards available)
y ≤ 320 (maximum number of black walnut boards available)
x + y ≤ 380 (maximum number of boards that can be sold)
To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).
b) The profit function P(x, y) can be defined as follows:
P(x, y) = 20x + 6y
To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).
One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.
The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).
P(0, 0) = 0
P(0, 320) = 6(320) = 1920
P(260, 0) = 20(260) = 5200
P(120, 260) = 20(120) + 6(260) = 4720
Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.
To know more about inequalities, visit:
https://brainly.com/question/30238989
#SPJ1
4. A polygon with area 10 square units is dilated by a scale factor of k. Find
the area of the image for each value of k. (Lesson 5-4)
a. k = 4
b. k = 1.5
c. k = 1
d. k = 1/3
Answer:
If a polygon is dilated by a scale factor of k, then its area is multiplied by k².
a. When k = 4, the area of the image is 10 × 4² = 160 square units.
b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.
c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)
d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.
Step-by-step explanation:
The _____ in which ratio is expressed is important
In mathematics, a ratio is a comparison of two quantities or numbers expressed in terms of division. The order in which the quantities are expressed in a ratio is also important.
Ratios are used in various mathematical applications such as in finance, geometry, and physics. The units or quantities being compared in a ratio are crucial in determining the meaning and significance of the ratio.
For example, if the ratio is expressed as 2:1, it could mean that the first quantity is twice the size of the second quantity, or it could mean that the second quantity is half the size of the first quantity. Therefore, it is important to clearly define the units or quantities being compared to avoid any ambiguity or misunderstanding.
In the example above, if the ratio was expressed as 1:2 instead of 2:1, the meaning of the ratio would be reversed. Therefore, the order of the quantities in a ratio should be consistent with the context in which it is being used. In summary, the units and the order in which the quantities are expressed in a ratio are important in conveying accurate and meaningful information.
To learn more about ratios
https://brainly.com/question/13419413
#SPJ4
Complete question:
In mathematics, the units or quantities being compared and the order in which they are expressed in a ratio are both important. The _____ in which ratio is expressed is important
a system of equations is shown below.
2x-6y=-6
y=1.5x-2.5
what is the value of x in the solution to the system?
Answer:
x = 3
Step-by-step explanation:
Solving systems of linear equations via substitution:
[tex]2x-6y=-6[/tex]
[tex]y=1.5x-2.5[/tex]
We are already given the value of y, so to find the value of x, we need to plug in the y value in the other equation.
[tex]2x-6(1.5x-2.5)=-6[/tex]
Distribute 6
[tex]2x-9x+15=-6[/tex]
Combine our like terms
[tex]-7x+15=-6[/tex]
Subtract 15 to both sides
[tex]-7x=-21\\[/tex]
Divide by -7
[tex]x=3[/tex]
