Answers
y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Relationship between two expressions or values that are not equal to each other is called 'inequality.
y≤-3x+4 is the given inequality.
The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
In the inequality we have lesser than or equal to symbol so we shade the below line.
Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
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Related Questions
Solve the inequality for x and identify the graph of its solution.
4|x + 2| < 8
Answers
Solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.
Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.
As given in the question,
Given inequality is :
4|x + 2| < 8
Divide by 4 both the side of inequality we get,
⇒(4|x + 2|)/ 4 < 8/4
⇒|x+2| < 2
⇒ (x+2) < 2 or (x+2) >-2
⇒ x< 2-2 or x > -2 -2
⇒ x < 0 or x > -4
Solution of its graph is shown by option B number line where open interval -4 is greater than and less than open interval 0.
Therefore, solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.
Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.
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A coffee company surveyed 40 potential customers to see where they would
like the company's new organic coffee sold. Respondents were given the
following four locations and asked to choose as many as they liked: grocery
stores, drugstores, health food stores, and big box stores. The results are
summarized in the bar graph below, with the number of times each location
was chosen noted above the corresponding bar.
Answers
According to the statistics presented in the bar graph of responders of four locations per 40 potential customers, the average number of places chosen per potential client is 2.5.
We are given;
Total number of potential customers =40
From the bar graph number of respondents are following;
At grocery stores = 40
At drugstores respondents = 32
At health food stores = 8
At big box stores = 20
So,
The average number = Total number of respondents / Total number of potential customers
The average number = (40 + 32 + 8 + 20) / 40
The average number = (100) / 40
The average number = 2.5
Thus, according to the statistics presented in the bar graph of responders of four locations per 40 potential customers, the average number of places chosen per potential client is 2.5.
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What is the slope of a line that is parallel to the line y = x 2?
Answers
We have to find the slope of a line that is parallel to the given line.
Since any line parallel to the given line
y = #* + 2 will have same slope as that of given
line
Bret Rockford bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan. At the end of 1 year he owes the bank $70,000. Since then interest rates have increased to 13%. The bank will renew the mortgage at this rate, or Bret can pay the bank $70,000. He decides to renew and will now pay $11.72 monthly per thousand on his loan. (You can ignore the small amount of principal paid during the year.)
The old monthly payment is $
.
The new monthly payment is $
.
The percent increase in her monthly payment (to the nearest tenth) is
%
Answers
The old monthly payment was = 10.67 x 70 = 746.9
The new monthly payment is = 11.72 x 70 = 820.4
The percent increase in his monthly payment is =9.8406%
Given,
Sandra Williams bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan
According to the question:
So, per thousand value of $70,000 is 70000/1000 =70
Now, the old monthly payment was = 10.67 x 70 = 746.9
He decides to renew and will now pay $11.10 monthly per thousand on his loan.
So, the new monthly payment is = 11.72 x 70 = 820.4
The percent increase in his monthly payment is= 11.72 /10.67 - 1 x 100
9.8406 % and to nearest tenth it is 9.8406%
Hence, the old monthly payment was = 10.67 x 70 = 746.9
the new monthly payment is = 11.72 x 70 = 820.4
The percent increase in his monthly payment is =9.8406%
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at a local college, 35.1% of students major in business, 12.3% of students major in economics, and 2.6% of students major in business and economics. what is the probability that a randomly selected student majors in business or economics? (write your answer as a percent rounded to 1 decimal place.)
Answers
The probability that a randomly selected student majors in business or economics is 44.8%.
Describe the union set in probability?A set that contains every element in at least one of two sets is called a union of two sets. The union is denoted by the symbols A∪B or “A or B” A fresh batch that includes every element from both sets is created when two sets intersect. The intersection is denoted by the symbols A∩B or “A and B”.Let 'B' be the students of business.
P(B) = 35.1%
Let 'E' be the students of business.
P(E) = 12.3%
Thus,
P(E ∩ B) = 2.6%
P(E ∪ B) = probability for student majors in business or economics.
P(E ∪ B) = P(B) + P(E) - P(E ∩ B)
Put the values-
P(E ∪ B) = 35.1% + 12.3% - 2.6%
P(E ∪ B) = 44.8%
Thus, the probability that a randomly selected student majors in business or economics is 44.8%.
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for a binomial probability distribution with 8 trials and probability of success equal 0.95. what is probability of exactly six successes? (use the binomial tables)
Answers
0.0515 is probability of exactly six successes .
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events. The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Binomial probability with
Number of trials (n) = 8
probability of success ( ρ ) = 0.95
ρ = 0.95
p + q = 1
q = 1 - p
= 1 - 0.95
q = 0.05
x ~ bin( n , ρ )
ρ( X = x ) = ⁿCₓ Pˣ . qⁿ⁻ˣ
the probability of exactly six success .
ρ ( X = 6 ) = ⁸C₆ ( 0.95)⁶ ( 0.05 )⁸ ⁻⁶
= 28 ( 0.7351 ) ( 0.05)²
= 28 ( 0.7351 ) ( 0.0025 )
= 0.051457
ρ( X = 6 ) = 0.0515
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2 1. The drama teacher is making bandanas for costumes. She is cutting yard of fabric into 6 bandanas of the same size. Write and solve an equation to find how much fabric there will be for each bandana. (Example 1)
Answers
The equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the equation to get fabric used in each bandana:
Fabric cutting out to make 6 bandanas is 1/2 yards.Then, the fabric in each bandana will be:
1/2 ÷ 6 = xSolve as follows:
1/2 ÷ 6 = x1/2 × 1/6 = x1/12 = xSo, 1/12 yards of fabric is used in each bandana.
Therefore, the equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].
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Complete question:
The drama teacher is making bandanas for costumes. She is cutting 1/2 yard of fabric into 6 bandanas of the same size. Write and solve an equation to find how much fabric there will be for each bandana.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The time taken to reach the maximum height is 1.25 seconds and the maximum height is 32 feet
The function is given that
h(t) = + 40t + 7
Where h is the height
t is the time taken
We know
[tex]-16t^2[/tex] + bx + c = 0
Compare the equations
a = -16
b = 40
c = 7
Compare both the equation
Time taken to reach maximum height = - b/2a
= - 40/2(-16)
= - 40/-32
= 5/4
= 1.25 seconds
Time taken to reach maximum height is t = 1.25 seconds
Substitute the value of t in the function to find the maximum height
h(1.25) = -16× + 40(1.25) + 7
= -25 + 50 + 7
= 32 feet
Hence, the time taken to reach the maximum height is 1.25 seconds and the maximum height is 32 feet
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Which equation represents a line which is perpendicular to the line y=2x-5y
Answers
Answer:
Step-by-step explanation:
y=-3x
I could be wrong, but I hope it helps at
For what value of X is Y= 4 a solution to the equation X-2 =XY+16
If x=-3 and y =2 , then x^y +xy^=?
Answers
a) The value of x is -6
b) The value of the expression is -3 .
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
a) x-2=xy+16
y= 4 a solution to the equation
Substitute y=4 into the equation.
x-2=x(4)+16
x-2=4x+16
-2-16=4x-x=3x
-18=3x
x=- 18/3= -6
The value of x is -6
b) [tex]x^y+xy^2[/tex]
substitute x= -3 and y =2
(-3)²+(-3)(2)²
= 9 - 12
= -3
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I am stuck on the last part can u please help me?
Answers
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
66.6% = 0.6666... = [tex]\frac{2}{3}[/tex]
Answer:
Fraction = 2/3
Step-by-step explanation:
Given information,
→ Percentage = 66.6%
→ Decimal = 0.6
→ Fraction = ??
Then the required fraction is,
→ Percentage ÷ 100
→ 66.6/100
→ 2/3
Hence, the fraction is 2/3.
I really need help on this one.The amount of milk needed for each of 5 recipes is shown on the line plot.What is the total amount of milk needed for the recipes?
Answers
The total amount of milk needed for the recipes, considering the line plot, is of:
5.25 cups.
How to obtain the total amount of milk needed for the recipes?The total amount of milk needed for the recipes is obtained adding all the measures of the line plots.
The measures of the line plot given by the image at the end of the answer are given as follows:
Two measures of 1/4 cups = 0.25 cups, which is half the distance between 0 and 1/2.One measure of 1.25 cups, which is the value at the midpoint between 1 and 1.5.One measure of 1.5 cups.One measure of 2 cups.The total amount is given by the sum of all these measures, hence:
2 x 0.25 + 1.25 + 1.5 + 2 = 5.25 cups.
Missing InformationThe line plot is given by the image at the end of the answer.
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a tire manufacturer has a 60,000 mile warranty for tread life. the manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. the manufacturer tests 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. with this data, we test the following hypotheses.h0: the proportion of tires that are worn out after 60,000 miles is equal to 0.05.ha: the proportion of tires that are worn out after 60,000 miles is less than 0.05.in order to assess the evidence, which question best describes what we need to determine?
Answers
the best question is that if they can examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, then how likely is that proportion to be 3.6% or less?
we are given the information that an A tire manufacturer has a 60,000-mile warranty and the manufacturer considers the overall tire quality to be accepted if less than 5% are worn out at 60,000 miles, also the manufacturer tested 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. So here the Hypotheses can be that:
1) The proportion of tires that are worn out after 60,000 miles is equal to 0.05 and
2) The proportion of tires that are worn out after 60,000 miles is less than 0.05.
We need to deny the first hypothesis with an alternative one. You cannot demonstrate that the average is 3.6%, but if you by one means or another decide that the probability the average is greater than 3.6% is lower than 100% minus your confidence level, at that point you'll be able to deny the first hypothesis and acknowledge the second one as new average.
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In a recent court case it was found that during a period of 11 years people were selected for grand jury duty and % of them were from the same ethnicity. Among the people eligible for grand jury duty, % were of this ethnicity. Use a significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the p-value method and the normal distribution as an approximation to the binomial distribution.
Answers
The Null and Alternative hypothesis are
Hₒ: π= 0.79
Hₐ: π > 0.79
Statistic Z = -26.38
P-value = 0
Conclusion : The null hypothesis is
rejected .
Final Conclusion : which implies that population proportion is different from
π= 0.79.. This sample proportion can notbe product of chance.
There is enough evidence to support to the claim that selection of people is biased against allowing this ethnicity to sit on the grand jury.
We have problem of proportion and we have to apply hypothesis testing in it .
We claim that the selection is biased against allowing this ethnicity to sit on the grand jury. This means that proportion of people of enthic selected for jeury in a way below from proportion that eligible for jury .
Null and Alternative hypothesis are
Hₒ: π= 0.79
Hₐ : π> 0.79
The significance level is 0.01
The sample we will use is total of 876 people that were selected for grand jury duty (n= 876). 42% of them were entnicity for which we are testing , so sample proportion is p= 0.42
The standard error is
σₚ= s√ (π(1-π)/n)= √ 0.79 (1-0.79)/ 876 = √0.00019 = 0.0137~ 0.014
Then we can calculate Z – value
Z = (p-π+0.5/n)/ σₚ =( 0.42 – 0.79 + 0.5/876 )/ 0.014 = - 0.03964/0.014 = - 26.387
P-value for this test statistic is 0
P-value (z<-26.38)= 0
P-value = 0 < 0.01
As we see that P-value is less lower then significance level . This sample result is unpredictable. The null hypothesis is rejected which implies that population proportion is different from π= 0.79
This sample proportion can not be product of chance.
There is enough evidence to support to the claim that selection of people is biased against allowing this ethnicity to sit on the grand jury.
#Complete Question:
In a recent court case it was found that during a period of 11 years 876 people were selected for grand jury duty and 42% of them were from the same ethnicity. Among the people eligible for grand jury duty, 79.5% were of this ethnicity. Use a 0.01 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Which of the following is the hypothesis test to be conducted?
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Select the correct answer. There are three cell phone models in a store. When selecting a new cell phone, 25% of the customers choose model A, 33% choose model B, and 32% choose model C. The remaining customers buy from an old collection on which the average profit is $50. If the average profit earned on models A, B, and C is $60, $75, and $40, respectively, what is the expected value of the profit earned on all models?
Answers
Given the average profits on the different cell phone models, the expected value of profit to be earned on all models is $57.55
How to find the expected value?The expected value of the profit on these models of cell phones can be found based on the number of customers who choose the model and the profit of that model.
The expected value of the profit on all the models is:
= ∑ ( percentage of customers x Profit per model)
= (Percentage of customers model A x Profit from model A) + (Percentage of customers model B x Profit from model B) + (Percentage of customers model C x Profit from model C) + (Percentage of customers old collection x Profit from old collection)
= (25% x 60) + (33% x 75) + (32% x 40) + ( (1 - 25% - 33% - 32%) x 50)
= $57.55
Options for this question are:
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solve for b: 84,250=b(1.008)120
Answers
Answer: 696.511
Step-by-step explanation:
84,250 = b(1.008)120
84250 = 120.96b
b = 696.511
Lin rode a bike 20 miles in 150 minutes. She rode at a constant speed. How long did it take her to ride 6 miles
Answers
Answer: 45 minutes
Step-by-step explanation:
She rides 150/20 minutes per mile which is 7.5 minutes per mile. So it would take her 45 minutes to ride 6 miles because 6 × 7.5 = 45.
Solve the system by substitution.
Answers
Answer:
(-7, -7)
Step-by-step explanation:
y = x; x = y
9x - 2y = -49
9(y) - 2y = -49
9y - 2y = -49
7y = -49
÷7 ÷7
----------------
y = -7
y = x
-7 = x
or
9x - 2y = -49
9x - 2(-7) = -49
9x + 14 = -49
-14 -14
-------------------
9x = -63
÷9 ÷9
---------------
x = -7
(-7, -7)
I hope this helps!
Evaluate if x³ if x = 6
This is a quiz but I was sick so I do now to do this pls show work
Answers
Answer:
Step-by-step explanation:
Answer: 108
Step-by-step explanation:
6 x 6 x 6=10
the graph shows the relationship between the amount of peaches in pounds xand the cost of peaches in dollars y
PLEASE HELP
Answers
The proportional relationship between the amount of peaches in pounds x and the cost of peaches in dollars y is given as follows:
y = 2.5x.
Direct proportional relationshipA direct proportional relationship is a special case of a linear function, with an intercept of zero, hence the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, as follows:
y = kx.
In this problem, we have to find the constant k taking a point of the graph.
The point taken is:
(2,5).
Meaning that when x = 2, y = 5.
Hence the constant is calculated as follows:
5 = 2k
k = 5/2
k = 2.5.
Then the equation is:
y = 2.5x.
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Paul had two catches during his football game. On his first catch, he lost 12 yards. On his second catch, he gained 26 yards. How many total yards did Paul gain from both of these catches?
Answers
Paul gained a total of 14 yards from both the catches during his football game.
Given,
Paul had two catches during his football game.
Paul lost 12 yards on his first catch.
Paul gained 26 yards on his second catch.
We have to find the total yards Paul gain from both the catches;
Here,
Total gained yards by Paul = Gained yards by Paul - Lost yards by Paul
Total gained yards by Paul = 26 - 12
Total gained yards by Paul = 14 yards
That is,
Paul gained a total of 14 yards from both the catches during his football game.
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the real estate group ny reports that the mean monthly rent for a one-bedroom apartment without a doorman in manhattan is $2886. assume the standard deviation is $586. a real estate firm samples 94 apartments. what is the probability that the sample mean rent is less than $2,918.03?
Answers
Probability that the sample mean rent is less than $2,918.03 is 0.050154
We are given that the Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2886. Assume the standard deviation is $586.
Also, a real estate firm samples 94 apartments.
Let X = sample mean rent
The sample mean's z-score probability distribution is provided by;
Z = X-u/σ/[tex]\sqrt{n}[/tex] ~ N(0,1)
where, u= population mean monthly rent = $2,886
σ = standard deviation = $586
n = sample of apartments = 94
Now, the probability that the sample mean rent is less than $2,918.03 is given by = P( < $2,918.03)
P( < $2,918.03) = P(Z < 0.52)= 0.050154
The above probability is calculated using z table by looking at value of x = 0.52 in the z table which have an area of 0.050154
Therefore, probability that the sample mean rent is less than $2,918.03is 0.050154
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Describe a data set that has an outlier. How does the outlier affect the residual? Explain.
Answers
A data point that is outrageously high or wildly low in comparison to the closest data point and the majority of the adjacent coexisting values is referred to as an outlier in the dataset or data graph you're working with.
What is a data set?A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.Data set with an outlier:
In a data graph or dataset, you're dealing with, an outlier is a data point that is wildly high or wildly low in comparison to the closest data point and the rest of the nearby coexisting values. Outliers are extreme values that significantly deviate from the dataset's or graph's normal distribution of values.Observed data points that deviate greatly from the least-squares line are known as outliers. They have significant residuals, which are measured as the vertical separation between the line and the point. It is important to carefully investigate outliers. Sometimes, for a variety of reasons, they ought to be excluded from the data analysis.Therefore, a data point that is outrageously high or wildly low in comparison to the closest data point and the majority of the adjacent coexisting values is referred to as an outlier in the dataset or data graph you're working with.
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On a coordinate plane, a parabola opens up. It goes through (negative 7, 5), has a vertex at (negative 4, negative 4), and goes through (negative 1, 5).
The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).
Answers
Answer:
B: The axis of symmetry is x + -4.
C: The domain is all real numbers.
F: The x-intercepts are at (-6, 0) and (-2, 0).
Step-by-step explanation:
worked on edge 2022
The answer is the First, Third, and Last
explain the difference between the types of inference that can be made as a result of random sampling and random assignment.
Answers
Since random sampling is representative of the entire group, conclusions about the population can be drawn from it. Since random assignment reduces variability, conclusions about cause and effect are possible.
What is random sampling?Random sampling is a sampling method where each sample has an equal chance of being chosen. It is the goal of a randomly chosen sample to fairly represent the entire population. A straightforward random sample might be 25 names chosen at random from a pool of 250 employees. The sample in this case is random, and the population in this case is the entire pool of 250 employees because each employee has an equal chance of being chosen.
What is random assignment?Cause and effect can only be proven with absolute certainty through an experimental study utilizing random assignment. In a study with random assignment, for example, the experimental group receives the medication while the control group does not in order to see if the drug cures the patient.
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Britney is buying a shirt and a hat at the mall. The shirt costs $30.70, and the hat costs $20.79. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
Answers
Answer:
$48.51
Step-by-step explanation:
30.70+20.79 = 51.49
100-51.94 = $48.51
your welcome :)
Answer: $48.51
Step-by-step explanation:
If you add both $30.70 and $20.79, you would get $51.49. Then you subtract it from the $100 & you get a total of $48.51. So Britney is going to receive $48.51.
given f(x) =2x^2+5, evaluate f(4)
Answers
Answer:
f(4) = - 27
Step-by-step explanation:
substitute x = 4 into f(x) , that is
f(4) = - 2(4)² + 5 = - 2(16) + 5 = - 32 + 5 = - 27
Answer:
69
Step-by-step explanation:
Replace x with 4
-2(4)^2 +5
-8^2+5
64+5
69
i need help with this asap please!!!
Answers
Answer:
54°
Step-by-step explanation:
m and the 54° angle are VERTICAL ANGLES. That means they are the same measure.
Answer:
Step-by-step explanation:
54 degree
I need help on this problem can anyone help me?
Answers
The polygon's WXYZ and ABCD are similar.
What is similar figures?
The same shape between two figures is referred to as similarity. If two figures have congruent corresponding angles and equivalent length ratios on their corresponding sides, they are said to be similar mathematically. The scale factor is the name of this often used ratio.
Consider, the polygons WXYZ and ABCD
The angles, "∠W and ∠A" and "∠Y and ∠C" are congruent to each other.
Also, the angles "∠Z and ∠D" and "∠X and ∠B" are congruent to each other.
Now consider, the sides
The sides "WZ and AD", "XY and BC" and "WX and AB" , "ZY and DC" are having the equivalent ratio.
Therefore, the polygons WXYZ and ABCD are similar.
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an inverted pyramid is being filled with water at a constant rate of 40 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 9 cm. find the rate at which the water level is rising when the water level is 2 cm.
Answers
The rate at which the water level is rising when the water level is 5 cm is;
dh/dt = 1.6 cm/s
What is a PYRAMID?A structure with triangle outside surfaces that converge to a single step at the summit is referred to as a pyramid (from Greek: pyrams)]. This shape is roughly a pyramid in the geometric sense. A pyramid foundation might be triangular, quadrilateral, or any other type of polygon. A pyramid therefore has at least three triangular exterior surfaces (at least four faces including the base). A typical variation is the square pyramid, which has a square base and four triangular exterior surfaces.Because a pyramid is built with the pyramidion at the top and the remainder of the weight closer to the ground[3], less material will be pressing down from above. Early civilizations could build stable structures thanks to this weight distribution.Acc to our question-
length of square side; s = 4 cmheight of pyramid; h = 8 cmvolumetric rate; dV/dt = 30 cm³/sSince the base is square shaped and we know that area of a square = s², then we can say that;Volume of pyramid = ¹/₃s²hThe pyramid has a height of 8 cm and length of its' square base side is 8 cm.Now, regardless of the water height, the surface of the water will always be square shaped. This implies that the ratio of the height to the top side of square will always be the same. Thus, we can say that; s = 4/8 h = h/2Thus, Volume is;V = ¹/₃ × (h/2)² × hV = ¹/₃ × h³/4V = h³/12dV/dt = (3h²/4) dh/dtPlugging in the relevant values gives;30 = (3 × 5²/4) dh/d120 = 75 dh/dtdh/dt = 120/75dh/dt = 1.6 cm/sHence,The rate at which the water level is rising when the water level is 5 cm is; dh/dt = 1.6 cm/s
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