A professor asserts that more than 77% of all scientists believe in evolution, and the p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).
what is null hypothesis ?A type of statistic hypothesis known as a hypothesis claims that a certain group of data has no statistical power. The viability of hypotheses is investigated using sample data. Sometimes refer to as "zero," and represented as H0. The premise that researchers make is that there is a link between the variables. The null hypothesis, on the contrary hand, asserts that such a link does not exist. Despite its inability to seem relevant, the null hypothesis is a critical component of research.
given
You must understand the distribution of your test statistic on the supposition that the null hypothesis is correct in order to calculate the p-value.
Left-tailed test: cdf as the p-value (x).
Test with a right-tail: p-value = 1 - cdf (x).
p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).
A professor asserts that more than 77% of all scientists believe in evolution, and the p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).
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1×0.1+6×0.01+8×0.001 in standard form
Answer:
the answer is 0.168
Step-by-step explanation:
have a good day!
The students in Class 6 vote to pick a class captain. The choice is Anton, Eva, Kofi or Petra. Anton gets 0.2 of the votes. Eva gets 10% of the votes. Petra gets of the votes. Kofi gets 9 votes. How many students are in class 6?
Answer:
There are 15 students in class 6
Step-by-step explanation:
Let's call the number of students in class 6 "n".
We know that:
Anton gets 0.2 * n votes
Eva gets 0.1 * n votes
Petra gets (1 - 0.2 - 0.1) * n votes
Kofi gets 9 votes
The total number of votes is n, so we can write:
n = 0.2 * n + 0.1 * n + (1 - 0.2 - 0.1) * n + 9
Simplifying this equation:
0.6 * n = 9
So:
n = 9 / 0.6
n = 15
seven times the quotient of 2 and 3
Answer:
4.666667, or you can round it to 4.67, depends on what it's asking!
Step-by-step explanation:
The quotient means to divide, so 2/3 = 0.666667
0.666667 * 7 = 4.666667
Hope that helps.
You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
Answer:
j3jejej
jwjitygueiejjejrjejejrjrjtjjturuejdvr7uejfnfnnrkrjdvev4j
Let X be a continuous random variable taking values between 0 and 2 with probability density function p(x) = 0.5. Find E(X) and Var(X). Plot its Cumulative Distribution Function.
E(X) = 2 and Var(X) = 4/3.
And then, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
Continuous Random Variable ExpectationsThe expected value (mean) of a continuous random variable X with probability density function p(x) is given by:E(X) = ∫x*p(x)dx, where the integral is taken over the range of X.
In this case, since p(x) = 0.5 for all x in [0,2], we have:E(X) = ∫x*0.5dx = 0.5∫xdx = 0.5(x²/2)|0 to 2 = (2²/2 - 0²/2)*0.5 = 2.
The variance of X is given by:Var(X) = E((X - E(X))²) = E(X²) - (E(X))².
We have to calculate E(X²), which can be found as:E(X²) = ∫x²*p(x)dx = 0.5∫x²dx = 0.5(x²/3)|0 to 2 = (2²/3 - 0³/3)*0.5 = 8/3.
So, Var(X) = E(X²) - (E(X))² = 8/3 - (2)² = 8/3 - 4 = 4/3.
The cumulative distribution function (CDF) of a continuous random variable X is given by:F(x) = P(X <= x) = ∫p(t)dt for all t <= x.
In this case, since p(x) = 0.5 for all x in [0,2], we have:F(x) = 0.5x for x in [0,2].
The CDF of X is a monotonically increasing function, and it tells us the probability that X takes a value less than or equal to x.
Now, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
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The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 390 minutes, the monthly cost will be $178. If the customer uses 940 minutes, the monthly cost will be $398.
A) Find an equation in the form y=mx+b where x is the number of monthly minutes used and y is the total monthly of the Splint plan.
B) Use your equation to find the total monthly cost if 866 minutes are used.
Answer: If 866 minutes are used, the total cost will be ------ dollars
The equation can be given as y = 0.4x +22 and the monthly cost is $368.4
What is a linear equation?
A linear equation is an expression whose degree is one. The most general linear equation is y = mx + c. Where m is the slope and c is the y-intercept.
A) To find the equation in the form y = mx + b.
We are given two points (390, 178) and (940, 398).
Now we substitute these points into the standard equation y = mx + c
We get
y = mx + b
178 = m * 390 + b
398 = m * 940 + b
We subtract the two equation we get,
550m = 220
m =0.4
Now we substitute these values in the equation 1 we get
178 = 0.4 * 390 + b
178 = 156 + b
b = 22
So the equation is:
y = 0.4x + 22
B) We are asked to find the cost for 866 minutes we substitute x = 866 in the equation
y = 0.4x + 22
y = 0.4 * 866 + 22
y = 346.4 + 22
y = 368.4
So if 866 minutes are used, the total monthly cost will be $368.4.
The equation can be given as y = 0.4x +22 and the monthly cost is $368.4
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Consider the following three random experiments: Experiment 1: Toss a coin. Experiment 2: Toss a die. Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9. (a) Specify the sample space of each experiment. (b) Find the relative frequency of each outcome in each of the above experiments in a large number of repetitions of the experiment. Explain your answer.
To fully get the answer on the sample space and relative frequency, let's go directly to the analysis of the experiments as given.
The random experiments and their outcome(a) Sample space:
Experiment 1: Toss a coin: The sample space of this experiment is {heads, tails}.Experiment 2: Toss a die: The sample space of this experiment is {1, 2, 3, 4, 5, 6}.Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9: The sample space of this experiment is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.(b) Relative frequency of each outcome:
Relative frequency of an outcome is the number of times the outcome appears divided by the total number of trials. In a large number of repetitions of an experiment, the relative frequency of each outcome approaches the theoretical probability of that outcome.
Experiment 1: Toss a coin: Since each outcome (heads or tails) is equally likely, the theoretical probability of each outcome is 0.5. In a large number of repetitions of the experiment, the relative frequency of heads and tails would approach 0.5.Experiment 2: Toss a die: Since each outcome (1 to 6) is equally likely, the theoretical probability of each outcome is 1/6. In a large number of repetitions of the experiment, the relative frequency of each outcome (1 to 6) would approach 1/6.Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9: Since each outcome (0 to 9) is equally likely, the theoretical probability of each outcome is 1/10. In a large number of repetitions of the experiment, the relative frequency of each outcome (0 to 9) would approach 1Learn more on relative frequency here https://brainly.com/question/3857836
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Find the global maxima and global minima of the function
f(x, y) =x^2 − 2xy + 2y on the rectangle D = {(x, y) ∶ 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}
The required global maximum value is 4 and the global minimum value is 3.
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
Here,
The critical points can be found by finding the partial derivatives of the function with respect to x and y and setting them equal to zero.
df/dx = 2x - 2y = 0
df/dy = -2x + 4y = 0
Solving the system of equations, we find that the critical points are (1, 2) and (2, 1).
Since (1, 2) is within the bounds of the rectangle D, we need to check the value of f(1, 2) to see if it is a local minimum or local maximum.
f(1, 2) = 1 - 2 + 4 = 3
(2, 1) is also within the bounds of the rectangle D, we need to check the value of f(2, 1) to see if it is a local minimum or local maximum.
f(2, 1) = 4 - 2 + 2 = 4
Since f(1, 2) < f(2, 1), the global maximum is at point (2, 1) and the global minimum is at point (1, 2).
The global maximum value is 4 and the global minimum value is 3.
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20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 2020 customers, 44 have enough cash to pay for their meal, 1616 have a credit card, and 33 have enough cash and a credit card. Using this information, answer each of the following questions.
Let AA be the event that a randomly selected customer has enough cash and BB be the event that a randomly selected customer has a credit card.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that a customer has enough cash?
the value of P(A∪B) is 17/20.
What is probability?Probability is a number expressing the likelihood or chance that a specific event will occur. Proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, A neighborhood restaurant is serving dinner to 20 patrons.
Both cash and credit are accepted as modes of payment at the restaurant. Of the 20 customers, 3 have enough cash and a credit card to pay for their dinner, 16 have a credit card, and 4 have enough cash to cover the cost of their meal.
From the general formula of probability:
Probability = (desired outcomes)/(Total outcomes)
Let "A" represent the situation in which a randomly chosen consumer has enough cash,
"B" represents the situation in which a randomly chosen customer has a credit card.
thus,
P(A) = 4/20
P(A) = 1/5
P(B) = 16/20
Also given,
P(A∩B) = 3/20
Since,
P(A∪B) = P(A) + P(B) -P(A∩B)
P(A∪B) = 4/20 + 16/20 - 3/20
P(A∪B) = 17/20
therefore, the value of P(A∪B) is 17/20.
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16. The elevation of City of Santa Clara is approximately 75 ft. What is the elevation in centimeters? (1ft = 12in; 1in = 2.54cm)
Answer:To convert the elevation of the City of Santa Clara from feet to centimeters, you can use the conversion factors:
1 ft = 12 in
1 in = 2.54 cm
First, convert feet to inches:
75 ft * 12 in/ft = 900 in
Then, convert inches to centimeters:
900 in * 2.54 cm/in = 2286 cm
So, the elevation of the City of Santa Clara is approximately 2286 cm.
Step-by-step explanation:
Helpppopoooooopppppppp
A. The solution set of the system is {7, 3}
About elimination methodThe elimination method is a method used to solve or find a set of solutions to a system of linear equations of two variables by eliminating one of the variables. If the variables are x and y, to determine the x variable we must first eliminate the y variable, or vice versa, if we want to find the y variable, we must first eliminate the x variable.
To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them. Then only can determine other variables that will be determined. So in the elimination method you need to eliminate the variable twice.
To eliminate y in order to find the value of x.
9x-y=60 (i) 9x-y=60
x+y=10 (ii) | times (-1)| -x-y= -10
___________ __________ _
10x=70
x=7
Substitute the value x=7 into equation (ii)
x+y=10
7+y=10
y=3
So the solution set is {7, 3}
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The water rate for a city in North Carolina is $1.39 per 755 gallons of water used. a) What is the water bill if a resident of that city uses 30,000 gallons? b) How many gallons of water can a customer use if the water bill is not to exceed $150?
The gallons of water a customer can use if the water bill is not to exceed $150 is 81474.82 gallons
What is the water bill if a resident of that city uses 30,000 gallons?
In order to determine the water bill, we need to calculate the price of one gallon of water (rate) using the given information.
Since $1.39 per 755 gallons
rate = 1.39/ 755
The water bill if a resident of that city uses 30,000 gallons will be:
1.39/ 755 * 30000 = $55.23
The gallons of water a customer can use if the water bill is not to exceed $150 will be:
Let x be gallons of water
(1.39/ 755)x ≤ 150
x ≤ 150/(1.39/ 755)
x ≤ 81474.82 gallons
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find the absolute value!! Need asap!!
Answer:
|-1/7| = 1/7 or approx .14
Let f(w) x 10x . We want to estimatef(1.07) using linear approximations. That is, using an appropriate tangent line_ First, we will build the tangent line at (€, y_ Enter as an ordered pair (a,6) The slope of the tangent line comes from f For this problem, f' (c) = And mtan The equation of the tangent line, in slope intercept form, is y = T(c) = Now, f(1.07) ~ T(1.07) Compare to actual value f(1.07)
The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.
First, we need to find the derivative of the function f(x) = x + 10x.
The derivative is given by:
f'(x) = 1 + 10
Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:
y - 6 = (1 + 10)(x - a)
y = (1 + 10)(x - a) + 6
Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).
Let's assume that the value of "a" is 1.
So, f(a) = f(1) = 1 + 10(1) = 11
And the equation of the tangent line is:
y = (1 + 10)(x - 1) + 6 = 11x - 4
Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:
T(1.07) = 11 * 1.07 - 4 = 10.77
Finally, we compare this value with the actual value of f(1.07), which is:
f(1.07) = 1.07 + 10 * 1.07 = 11.77
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The height of a rectangular box is 4 times its length, and its width is 7 in more than its length. The volume of the box is 102 in^3. Use the ALEKS graphing calculator to find the length of the box. Round your answer to two decimal places.
Answer: Let's call the length of the box "x". Then, the height of the box is 4x and the width is x + 7. The volume of the box is given by the equation:
x * 4x * (x + 7) = 102
Expanding and simplifying the equation, we get:
4x^3 + 28x^2 - 102 = 0
To find the length of the box, we need to solve for x in this equation. One way to do this is to use the cubic formula. However, this formula can be quite complex, so a simpler method would be to use numerical methods such as the bisection method or Newton's method.
Step-by-step explanation:
can someone help me pls
a. The two pentagons are congruent as the transformations they underwent were only translation and rotation, which are rigid motions.
b. The side lengths of ABCDE are given as follows:
CD = 3.2.DE = 4.1.EA = 2.8.AB = 2.2.BC = 1.4.The angle measures of FGHIJ are given as follows:
<F = 59º.<J = 162º.<I = 108º.< H = 117º.<G = 94º.What are the effects of each transformation?Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.Congruence is only changed with a dilation, as the side lengths are changed.
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The Bitcoin economy had reported year-on-year growth from 2017 to 2019 at a yearly rate of 7%. In 2020 it went into a downward trend. That year the growth turned negative at -5%. If the negative growth doubled the next year, what was the approximate percentage increase or decrease of the bitcoin economy in that year, compared to 2018?
SELECT ONLY ONE
Approximately 9% decrease
Approximately 13% decrease
Approximately 3% increase
Approximately 5% increase
If the Bitcoin economy had a yearly growth rate of 7% from 2017 to 2019, then the value in 2019 would be $1.07^3 = $1.225. If the economy had a negative growth rate of 5% in 2020, then the value in 2020 would be $1.225 x 0.95 = $1.1638. If the negative growth rate doubled in the next year, then the value in the next year would be $1.1638 x 0.9 = $1.04742.
To calculate the percentage change from 2018 to the next year, we can compare the values of the Bitcoin economy in those two years. The value in 2018 would be $1.07^2 = $1.1449. The percentage change would be ((value in next year - value in 2018) / value in 2018) x 100%. Substituting the values, we get ((1.04742 - 1.1449) / 1.1449) x 100% = -8.5%.
Therefore, the approximate percentage decrease of the Bitcoin economy in the next year, compared to 2018, is approximately 9%. The closest option is "Approximately 9% decrease".
I need help………………………
Step-by-step explanation:
could you answer to my question
I'll need more than I need help in a picture to answer your question
please answer to this with what you need help with I am only seeing a question which I do not know and what I need to focus
thank you for cooperating - yuri
I keep messing up somebody please help me
Answer:
23 and 16
Step-by-step explanation:
The pattern is to subtract 7 each time.
51 - 7 = 44
44 - 7 = 37
37 - 7 = 30
30 - 7 = 23
23 - 7 = 16
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
How much more would the value of y be on the graph than its value in the table when x = 12? (1 point)
a
20
b
90
c
150
d
180
Select the correct answer. Which expression is equivalent to this polynomial? x2 + 8
A. ( x + 2 2 ) ( x − 2 2 )
B. ( x + 4 i ) ( x − 4 i )
C. ( x + 2 2 ) 2 D.
Answer: C.
Step-by-step explanation:
Joana is meeting her friend at the Fair and the admission to get in is $10. Each ride/food costs $1.25 each Create an equation for Joana to use so she can calculate how much money she will be spending while she’s at the fair.
Answer:
y=1.25x+10
Step-by-step explanation:
you can put this into the formula “y=mx+b”. y is the final amount, x is how many times joana gets food or goes on a ride. You can plug into the equation the two parts we know. We know that no matter what, if she goes into the fair, she is going to spend $10 on the admission, even if she does not go on any rides or gets any food. So we put 10 where the “b” is. Then each time she gets food or goes on a ride, she pays another $1.25. Therefore, you can plug 1.25 into where the m is. That leaves you with “y=1.25x+10”.
1513 ÷ 3 Enter your answer by filling in the boxes. I need help.
Required value of (1513÷3) is 504R1.
What is division?
Division is the opposite of multiplication. If 3 groups of four are multiplied by 12, 12 divided into three equal groups gives 4 in each group.
The main purpose of distribution is to see how many equal groups are formed or how many are in each group in a fair distribution.
In the above example, to divide the 12 donuts into 3 similar groups, you need to put 4 donuts in each group. So, 12 divided by 3 is 4.
Here given two digits are 1513 and 3.
We want to find value of 1513 ÷ 3.
Now,
[tex]1513 ÷ 3 = \frac{1513}{3} = 504 R1[/tex]
Therefore, the quotient is 504 and the remainder is 1.
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is the data below at represented by a comparative bar chart, the bar representing which of these will be the tallest
If the data below are represented by a comparative bar chart, the bar representing the following will be the tallest:
Cat Failed
Which bar will be the tallest?The tallest bar of all of these will be the cat failed bar. A comparative bar chart is often designed to compare a set of observations.
From what we can see in the passage, it is clear that the bar chart representing the cat failed group contains the highest number and will likely have the tallest chart of all the others listed. So, the point is to look out for the observation with the highest number and the cat failed group meets the requirement.
Complete Question:
If the data below are represented by a comparative bar chart, the bar representing which of these will be the tallest?
Passed Failed
Cat. 24. 30
Dog 26. 28
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38. PROBLEM SOLVING The paths of water from three
different garden waterfalls are given below. Each
function gives the height h (in feet) and the horizontal
distance d (in feet) of the water,
Waterfall 1h
-3.1d² + 4.8
Waterfall 2h-3.5d² + 1.9
Waterfall 3 h = -1.1d2 + 1.6
a. Which waterfall drops water
from the highest point?
b. Which waterfall follows the
narrowest path?
c. Which waterfall sends water the farthest?
Answer:
a. 1; b. 2; c. 1.
Step-by-step explanation:
1] if the given functions are:
[tex]1: \ h=-3.1d^2+4.8;\\2: \ h=-3.5d^2+1.9;\\3: \ h=-1.1d^2+1.6, \ then[/tex]
2] a. d=0, ⇒ max[h] is no.1 (h=-3.1d²+4.8);
b. h=0, ⇒ min[d] is no.2 (h=-3.5d²+1.9);
c. h=0, ⇒ max[d] is no.1 (h=-3.1d²+4.8).
I NEED HELP ASAP PLEASE!!! Determine which integer will make the inequality x − 3 > 15 true.
S:{15}
S:{17}
S:{18}
S:{30}
Answer:
c) S : {30}
So, it is correct answer.
Step-by-step explanation:
mental math be like :-)
Patsy Bonner buys 200 shares of Target at $ 56.30 and 100 shares of Pepsico at $68.73. Find the total cost ignoring commissions.
Answer:
[tex]\$25,006[/tex]
Step-by-step explanation:
The total cost of Target shares is [tex](200)(\$56.30)=\$11,260[/tex].
The total cost of Pepsico shares is [tex](200)(\$68.73)=\$13,746[/tex].
Adding these costs together yields [tex]\$11,260+\$13,746=\$25,006[/tex].
Choose a new vehicle sold in the United States in December at random. The probability distribution for the type of vehicle chosen is given here. (a) What is the probability that the vehicle is a crossover? Round your answer to decimal places. Leave your answer in decimal form. (
b) Given that the vehicle is not a passenger car, what is the probability that it is a pickup truck? Round your answer to decimal places. Leave your answer in decimal form. (c) What is the probability that the vehicle is a pickup truck, SUV, or minivan? Round your answer to decimal places. Leave your answer in decimal form.
(a) The probability that the vehicle is a crossover is 0.30.
(b) Given that the vehicle is not a passenger car, the probability that it is a pickup truck is 0.50.
(c) The probability that the vehicle is a pickup truck, SUV, or minivan is 0.90.
Vehicle Type Probability CalculationI determined the probabilities based on the information provided in the problem. The problem states that the probability distribution for the type of vehicle chosen is given and lists the probabilities for each type of vehicle (crossover, pickup truck, SUV, minivan, and passenger car). To find the requested probabilities, I simply used basic probability formulas and the given probabilities for each type of vehicle.
For example, for part (a), the probability that the vehicle is a crossover is simply the given probability of 0.30.For part (b), given that the vehicle is not a passenger car, the probability that it is a pickup truck is found by using Bayes' Theorem:P(pickup truck | not passenger car) = P(not passenger car | pickup truck) * P(pickup truck) / P(not passenger car).
0.40 / (1 - 0.20) = 0.50.
The denominator P(not passenger car) is found by subtracting the probability of a passenger car (0.20) from 1, and the numerator P(not passenger car | pickup truck) is 1, since a vehicle can either be a pickup truck or not a pickup truck but not both. The requested probability is then equal to 0.50.
For part (c), the probability that the vehicle is a pickup truck, SUV, or minivan is found by adding the individual probabilities for each type of vehicle: 0.40 + 0.30 + 0.20 = 0.90.Learn more about Vehicle Type Probability Calculation here:
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Anita attends a private school where she must wear a uniform. This year, the price of the uniform is $86.80, which is 9.6% more than it cost last year. How much were uniforms last year?
Help please
Answer:
The price of the uniforms last year was about $79.20.
Step-by-step explanation:
In order to calculate the price of the uniforms last year, it is important to understand two important thing that can be inferred by what is told in the problem. This year's uniforms are 9.6% more than last year's. The easiest way to understand this line of information is that if we view the prices of the uniform from the perspective of last year's price, we can set the price of last year's uniform as 100% of the original price, and this year's uniform as 109.6% of the original price. Essentially, this year's uniform price is 109.6% of what it would cost you to buy a uniform last year.
Since you are given the information that this year, the uniforms cost $86.80, you know that $86.80 is 109.6% of last year's uniform cost. Now you can write an equation to solve for last year's price.
Set last year's uniform price to be represented by the variable [tex]x[/tex], and you will have the function of [tex]109.6[/tex]% · [tex]x = 86.8[/tex]. In order to solve for [tex]x[/tex], you simply divide both sides of the equation by 109.6%, which you will then get [tex]x = 86.8[/tex] ÷ 109.6%, which can be rewritten as [tex]x=86.8[/tex] ÷ [tex]\frac{109.6}{100}[/tex] or [tex]x=86.8[/tex] · [tex]\frac{100}{109.6}[/tex] ≈ $79.20. Hence, last year's uniforms costed $79.20.
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1. Describe the shape of the graph and any special features you see.
2. What is the greatest area possible for a rectangle with this perimeter? What are the dimensions of this rectangle?
3. What is the area of the rectangle whose length is 10 meters? What is the area of the rectangle whose length is 30 meters> How are these rectangles related?
Answers:
1. The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).
2. The greatest area possible for a rectangle with a perimeter of 80 meters is 400 [tex]m^2[/tex], and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.
3. The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300 [tex]m^2[/tex]. This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.
For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.
For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300 [tex]m^{2}[/tex], so the way these two rectangles are related is that they have the same area.
Have a great day! Feel free to let me know if you have any more questions :)
Answer:
1. See below.
2. 400 m²
20 m x 20 m
3. 300 m²
Step-by-step explanation:
Question 1The graph is a parabola that opens downwards.
Its vertex is (20, 400) and its axis of symmetry is x = 20.
Question 2From inspection of the given graph, the greatest possible area (y-value) is 400 m². This is when the length of the rectangle is 20 m.
The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:
width = 20 mlength = 20 mQuestion 3From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².
Similarly, when the length of the rectangle is 30 m, its area is also 300 m².
A rectangle has two pairs of parallel sides of equal length.
Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length. The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.