The length of one side of a golden rectangle is 0.82 centimeters. Find the length of the other side. Notice that the other side could be either longer or shorter than the given side
Answer:
A golden rectangle is a rectangle whose length and width are in the golden ratio, which is approximately 1.618. This means that if one side of the rectangle is x, then the other side is approximately 1.618x.
In this case, we know that one side of the rectangle is 0.82 centimeters. To find the length of the other side, we can multiply this value by the golden ratio:
1.618 × 0.82 ≈ 1.327
Therefore, the length of the other side of the rectangle is approximately 1.327 centimeters.
A group of consumers were asked whether they preferred Brand A or Brand B.
The table shows the probabilities of results.
Male
Female
Total
Brand A
0.5
0.3
0.8
Brand B
0.15
0.05
0.2
Being male and preferring Brand A are
P (male | Brand A)
Total
Drag a response to each box to correctly complete each statement.
P (male)
0.65
0.35
1
independent not independent
2
Being male and preferring Brand A are independent, as:
P(male|Brand A) = P(male).
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
From the table, we are already given the relative frequencies, hence we must simply identify the desired outcomes and the probability of being male is given as follows:
0.5 + 0.15 = 0.65.
The conditional probability of being male, given that the person prefers brand A, is given as follows:
P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 = 0.625.
As the probabilities are equal, the events are independent.
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An investment of R1 500 000, made two years ago, has increased in value to R1 700 000, and has delivered R40 000 worth of dividends over the two years. What is the return on the investment? 1.6% 2.16% 3.28% 4.33%
Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.
We can use the following formula to calculate ROI:
ROI = (gain from investment - cost of investment) / cost of investment
where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.
Using the values given in the question, we can calculate the ROI as:
ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000
ROI = 0.16 or 16%
Therefore, the return on the investment is 16%.
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5x-y=1/4 write in slope-intercept form
The slope intercept form of the given equation is,
y = 5x - 1/4
Given an equation of a line as,
5x - y = 1/4
We have to write the equation of the line in slope intercept form.
Equation of the line in slope intercept form is,
y = mx + c
Here m is the slope and c is the y intercept.
Rearranging the given equation,
5x = y + 1/4
5x - 1/4 = y
or,
y = 5x - 1/4
Hence the slope intercept form is y = 5x - 1/4.
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Determine the type of tax described in each sentence. payroll tax property tax corporate tax sales tax excise tax gift tax Sharon's employer deducts taxes from her salary to pay the federal government directly. arrowRight Nelson's company pays taxes based on a percentage of profits for the year. arrowRight Priscilla pays more than the value listed on the price tag of a summer dress. arrowRight Lincoln pays taxes directly to the government for the land he owns. arrowRight
Sharon's employer deducts taxes from her salary to pay the federal government directly, which is a type of payroll tax. Nelson's company pays taxes based on a percentage of profits for the year, which is a type of corporate tax.
Priscilla pays more than the value listed on the price tag of a summer dress, which is a type of sales tax. Lincoln pays taxes directly to the government for the land he owns, which is a type of property tax.
Payroll taxes are levied on the earnings of employees and are used to fund social security, Medicare, and other federal and state programs. Corporate taxes are taxes on the profits earned by businesses.
Sales taxes are levied on the price of goods or services sold to consumers. Property taxes are levied on real estate owned by individuals or businesses based on the assessed value of the property.
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this is gonna be easy for some is can someone help with this please? hurry and try to make it sound a little simpler (zoom up to see)
The values of the products of the given fractions are 4 and 1 11/16.
Given are fractions we need to divide them,
We know that the in dividing the fraction we just flip the second fraction and change the sign of division by the sign of multiplication,
Here we will use the same concept,
1) 4/5 ÷ 1/5
Flipping the second fraction, and changing the sign of division by the sign of multiplication,
4/5 ÷ 1/5
= 4/5 × 5/1
= 20/5
= 4
Similarly,
2) 2 1/4 ÷ 1 1/3
Here the fractions are given in mixed form, firstly we will change them into proper fractions, then apply the same concept as above,
2 1/4 ÷ 1 1/3
= 9/4 ÷ 4/3
= 9/4 × 3/4
= 27/16
= 1 11/16
Hence the values of the products of the given fractions are 4 and 1 11/16.
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A randomized study compared the effectiveness of two
different flea collars for dogs. The dogs in the treatment
group using Flea Collar A had a mean of 2.8 fleas. The dogs
in the treatment group using Flea Collar B had a mean of 3.3
fleas.
To determine if the results are significant, the data are
rerandomized and the differences of the means are shown in
the dot plot
What is the best conclusion to make based on the data?
AThe difference of the means is not significant
because the rerandomizations show that it is
outside the range of what could happen by
chance.
B)The difference of the means is significant
because the rerandomizations show that it is
outside the range of what could happen by
chance.
C)The difference of the means is significant
o because the rerandomizations show that it is
within the range of what could happen by chance.
D)The difference of the means is not significant
O because the rerandomizations show that it is
within the range of what could happen by chance.
Difference of Means
The best conclusion to make based on the data is B The difference of the means is significant because the rerandomizations show that it is outside the range of what could happen by chance.
How to explain the informationGiven the details and dot plot, option B) is considered to be the most beneficial conclusion. This would imply that the difference between the means of fleas for two various treatment groups is not merely due to happenstance and is in fact statistically noteworthy.
Examining the randomizations further confirms that this deviation lies out of the expected parameter based on mere chance.
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Can someone help me with this question please? I really need help and the assignment is already late :(
The image of A after a reflection using the y-axis is (-2, -1).
Given that, the coordinate of point A is (2, -1).
The image of A after a translation 2 units to the right.
Translation rules:
When the shape is moved towards the right by k units, then replace x with x + k.
Here, (2+2, -1)=(4, -1)
The image of A after a reflection using the y-axis.
The reflection of point (x, y) across the y-axis is (-x, y).
So, the image of point A is (-2, -1)
The image of A after a rotation of 180° using center (0, 0)
Rule: (x, y) becomes (-y, x)
So, the image of point A is (1, 2)
Therefore, the image of A after a reflection using the y-axis is (-2, -1).
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Which of the points is not one of the vertices (s, t) of the shaded region of the
set of inequalities shown below?
OA. (0,5)
OB. (0,20)
O C. (10,0)
OD. (0, 10)
s≤ 10-0.5t
825-t
s≤ 20-t
820
120
All the points of the vertices are in the shaded region
Which of the points is not one of the vertices (s, t) of the shaded regionFrom the question, we have the following parameters that can be used in our computation:
s ≤ 10 - 0.5t
s ≥ 5 - t
s ≤ 20 - t
s ≥ 0
t ≥ 0
Next, we plot the graphs of the above inequalities
In the graph, we can see that all the points are in the shaded region
Hence, none of the points is not one of the vertices (s, t) of the shaded region
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simplify:2/x-1 -x/x^2+1 -1/x+1
To simplify the expression 2/(x-1) - x/(x^2+1) - 1/(x+1), we need to find a common denominator for all three terms.
The common denominator for the three terms is (x-1)(x^2+1)(x+1). We can rewrite each term using this denominator as follows:
2/(x-1) = 2*(x^2+1)*(x+1) / [(x-1)(x^2+1)(x+1)]
x/(x^2+1) = x*(x-1)*(x+1) / [(x-1)(x^2+1)(x+1)]
1/(x+1) = (x^2+1) / [(x-1)(x^2+1)(x+1)]
Now, we can combine the three terms by subtracting the second and third terms from the first, and simplify as follows:
2*(x^2+1)*(x+1) / [(x-1)(x^2+1)(x+1)] - x*(x-1)*(x+1) / [(x-1)(x^2+1)(x+1)] - (x^2+1) / [(x-1)(x^2+1)(x+1)]
= [2*(x^2+1)*(x+1) - x*(x-1)*(x+1) - (x^2+1)] / [(x-1)(x^2+1)(x+1)]
= [2x^3 + 2x - x^3 + x^2 - x^2 - 1] / [(x-1)(x^2+1)(x+1)]
= (x^3 + 2x - 1) / [(x-1)(x^2+1)(x+1)]
Therefore, the simplified expression is (x^3 + 2x - 1) / [(x-1)(x^2+1)(x+1)].
Find the area of this triangle! Round to the nearest tenth!!
Answer:
180 cmStep-by-step explanation:
NEED HELP FAST HOMEWORK
The practical use of the confidence interval will be C. The confidence interval can be used to estimate that, with 90% confidence, the interval from true mean DNA base of all people
How to calculate the confidence intervalCI = 2.7 ± 1.645 * (1.0801/√10) ≈ (1.4, 4.0)
Therefore, the 90% confidence interval for the population mean µ is (1.4, 4.0).
The efficacy of confidence intervals lies in their aptitude to determine the probable range of values wherein the authentic populace mean probably resides, with a provided level of assurance. Consequently, we can assert with 90% sureness that the true population mean of DNA bases are likely to rest between 1.4 and 4.0.
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Compute AB, if possible:
The multiplication of the given two matrices A and B gives,
AB = [tex]\left[\begin{array}{ccc}-9&0\\9&9\end{array}\right][/tex]
Given two matrices,
A = [tex]\left[\begin{array}{ccc}1&3&-1\\3&0&3\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}3&0\\-4&1\\0&3\end{array}\right][/tex]
We have to find the product of these matrices.
We have to multiply each row of A with each column of B.3
(AB)₁₁ = (1 × 3) + (3 × -4) + (-1 × 0) = -9
(AB)₁₂ = (1 × 0) + (3 × 1) + (-1 × 3) = 0
(AB)₂₁ = (3 × 3) + (0 × -4) + (3 × 0) = 9
(AB)₂₂ = (3 × 0) + (0 × 1) + (3 × 3) = 9
Hence the product is,
AB = [tex]\left[\begin{array}{ccc}-9&0\\9&9\end{array}\right][/tex]
Hence the product is AB = [tex]\left[\begin{array}{ccc}-9&0\\9&9\end{array}\right][/tex].
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solve the set of algebraic equationsc11 c12 c13 0 h1 1-5c14c21 c22 c23 0 h2 -5c24c31 c32 c33 0 h3 -5c340 0 0 1 h4 5
The solution to the set of equations are:
x = 17/7
y = 20/7
We have,
The two equations are:
x + y = 7 ______(1)
x² - y² = 15 _______(2)
We can use the method of substitution.
From the first equation.
y = 7 - x
We can substitute this expression for y into the second equation.
x² - (7 - x)² = 15
Expanding the square in the second term gives:
x² - (49 - 14x + x²) = 15
Simplifying this equation.
-14x + 34 = 0
Solving for x gives:
x = 17/7
Substituting this value of x into the first equation.
y = 7 - x = 20/7
Therefore,
The solution to the set of equations are:
x = 17/7
y = 20/7
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The complete question:
Solve the set of algebraic equations.
x + y = 7
x² - y² = 15
You need to make 48 servings of mushroom gravy. Each serving takes .75 cups of brown stock. How many quarts of brown stock do you have to make
Using proportions, it is found that you need 900 quarts of brown stock to make the servings of mushroom gravy.
We know that;
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Now, In this problem,
Each serving takes 75 cups of brown stock is,
= 75/4
= 18.75 quarts.
So, 48 servings will be made,
hence the number of quarts is given by:
n x Q = 48 x 18.75
= 900 quarts.
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The town manager of Greenville wants to survey tax-paying residents for their opinion regarding increasing real estate taxes in
support of improvements to the sports field park on the west side of town.
Which method results in a random sample of the population?
A)Ask everyone that enters the Town Hall over the course of one month to complete a survey until 100 surveys have been
completed.
B)Randomly select 100 parents of parents that play soccer for the town, using the town's list of players and a random
number generator.
C)Survey every 10th person entering a supermarket on the east side of town until 100 surveys have been completed.
D)Randomly select 100 residents paying real estate taxes, using the town's list of taxpayers and a random number
generator.
By selecting 100 inhabitants who pay real estate tax, using the town's list of taxpayers and a random number generator, Option D offers an arbitrary population sample.
Why is this a random sample of the population?This approach guarantees that each taxpayer has an equal likelihood of being chosen for the study, resulting in a diversified sample representation.
Conversely, the other options have possible biases or restrictions; like surveying solely soccer player's guardians might narrow it down to one particular group or only conducting them in designated areas could lead to misrepresentation within the frame of the entire general opinion poll.
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write an equation for the line of best fit below
Answer:
[tex]m = \frac{29 - 20}{33 - 8} = \frac{9}{27} = \frac{1}{3} [/tex]
[tex]20 = \frac{1}{3} (8) + b[/tex]
[tex] \frac{60}{3} = \frac{8}{3} + b[/tex]
[tex]b = \frac{52}{3} [/tex]
[tex]y = \frac{1}{3} x + \frac{52}{3} [/tex]
[tex]3y = x + 52[/tex]
[tex] - x + 3y = 52[/tex]
[tex]x - 3y = - 52[/tex]
HELP HELP HELP HELP HELP HELPHELP HELP HELPHELP HELP HELPHELP HELP HELPHELP HELP HELP PLS PLE PLS PLS PLs
The answers to the box plot are given as follow;
1) the highest level of snow fall was 50inches. This is the maximum value on the plot
2) The data is most concentrated in the 3rd quarter. More cities has snow fall closer to 40 inches than to 13 inches.
3) the data is most spread all over the 4th quarter.
1) As per the data depicted in a box plot, it can be inferred that no urban center witnesses snowfall exceeding 50 inches.
2) The highest point on this chart supports this observation.
Furthermore, an overwhelming number of cities seem to report moderate levels of snowfall between 13-40 inches as indicated by most of these values lying within that particular section.
To buttress my argument further, I would note how close to its top edge is located the median line for this section. It is apparent that the data exhibits the highest degree of variability during the final quarter, signifying the top 25% of values.
The elongated vertical line extending from the upper end of the box up to the maximum value, which reaches 50 inches, is considerably lengthier than its counterpart at the bottom concluding with a minimum value of 5 inches.
This suggests that there is a greater disparity among snowfall measurements among cities receiving copious amounts.
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Find the missing side of the triangle. Leave your answer in simplest radical form.
O √31 mi
O 2√14 mi
O √106 mi
O √137 mi
The value of x is 2√14 mi
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Therefore, if a and b are the legs of the triangle and c is the hypotenuse, then
c² = a²+b²
here, x and 5 are the legs and 9 is the hypotenuse of the triangle.
therefore;
x² = 9²-5²
x² = 81-25
x² = 56
x = √56
x = √4×14
x = 2√14
Therefore the value of the Missing side is 2√14 mi
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One jar of spaghetti sauce is made with 1/4 of a cup of tomatoes. How many full jars of spaghetti sauce can be made with 3 cups of tomatoes?
Answer:
you can make 12 cans of them
Find the value of x
Answer:
Step-by-step explanation:5.7
Point N is located at (-4,-3) on the coordinate plane. Point N is reflected over the y-axis to create point N'. Point N' is then reflected over the z-axis to create point N". What ordered pair describes the location of N"?
The point (-4, -3) after the reflection across the y-axis and z-axis will be (-4, 3).
Given that:
Point, N(-4, -3)
A point's x-coordinate gets negated but its y-coordinate stays the same when it is reflected across the y-axis. Thus, the point N'(4, -3) would be produced by reflecting point N(-4, -3) across the y-axis.
A point's y-coordinate is negated but its x-coordinate remains unchanged when it is reflected across the z-axis. Thus, the point N"(-4, 3) would be produced by reflecting N'(4, -3) across the z-axis.
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A study is conducted to determine how playing a sport affects a student's overall health and well-being. The study includes 100
high school students on various sports teams. The study includes a survey composed of 5 statements to which students
respond on a scale of 1-5. A response of 5 indicates strong agreement with the statement and a response of 1 indicates
strong disagreement with the statement. The results of the statement, "Participating in a sport helps to improve a person's
ability to prioritize his or her free time," shows an average response score of 3.2 and a standard deviation of 1.2. One
conclusion in the report of the study states that participation in sports markedly improves a student's ability to make good use
of free time.
Which statements regarding the report are true?
Select each correct answer.
A)The report should be considered accurate only if the sample is a stratified sample of students playing sports.
The study is biased since the survey includes only students playing a sport so the report should not be considered
accurate.
B)The report accurately states the results because a mean score of 3.2 is greater than the predicted average of 3 on
the statement regarding prioritizing free time.
C)The report does not accurately interpret the result of the statement regarding prioritizing free time.
D)The report of the study should state that there is a strong correlation between participation in sports and ability to
prioritize free time rather than make a broad conclusion.
The requried, correct statment is shown below,
B) The report accurately states the results because a mean score of 3.2 is greater than the predicted average of 3 on the statement regarding prioritizing free time.
C) The report does not accurately interpret the result of the statement regarding prioritizing free time.
D) The report of the study should state that there is a strong correlation between participation in sports and the ability to prioritize free time rather than make a broad conclusion.
Statement A is not true as it suggests a specific sampling method is necessary for accuracy, which is not necessarily the case. The study can still be accurate if the sample is randomly selected and sufficiently large.
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Please help me with this
The volume of rectangular prism is 90 unit³.
We can consider the 1 block = 1 unit.
Length of prism = 5 unit
width of prism = 6 unit
Height of prism = 3 unit
So, Volume of rectangular prism
= l w h
= 5 x 6 x 3
= 90 unit³
Thus, the volume of rectangular prism is 90 unit³.
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What is the surface area of the cone?
Answer:
V=1/3*pi*radius(to the power of two)*height
Answer: 14 in squared
7.
The lateral area of the triangular prism is [A. 288 B. 336 C. 960]
square inches, and the surface area is [A. 288 B. 336 C. 960] square inches.
8 in.
10 in.
12 in.
The lateral area of the triangular prism is 288 square inches and the surface area is 336 square inches
How to find the lateral area and surface area of a triangular prism?The lateral area of a right triangular prism is given by:
LA = perimeter of base triangle * height
LA = (a + b + c) * h (check attached image for labeling)
where a, b and c are the bases of the rectangular faces and h is the total height of the prism.
a = 10 in, c = 8 in and h = 12 in
b = √(10² - 8²) (Pythagoras)
b = 6 in
LA = (10 + 6 + 8) * 12
LA = 288 square inches
The surface area of a right triangular prism is sum of the areas of the faces that make the prism.
The surface area of a right triangular prism is given by:
SA = (a + b + c)h + bc
SA = [(10 + 6 + 8)*12] + [6 * 8]
SA = 288 + 48
SA = 338 square inches
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Complete Question
Check image
I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer:
Let x be the number of additional outfits.
5 + x < 11
In 1999, the country of Monaco had a population of approximately 32,000 people. The area of the country is approximately 3/4 of a square mile. What was the approximate population density of Monaco in persons per square mile?
The approximate population density of Monaco in persons per square mile in 1999 was 42,666.67.
To calculate the population density of Monaco in persons per square mile, we need to divide the population of Monaco by the area of the country in square miles.
First, we need to convert the area of Monaco from square miles to square feet because the population figure is in persons per square mile.
1 square mile = 5280 feet × 5280 feet = 27,878,400 square feet
So, the area of Monaco in square feet is approximately:
(3/4) × 27,878,400 = 20,908,800 square feet
Now, we can calculate the population density in persons per square mile:
Population density = Population / Area
Population density = 32,000 / (20,908,800 / 27,878,400)
Population density = 32,000 / 0.75
Population density = 42,666.67 persons per square mile (rounded to two decimal places)
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PLEASE HELP
Label all the following values of the box and whisker plot:
You may label the graph or write the approximate values.
Answer:
A= 7
B= 4
C= 10
D= 0
E= 13
answers in attachment below
Evaluate the function below it’s a given output value of 15
f(x)=60/3x+5
The input value that corresponds to an output value of 15 is x = -1/3.
Understanding functionTo find the input value (x) that corresponds to an output value of 15, we need to derive an equation:
15 = 60 / (3x + 5)
Multiplying both sides by (3x + 5), we get:
15(3x + 5) = 60
Expanding the left side, we get:
45x + 75 = 60
Subtracting 75 from both sides, we get:
45x = -15
Dividing both sides by 45, we get:
x = -1/3
Therefore, the input value that corresponds to an output value of 15 is x = -1/3.
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