Answer:
The ratio to represent the relationship between Hallie's donation of blue jeans and Mattie's donation of blue jeans is 4 : 6, or 2 : 3.
The right triangle shown needs to be enlarged such that each side is multiplied by the value of the hypotenuse, 4c. Find the
simplified expression that represents the perimter of the new triangle.
A
B
4c
8c+1
6c+4
C
The simplified expression that represents the perimeter of the new triangle
is 72c² + 20c.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the perimeter of any two-dimensional planer figure is the sum of the lengths of it's all the sides except the circle.
The given perimeter of the right angle triangle is,
= (4c + 6c + 4 + 8c + 1).
= 18c + 5.
Therefore, The new perimeter of the triangle will be,
= 4c(18c + 5).
= 72c² + 20c.
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Identify the probability distribution. A spinner with a yellow, blue, red, and green section is shown. The arrow is pointing at the yellow section. The fair spinner shown is spun 1 time. There are four possible outcomes, one for each color. Based on the picture, which statements are true? The probability of each outcome is equal The probability of each outcome is different. The outcomes have a uniform probability distribution. The outcomes have a nonuniform distribution What is the probability of spinning a yellow? 1 /4 What is the probability of spinning a yellow or a green?
The probability of each outcome is equal, and the outcomes have a uniform probability distribution.
The probability of spinning a yellow is 1/4,
The probability of spinning a yellow or green is 1/2.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given A spinner with yellow, blue, red, and green sections,
total outcomes = 4
and the possibility for occurring of each color is 1,
probability = favorable outcome/total outcome
P(yellow) = 1/4
P(Red) = 1/4
P(blue) = 1/4
P(green) = 1/4
so the probability of each color is equal,
and a probability distribution known as a "uniform distribution" assumes that all possible outcomes are equally likely to occur.
The probability of spinning a yellow or green,
a favorable outcome for a yellow or a green = 2
P( yellow or green) = 2/4 = 1/2
Hence the probability of each outcome is equal and the outcomes have a uniform probability distribution.
and P(yellow) = 1/4, and P( yellow or green) = 1/2.
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\frac{x-5}{x-2}=\frac{8}{9}
Anand bought snacks for his team's practice. He bought a bag of popcorn for $2.65 and a 15-pack of juice bottles. The total cost before tax was $34.45. How much was each bottle of juice?
Answer: $2.12
Step-by-step explanation: Subtract $2.65 from 34.45 and then divide that number by 15.
a sample is a subset of all possible data values for a given subject under consideration.
False. A sample is a subset of all possible data values for a given subject under consideration, not the set of all possible data values.
What is sample space?
The set of all potential outcomes for an experiment is referred to as the sample space S in a random experiment. The results of a random experiment, also known as sample points, are incompatible (i.e., they cannot occur simultaneously).
According to question:A sample is a portion of a larger set of data that is selected for analysis or representation. It is not the entire set of all possible data values for a given subject, but rather a smaller subset chosen for the purpose of study.
Sampling is important because it allows researchers to study and make inferences about a larger population with a smaller, more manageable amount of data.
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Isaac has a total of ninety pennies, nickels, and quarters. He has three and a half times as many quarters as nickels and one-half as many pennies as nickels. How many of each coin does he have?
The equivalent values of the variables {x}, {y} and {z} are -
x = 28.33
y = 29.83
z = 31.83
What is a function?An function in mathematics defines a relationship between one variable (the independent variable {x}) and another variable (the dependent variable {y}). Example -
y = f{x} = ax + b
Given is that Isaac has a total of ninety pennies, nickels, and quarters. He has three and a half times as many quarters as nickels and one-half as many pennies as nickels.
Assume that he has {x} nickels, {y} pennies and {z} quarters.
So, we can write -
z = x + 3.5
y = x + 1.5
x + y + z = 90
Substituting the values of {y} and {z}, we get -
x + x + 1.5 + x + 3.5 = 90
3x + 5 = 90
3x = 85
x = 28.33 .... Eq { 1 }
y = 28.33 + 1.5 = 29.83
y = 29.83 .... Eq { 2 }
z = 31.83 .... Eq { 3 }
Therefore, the equivalent values of the variables {x}, {y} and {z} are -
x = 28.33
y = 29.83
z = 31.83
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the local library has a child section with picture books and chapter books the ratio is 2 to 3 if there are a total of 500 books in childrens sections then how many chapter books are there?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.
If the ratio is 2: 3, (children's section: chapter books) we can use this equation to figure out how many chapter books there are if there are 500 children's section books:
500 × 1.5 = 750Why do we multiply by 1.5?In the ratio 2: 3, 2 is being multiplied by 1.5 to get to 3. If the relationship between the numbers 2 and 500 stays proportional, we multiply 500 by 1.5.
Therefore, the ratio of children's books to chapter books is 500: 750, meaning there are 750 chapter books.
when data are collected in a statistical study for only a portion or subset of all elements of interest we are using a:
When data is collected in a statistical study for only portion or subset of all element of interest we are using a sample.
We frequently collect data from samples, or smaller subsets of the population, as opposed to the entire population as a whole.
A sample is a subset of units chosen to represent all the individuals in the population. Because just a portion of the population was counted, it is only a partial enumeration. To estimate the characteristics for the total population of interest, data from the sampled units is used.
For instance, a medical study looks at how a certain disease spreads among city's stray canines. The population of interest in this case are the city's street dogs. This sample or population of interest corresponds to the overall population on which you want to draw conclusions.
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show the work 5/6 and thank you
The decimal form of the fraction 5 / 6 is 0.84.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the fractional number is 5 / 6.
The decimal form of the number will be calculated by dividing the number 5 by the number 6.
Decimal number = 5 / 6
Decimal number = 0.8333333333333
Decimal number = 0.84
Hence, the decimal form will be 0.84 for the fraction 5 / 6.
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What is the scale factor of the enlargement of shape A to shape B?
HELP PLEASEEEEEEEEEE
Vertex is (7, -6).
Vertex form is y = -9/121 (x + 7)² + 6
Standard form is y = (-9/121)x² - (126/121)x + 285/121
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph,
(4, -3), (10, 3), and (7, -6)
Now,
The vertex form of an equation is y = a(x - h)² + k
From the graph,
The vertex is (-7, 6).
Vertex form.
(-7, 6) = (h, k)
y = a(x - h)² + k
y = a(x + 7)² + 6
Now,
(4, -3) = (x, y)
So,
-3 = a(4 + 7)² + 6
-3 = a x 11² + 6
-3 = 121a + 6
-3 - 6 = 121a
a = -9/121
Now,
y = a(x + 7)² + 6
y = -9/121 (x + 7)² + 6
y = -9/121 (x² + 14x + 49) + 6
y = (-9/121)x² - (9/121 x 14)x - 9/121 x 49 + 6
y = (-9/121)x² - (126/121)x - 441/121 + 6
y = (-9/121)x² - (126/121)x + 285/121
This is the standard form.
Thus,
Vertex form is y = -9/121 (x + 7)² + 6
Standard form is y = (-9/121)x² - (126/121)x + 285/121
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I need some help with this question
Answer:
1/15
Step-by-step explanation:
If you divide all the fractions, only 1/15 has a repeating decimal. Hope you pass, Alyssa
At hockey practice, Ajay saved 73 out of the 126 shots on goal. At this pace, how many saves would he make out of 200 shots on goal?
We have two fractions, 3/4 and 7/6, and we want to rewrite them so that they have a common denominator (and whole number numerators).
What numbers could we use for the denominator?
Choose 2 answers: a) 24 b) 12 c) 18 d) 8 HURRY PLSSS!!!!
Answer:
A & B
Step-by-step explanation:
24 and 12 are both multiples of 4 & 6
the population of a city increases by 2.5% each year. how many years , to the nearest tenth, will it take until the population if the city increases from 120000 people to 180000 people?
To find the number of years it will take for the population of a city to increase from 120000 to 180000, we need to use the formula:
Years = log (target population / starting population) / log (1 + annual growth rate)
Where the annual growth rate is 2.5% or 0.025.
Plugging in the values, we get:
Years = log (180000 / 120000) / log (1 + 0.025)
Years = log (1.5) / log (1.025)
Years = 7.36 years
Rounding to the nearest tenth, we get:
Years = 7.4 years
So it will take approximately 7.4 years for the population of the city to increase from 120000 to 180000 people, assuming a constant annual growth rate of 2.5%.
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how to find the volume of the solid generated by revolving ?
The solid's volume will be determined by rotating the area enclosed by the specified curve and the lines y = 2x, y = 2, and x = 0 around the x-axis.
V = 8π/3
Volume integration: What is it?
We refer to an integration as a volume integration when it is carried out in three dimensions using the three variables x, y, and z.
In order to establish my integration borders, I set y=2x y=2 to determine their intersection point.
Your aim is to locate the region so you can settle there. The region is going to be circular because we are rotating around the x-axis.
V = (r2)dr = A(x)dx
We subtract the two radiuses from one another since they are different.
∫(πr₂² - πr₁²)dr
∫(π(2)² - π(2x)²)dr
∫(4π - 4πx²)dr
4π∫(1 - x²)dr
Since our boundary is at 1, integrate between 0 and 1.
V = 4π∫(1 - x²)dr = 8π/3
Therefore, V = 8/3 will be the volume of the solid produced by rotating the area enclosed by the specified curve and lines y = 2x, y = 2, and x = 0 about the x-axis.
What Does a Solid's Volume Mean?
The amount of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid is used to calculate it.
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Among fatal plane crashes that occurred during the past 70 years, 503 were due to pilot error, 90 were due to other human error, 326 were due to weather, 382 were due to mechanical problems, and 643 were due to sabotage.What is the most serious threat to aviation safety, and can anything be done about it?
A. Sabotage is the most serious threat to aviation safety. Airport security could be increased.
B. Mechanical problems are the most serious threat to aviation safety. New planes could be better engineered.
C. Weather is the most serious threat to aviation safety. Weather monitoring systems could be improved. D. Pilot error isPilot error is the most serious threat to aviation safety. Pilots could be better trained.
Sabotage is the most serious threat to aviation safety. Airport security could be increased.
The relative normal probability plot of aeroplane crashes is derived by using its concept:
Error of the pilot: 503/1944 = 0.258.
90/1944 erroneous by humans: 0.046.
326/1944 = 0.167 for weather.
issues with the mechanics: 382/1944 = 0.196.
643/1944 = 0.330 sabotage.
Sabotage provide the chief concern as a result of the higher relative frequency; therefore, airport security could be increased.
Define Relative Frequency.
The number of desired outcomes divided by the total number of outcomes yields a relative frequency.
The total number of accidents in this problem is provided by:
503+90+326+382+643 = 1944
Following are the relative frequencies of each cause:
Error of the pilot: 503/1944 = 0.258.
90/1944 erroneous by humans: 0.046.
326/1944 = 0.167 for weather.
issues with the mechanics: 382/1944 = 0.196.
643/1944 = 0.330 sabotage.
Due to Sabotage provide the greatest concern as a result of the increased relative frequency; therefore, airport security should be increased.
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Can someone please help me with this parallelogram proof
prove angle LMN is congruent to NPL ; PLM is congruent to MNP
Opposite angles are equal in a parallelogram.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Given is a parallelogram LMNP which is attached below.
Consider ΔLMP and ΔNMP.
MP = MP, common side.
LM and NP are parallel lines.
∠NPM = ∠LMP, alternate interior angles.
Also ∠LPM = ∠NMP, alternate interior angles.
By the ASA congruence rule, both the triangles ΔLMP and ΔNMP are congruent.
So ∠PLM congruent to ∠MNP.
Similarly, by considering the triangles ΔLNP and ΔLMN, we can prove that angle LMN is congruent to NPL by similar steps.
Hence the opposite angles of a parallelogram are equal.
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The perimeter of the rectangle below is 128 units. Find the length of side CD. Write your answer without variables. 3x + 3 C 4x - 2 B CD =
The length CD of the rectangle is 34 units
How to determine the length CDFrom the question, we have the following parametes that can be used in our computation:
The perimeter of the rectangle below is 128 units
This means that
2 * (3x + 3 + 4x - 2) = 128
So, we have
7x + 1 = 64
Evaluate the like terms
7x = 63
This gives
x = 9
Recall that
CD = 4x - 2
So, we have
CD =4 * 9 - 2
CD = 34
Hence, the length is 34 units
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please help me. it’s a practice assignment and i don’t know what to do.
This equation cannot be solved as e to the power of any number cannot be negative. The population of a town cannot be negative. Hence, the population cannot reach 60,000.
Why do you say so ?To approximate the number of years it will take for the population to reach 40 thousand using the graph, you can look at the x-axis and visually estimate the point where the population line intersects with the 40,000 line. It looks like this will occur around year 25.
To find the number of years it will take for the population to reach 60 thousand without using the graph, you can set up the equation p(n) = 18 - e = 60,000 and solve for n.
p(n) = 18 - e = 60,000
18 - e = 60,000 + e
36 = 120,000
e = -84,000
n = log(-84,000)/log(e)
This equation cannot be solved as e to the power of any number cannot be negative. The population of a town cannot be negative. Hence, the population cannot reach 60,000.
What is data integration ?Data integration is the process of combining data from multiple sources into a single, coherent view. This can involve the merging of data from multiple databases, files, or other data storage systems into a centralized repository, or it can involve the creation of a new, unified dataset from disparate sources. The goal of data integration is to provide a single version of the truth by removing duplicates, inconsistencies, and errors, and providing a comprehensive, accurate, and up-to-date view of all relevant data. Data integration is a critical step in many data management and analytics processes and is important for ensuring the reliability and usefulness of data for decision-making.
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How can data displays be used to compare populations?
The data displays be used to compare populations as
(i)they quickly illustrate measures of center
(ii)they show trends in data that can be compared.
Data Display is basically displaying of useful data which has been extracted from bundles of raw data or raw data points. That useful data can be used to compare two different datasets as well.
It says that it quickly illustrate measures of centre. True, because it presents you quick display so that everyone seeing the data in form of charts or tables easily catch the information to be conveyed.
It says, they show trends in data that can be compared. Yes again true. Data displays show you trends of different things in one clear picture and it can be compared with other datasets through the use of data displays.
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A gardener wants to fence a circular garden of diameter 35 m. Find the length of the rope he needs to purchase, if he makes 5 rounds of fence. Find the cost of the rope if it costs 20 per metre. (==)
Answer:
Below
Step-by-step explanation:
Circumference (distance around) a circle = pi * diameter
= 3.14 * 35 m = 109.9 m
FIVE of these would be 109.9 * 5 = 549.5 meters
at 20 per meter would be 549.5 * 20 = 10 990 (units)
RS=27. Find QS.
I been trying my hardest to get the answer
The length of the Line segment QS is; QS = 63
How to find the length of the line segment?From the given diagram attached which is a straight line segment, we can see that;
QR = 9x
RS = 12x - 21
We are told that the length of line segment RS = 27. Thus;
12x - 21 = 27
12x = 27 + 21
12x = 48
x = 48/12
x = 4
Thus;
QR = 9*4 = 36
RS = 12(4) - 21
RS = 27
Thus, we can say that;
QS = 36 + 27
QS = 63
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Terri will be able to purchase a condominium by making a 5% down payment on its 64,000 purchase price. she estimates her closing costs to be 3.5% of the purchase price.
Terri will need a total cash of $66,240 where $3200 is the down payment and $2240 is the closing cost.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Percentage is usually denoted by the symbol '%'.
1. Purchase price = $64,000
Percent of down payment = 5% of purchase price
Amount of money needed to pay down payment = 64,000 × 5%
= 64,000 × 0.05
= $3200
2. Purchase price = $64,000
Percent of closing cost = 3.5% of purchase price
Amount of money needed to pay closing cost = 64,000 × 3.5%
= 64,000 × 0.035
= $2240
3. Down payment is included in the purchase price.
Closing cost is in addition to the purchase price.
Total cash needed = $64,000 + $2240 = $66,240
Hence the total cash needed to purchase condominium is $66,240.
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in bioengineering, the adhesion of various biofilms to solid surfaces for possible use in environmental technologies is studied. adhesion assay is conducted by measuring absorbance. suppose that for the bacterial strain acinetobacter, five measurements gave readings of 2.69, 5.76, 2.67, 1.62, and 4.12 dyne-cm2. assume that the standard deviation is known to be 0.66 dyne-cm2. a. find a 95% confidence interval for the mean adhesion. b. if the scientists want the confidence interval to be no wider than 0.55 dyne-cm2, how many observations should they take? problem 3 a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the
As per the given data, the required confidence interval is (2.79) or (3.95) and the required sample size is 22.
The table which shows the calculation for mean and sd is attached below the answer ;
Given that :-
The sample mean is X = ∑x/n = 3.372
Sample standard deviation = √∑(x- X)² /√n-1 = 1.6
and the population standard deviation (σ) = 0.66
(a).
For 95% conifdence interval z-critical value is 1.96. A 95% confidence interval for the mean adhesion is :-
= X ± [tex]Z_{c}[/tex] • σ/√n
= 3.72 ± 1.96 • 0.66/√5
= 3.72 ± 0.5785
= (3.72 + 0.57) or (3.72 - 0.57)
= (2.79) or (3.95)
Hence, the required confidence interval is (2.79) or (3.95).
(b).
Here we have, E = 0.55/2 = 0.275
so, the required sample size (n) = [tex]Z^{2}_{c}[/tex] • σ²/ E²
(n) = 1.96² • 0.622²/0.275²
(n) = 22.13
Hence, the required sample size is 22(approx).
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------------- Correct format of the question is given below ------------
(Q). Ishikawa et al. (Journal of Bioscience and Bioengineering, 2012) studied the adhesion of various biofilms to solid surfaces for possible use in environmental technologies. Adhesion assay is conducted by measuring absorbance at A590. Suppose that for the bacterial strain Acinetobacter, five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm2. Assume that the population standard deviation is known to be 0.66 dyne-cm2, and the population distribution is normal.
(a) Find a 95% confidence interval for the mean adhesion.
(b) If the scientists want the confidence interval to be no wider than 0.55 dyne-cm2, how many observations should they take? (Note that, the width of the confidence interval is two times the margin error E, so E = 0.55/2).
when the measurement scale provides information regarding greater than or less than, but not how much greater or less, it is in the form of
When the measurement scale provides information regarding greater than or less than, but not how much greater or less, it is in the form of ordinal data.
Ordinal data is a type of categorical data, which is a type of data that fits into discrete categories, such as gender, or levels of education. Ordinal data does not provide numerical values for comparison, only information on the order of the categories.
For example, a survey may ask respondents to rate their opinion of a product on a scale of one to five. The scale provides information on the order of the categories (one being least favorable and five being most favorable), but it does not provide numerical values that can be used to calculate the average opinion of the product.
Mathematically, ordinal data is usually represented using an ordered set of numbers, with each number representing the order of the categories. For example, the survey mentioned above would be represented this way: 1, 2, 3, 4, 5. This set of numbers can then be used to calculate the median, mode, and range of the data. For example, the median value of the example survey would be 3, the mode would be 5, and the range would be 4 (5 - 1 = 4).
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Given the following summary statistics, determine the regression equation used to predict y from x. Sy= 2.33, Sx 2.35, r= 0.25, x- = 22.85, y -=77.34. Round all answers to 2 decimal places. Slope (Please use the exact value of slope.) Intercept
The regression equation used to predict y from x is: y = -2.93x + 95.45. The slope of the regression line is -2.93 and the intercept is 95.45.
Regression analysis is a process used to estimate the relationship between two or more variables. It is used to examine the strength of the relationship between a response variable (y) and one or more predictor variables (x).
The coefficients of the regression equation are estimated by minimizing the sum of squared errors between the predicted and actual values of y. The strength of the relationship is indicated by the coefficient of correlation (r), which is a measure of how closely the data points fit the regression line.
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Solve by square root. (X-8)*2-7=25 *2 is an exponent
The solution is X =13.66.
What is Square root?A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
here, we have,
given that,
(X-8)^2-7=25
(X-8)^2= 25+7
(X-8)^2=32
by, thaking sq.root both side we get,
(X-8)= √32
X= 5.66+8
X =13.66
Hence, The solution is X =13.66.
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Find b.
O 35
O 55
O 72.5
O 90
Check the picture below.
so by the "inscribed angle theorem" that means "c" is half of 70°, and by Thales Theorem "a" is a right-angle, btw that can also be derived by the "inscribed angle theorem", that makes angles "b" and "c" complementary angles.
what is three minus 1third
Answer: 1/9
Step-by-step explanation:
Answer:
3 - 1/3 = 2 2/3
if you take 1/3, then you can just take 1 from 3 for a moment, and then add it back, as shown:
1 - 1/3 = 2/3
Then just add it back:
2/3 + 2 = 2 2/3
Step-by-step explanation:
Hope it helps! =D