Answer: (a-b+c)²-(b-c+a)²
=((a-b+c)) - ((b-c+a)) ((a-b+c)) - ((b-c+a))
= (a-b+c-b+c-a) ( a-b+c+b-c+a)
= (-2b + 2c ) (2a)
= (2( -2b/2+2c/2)) (2a)
=(2(-b+c)) (2a)
=2(-b+c) (2a)
A company charges $7 for a t-shirt and ships any order for $22. a school principal ordered a number of t-shirts for the school store. the total cost of the order was $1,520. how many t-shirts did the principal order?
The total number of t-shirts principal ordered in $1520 for the school store is given 214.
Let us consider the number of t-shirts the principal ordered be equal to 'x'.
The cost of each t-shirt is equal to $7.
⇒ The total cost of 'x' t-shirts = 7x dollars.
Shipping cost is a flat rate for any order, regardless of the number of t-shirts = $22
Total cost of the order (including shipping) = $1520.
Required equation is equal to,
7x + 22 = 1520
Subtract 22 from both sides of the equation we get,
⇒ 7x = 1498
Divide both sides of the equation by 7 we get,
⇒ x = 214
Therefore, the number of t-shirts ordered by principal for the school store is equal to 214.
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Gardening is planting a garden. It has the shape of a right triangle. Wants plants for each square of area. How many plants does want in the garden? 7 yards 24 yards 25 yards
The garden would require 84 plants, which is the same number of plants as the garden's surface area.
The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.
Area of the garden = (1/2) x Base x Height
Area of the garden = (1/2) x 7 x 24
Area of the garden = 84 square yards
Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.
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the volume of a cube (in cubic inches) plus three times the total length of its edges (in inches) is equal to twice its surface area (in square inches). how many inches long is its long diagonal? express your answer as where is a prime number. find .
The length of the long diagonal of the cube is 3sqrt(3) inches.
Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).
Using the given equation, we can write
a^3 + 3(12a) = 2(6a^2)
Simplifying this equation, we get
a^3 + 36a = 12a^2
a^3 - 12a^2 + 36a = 0
a(a^2 - 12a + 36) = 0
a(a - 6)^2 = 0
The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.
To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".
Using the Pythagorean theorem, we can write
d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2
d^2 = 3(6^2)/4
d = (sqrt(3)×6)/2
d = 3sqrt(3) inches
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Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails. To the nearest percent, what is the experimental probability of Project A?
Answer:
Step-by-step explanation:
Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails.
To the nearest percent, what is the experimental probability of Project B?
The experimental probability of Project A is 0.53.
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
As per the given data:
We are given that there are two projects, Project A and Project B.
A student has to choose one out of the two projects and, the student's choice is represented by the flip of a coin where heads representing Project A and tails representing Project B.
Head's = Project A
Tail's = Project B
Total number of trials = 110
Number of heads in the trials = 58 heads
Number of tails in the trials = 52 tails
For finding out the experimental probability of Project A:
= Number of favorable outcomes / Total number of trials
Number of favorable outcomes = Number of heads
= Number of heads / Total number of trials
= 58 / 110
= 0.53 (approx)
The experimental probability of Project A is 0.53.
Hence, The experimental probability of Project A is 0.53.
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what is the answer for 239.3 x 55
Answer:
13,161.5
Step-by-step explanation:
5x3= 15 then go over and carry the one then do 5x9= 45+1= 46 then go over to 3 and carry the four and 5x3= 15+4= 19 put 9 down and carry the one then 5x3= 10+1= 11 after x the 0 the repeat what you did and add up the final numbers so 239.5x 55= 13161.5
the goal of the calculating an acceptance interval is to: a. find the probability that the true mean lies between two values. b. determine a range within which sample means are likely to occur, given a population mean and variance. c. determine a range within which no sample means would occur, given a population mean and variance. d. none of the above.
The goal of calculating an acceptance interval is to find the probability that the true mean lies between two values, hence the correct answer is option a.
The acceptance interval is a method for developing a tolerance interval for a specified percentage of future measurements in a distribution. The tolerance interval specifies the interval into which a specified percentage of future measurements will fall.
An acceptance interval is a quality control tool for assessing whether the characteristics of a production lot meet predetermined quality criteria. These predetermined criteria are usually in the form of upper and lower limits for the interval.
The acceptance interval is utilized to detect whether a production lot's results are within the tolerances or specifications of the quality criteria.
The purpose of calculating an acceptance interval is to locate the probability that the true mean falls between two values. In conclusion, the goal of calculating an acceptance interval is to find the probability that the true mean lies between two values.
Therefore, option a is the correct answer.
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the probability that the splices in a rope splicing shop are weak is 1/1000 and the probability that the splices are ugly is 1/20. the probability that the weak splices are ugly is 2/3. find the probability that an ugly splice is weak.
The probability that an ugly splice is weak is 2/3.
This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).
In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).
The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.
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PLS HELP! WILL MAKE U BRAINLIST!
Find the point of intersection using substitution. DO NOT USE ANOTHER METHOD. Show all your thinking.
Answer:
(-2,-3)
Step-by-step explanation:
3x+y=-9
-3x -3x
y=-3x-9
5x-3(-3x-9)=-1
14x+ 27= -1
-27 -27
14x= -28
/14 /14
x=-2
plug in x
3(-2)+y=-9
-6+y=-9
+6 +6
y=-3
the support for a basketball hoop forms a right triangle as shown. what is the length, x, of the horizontal portion of the support?
According to Pythagorean Theorem, The length of the horizontal portion of the support, x, is 3.87 feet.
The length of the horizontal portion of the support, x, can be determined by using the Pythagorean Theorem. The Pythagorean Theorem states that a2 + b2 = c2, where a and b are the sides of a right triangle and c is the hypotenuse.
In this case, a = 7 feet, b = x, and c = 8 feet. We can use the Pythagorean Theorem to solve for x: 72 + x2 = 82, or 49 + x2 = 64. This can be solved for x to get x2 = 15 and x = √15 ≈ 3.87 feet.
Therefore, the length of the horizontal portion of the support, x, is 3.87 feet.
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Please help! Im a struggling depressed student that needs to desperately catch up.
Answer:
25%
Step-by-step explanation:
30/120 = 1/4
1/4 = 25%
what are coordinate planes explain:
Answer:
a two-dimension surface formed by two number lines.
a sample survey is to be conducted to determine the mean family income in an area. the question is how many families should be sampled? in order to get more information about the area, a small pilot survey was conducted, and the standard deviation of the sample was computed to be $400 with the mean of $60,000. the sponsor of the survey wants you to use the 0.99 degree of confidence. the estimate is to be within $90. how many families should be interviewed?
The sample size required is 182 families should be interviewed.
To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.
Sample size formula: n = (Z² * s²) / E²
The formula for the degree of confidence: Z = 2.576
Sample size formula: n = (Z² * s²) / E²
Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.
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question 2 theorem: if r and s are rational numbers, then the product of r and s is a rational number. which facts are assumed in a direct proof of the theorem?
In a direct proof of the theorem "if r and s are rational numbers, then the product of r and s is a rational number," the following assumptions or facts are typically used:
Definition of rational numbers: A rational number is defined as any number that can be expressed as the ratio of two integers.Closure property of rational numbers under multiplication: When two rational numbers are multiplied, the result is always a rational number.Properties of integers: When two integers are multiplied, the result is always an integer.Properties of fractions: When two fractions are multiplied, the result is obtained by multiplying their numerators and denominators separately.Using these facts, a direct proof of the theorem can be constructed by assuming that r and s are rational numbers and then showing that their product is also a rational number. Specifically, we can express r and s as fractions with integer numerators and denominators, multiply their numerators together to obtain the numerator of the product.
Since the numerator and denominator of the product are both integers, and the denominator is nonzero, the product is a rational number.
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The length of a rectangular porch is (x + 7) feet. The area of the porch is (x² + 9x + 14) square feet. Factor the expression for the area in order to find an expression for the width of the porch.
We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
area of a rectangle
Area = length x width
To do this, we can factor the expression for the area, which gives us:
x² + 9x + 14 = (x + 2)(x + 7)
Area = length x width
(x + 2)(x + 7) = (x + 7) x width
x + 2 = width
Therefore, the expression for the width of the porch is x + 2 feet.
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Nhan is getting dressed. He considers two different shirts, three pairs of pants, and three pairs of shoes. He chooses one of each of the articles at random. What is the probability that he will wear his jeans but not his sneakers?
Shirt
Pants
Shoes
collared
khakis
sneakers
T-shirt
jeans
flip-flops
shorts
sandals
Please HELP ME HELPPPPP
Answer:
bar chart
Step-by-step explanation:
you are right box plot, histogram and a circle graph aren't the right ones
10 ft
20 ft
15 ft
Find the area.
A = [?] ft²
Round to the nearest
hundredth.
The total area of the composite figure is 114.25 square feet.
How to find the area of the shape?The area of a circle of diameter D is:
A = 3.14*(D/2)²
And the area of a triangle of base B and height H is:
A = B*H/2
We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:
A = 10ft*15ft/2 = 75ft²
And half of a circle of diameter of 10ft, whose area is:
A = 0.5*3.14*(10ft/2)² = 39.25 ft²
Then the total area of the figure is:
area = 75ft² + 39.25 ft² = 114.25 ft²
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Which of these investments would be considered high-risk?
Stocks
Pension Plans
Certificate of Deposit
Annuities
Answer: Stocks
Step-by-step explanation: People mainly live on wim's so stocks at times can be unpredictable.
Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Let m represent the monthly cost.
Solving a linear equation we can see that the answer is 40 months.
How many months is it until your cost is the same as Plan A's?We know that company A only charges $70 per month, so the cost in dollars after x months is given by the linear equation:
A(x) = 70*x
For company B you need to pay $50 per month plus the $500 phone, so here the cost is:
B(x) =500 + 50*x
We want to find for what value of x we have B(x) = A(x), then we needto solve:
70x = 500 + 50x
70x - 50x = 500
20x = 500
x = 500/20
x = 40
After 40 months the cost will be the same one than in company A.
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If the area of a bookshelf is 216 in.² if the length of the bookshelf is 36 inches what is the width of the bookshelf
The width of the bookshelf will be 6 inches when the area and length are 216 in and 36 inches.
What is the width?
Width is a dimension of a geometrical figure that tells about the structure of the figure. In general, width is used to measure the object.
What is formulae of width?
Width is obtained by dividing area and length.
W=A/L
substitute values, 216/36= 6inches.
The width is gonna be 6 because all you have to do is divide 216 and 36
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which statistical method could a scientist use to estimate the strength of evidence that a particular node in a phylogeny exists?
A scientist can use bootstrap analysis to estimate the strength of evidence that a particular node in a phylogeny exists.
Bootstrap analysis is a statistical method used to determine the reliability and robustness of phylogenetic trees' topologies. In bootstrap analysis, a series of random resampling with replacement is used to assess how well the observed data fit the phylogenetic hypothesis.
Bootstrap values range from 0 to 100 and reflect the proportion of times that a particular node or branch occurs in the bootstrap replicate trees. Bootstrap values greater than 70% are usually considered strong evidence that a particular node or branch exists in the phylogenetic tree.
Bootstrap analysis is an important tool for understanding the reliability of phylogenetic trees and the evolutionary relationships among organisms.
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.a semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. find the height of the arch at a distance of 1.5 m from the center of the arch.
The height of the arch at a distance of 1.5 meters from the center is approximately D. 1.73 meters
The shape of a semi-elliptical arch can be described by the equation:
y = c * sqrt(1 - (x/a)^2)
where "a" is half the span of the arch, "c" is the central height of the arch, and (x,y) are the coordinates of a point on the arch, measured relative to the center of the arch.
In this case, we have a span of 6 meters, so a = 3 meters. The central height of the arch is 2 meters, so c = 2 meters. We want to find the height of the arch at a distance of 1.5 meters from the center, so x = 1.5 meters.
Substituting these values into the equation, we get:
y = 2 * sqrt(1 - (1.5/3)^2)
y = 2 * sqrt(1 - 0.25)
y = 2 * sqrt(0.75)
y = 2 * 0.866
y = 1.732
Therefore, the height of the arch at a distance of 1.5 meters from the center is approximately 1.73 meters. Answer D
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Your question is incomplete, but probably the complete question is :
A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
A. 1.41 m C. 1.56 m
B. 1.63 m D. 1.73 m
Solve the equation x² = 4.
Do u know what is x ?
Answer:
x= 2
Step-by-step explanation:
² means times the number itself 2 times.
2×2=4
bisphenol a in your soup cans: is this a randomized comparitive experiment or a matched pairs experiment?
The study described in the question is a randomized crossover trial, where each participant serves as their own control by receiving both treatments in a randomized order
In a matched pairs experiment, each subject is paired with another subject who is similar in some relevant characteristic, and one subject receives the treatment while the other serves as a control. The two subjects in each pair are matched on this characteristic to reduce the effect of confounding variables.
In contrast, a randomized crossover trial is a type of experiment in which each participant receives both treatments (in this case, canned soup and fresh soup) in a randomized order, with a washout period between the treatments to minimize carryover effects. In this study, the participants were randomly assigned to either start with canned soup or fresh soup and then switched to the other treatment after a two-day break. Each participant thus serves as their own control, and the difference in outcome between the two treatments is compared within each individual.
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The given question is incomplete, the complete question is:
Bisphenol A in Your Soup Cans Bisphenol A (BPA) is in the lining of most canned goods, and recent studies have shown a positive association between BPA exposure and behavior and health problems. How much does canned soup consumption increase urinary BPA concentration? That was the question addressed in a recent study1 in which consumption of canned soup over five days was associated with a more than 1000 % increase in urinary BPA. In the study, 75 participants ate either canned soup or fresh soup for lunch for five days. On the fifth day, urinary BPA levels were measured. After a two-day break, the participants switched groups and repeated the process. The difference in BPA levels between the two treatments was measured for each participant. The study reports that a 95 % confidence interval for the difference in means (canned minus fresh) is 19.6 to 25.5 ?g/L. 1Carwile, J., Ye, X., Zhou, X., Calafat, A., and Michels, K., ‘‘Canned Soup Consumption and Urinary Bisphenol A: A Randomized Crossover Trial,” Journal of the American Medical Association, 2011; 306(20): 2218–2220.Is this a randomized comparative experiment or a matched pairs experiment?
4. Financial Literacy Tickets to a play cost $10 for
members and $24 for nonmembers. Write an expression
to find the total cost of 4 nonmember tickets and
2 member tickets. Then find the total cost. (Example 6)
H
the total cost of 4 nonmember tickets and 2 member tickets would be $116.
Why it is and what is financial literacy?
The expression to find the total cost of 4 nonmember tickets and 2 member tickets would be:
4($24) + 2($10)
This expression represents the cost of 4 nonmember tickets at $24 each, and 2 member tickets at $10 each.
To find the total cost, we simply need to evaluate this expression using basic arithmetic:
4($24) + 2($10) = $96 + $20 = $116
Therefore, the total cost of 4 nonmember tickets and 2 member tickets would be $116.
Financial literacy is the knowledge and skills required to manage one's personal finances effectively. It encompasses a range of topics, including budgeting, saving, investing, managing debt, understanding financial products such as credit cards and loans, and planning for retirement. Financial literacy also involves an understanding of financial concepts such as interest rates, inflation, and risk management.
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What is the vertical distance between (2, 11/3)
and (2, - 4/3)?
The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.
Define distance formulaThe distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:
d = √((x₂- x₁)²+ (y₂ - y₁)²)
The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.
The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:
Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)
= (-4/3) - (11/3)
= -15/3
= -5
Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.
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Patrick owns a business that makes chandeliers. He wants to make
greater than 470 chandeliers. The company made 163 chandeliers so
far. If 10 chandeliers can be made in an hour, how long will it take to
reach Patrick's goal?
Write a two-step inequality, using the values provided in the problem,
that represents this situation. Use x as the variable.
Patrick's goal will reached by 30.7 hours
The inequality is 163 + (10x) > 470
How to write the inequalityLet's use x to represent the number of hours it will take to reach Patrick's goal.
First step: The total number of chandeliers made must be greater than 470.
163 + (10x) > 470
Second step: Solve for x by isolating it on one side of the inequality.
10x > 307
x > 30.7
Therefore, it will take more than 30.7 hours to reach Patrick's goal of making greater than 470 chandeliers.
The inequality can be written as: 163 + (10x) > 470
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suppose that the number of log-ons to a computer network follow a poisson process with an average of three counts per minute, a. what is the mean time between counts? b. what is the standard deviation of the time between counts?
a) Mean time between counts is 0.3333 minutes.
b) Standard deviation of time between counts is 0.5774 minutes.
a. Mean time between counts: The mean time between counts can be computed as the inverse of the Poisson rate parameter (λ): Mean time between counts = 1/λ.
The average of 3 counts per minute is the same as the rate parameter λ in a Poisson process. Thus, the mean time between counts is: Mean time between counts = 1/λ = 1/3 = 0.3333 minutes (20 seconds approximately).
b. Standard deviation of the time between counts: The standard deviation of a Poisson process is equal to the square root of the mean.
Therefore, the standard deviation of the time between counts can be calculated as follows: Standard deviation of time between counts = sqrt(mean) = sqrt(1/λ) = sqrt(1/3) = 0.5774 minutes (approximately 35 seconds).
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bobby has 37 pineapples and johnny has 35 times more pineapples than bobby. how many more pineapples does johnny have than bobby?
Johnny has 1258 more pineapples than Bobby.
Bobby has 37 pineapples, Johnny has 35 times more pineapples than Bobby. To find how many more pineapples does Johnny have than Bobby, we can use the below formula,
More pineapples = Johnny's pineapples - Bobby's pineapples
Let x be the number of pineapples that Bobby has. Therefore, the number of pineapples owned by Johnny is 35x.
It is given that Bobby originally has 37 pineapples, thus x = 37. The number of pineapples Johnny has = 35*37 = 1295
Thus, difference in number of pineapples between Johnny and Bobby:
=1295-37 = 1258
Therefore, Johnny has 1258 more pineapples than Bobby.
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g suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. you find an individual that reads 46.2 word per minute. you do some research and determine that the reading rates for their grade level are normally distributed with a mean of 85 words per minute and a standard deviation of 22 words per minute. a. at what percentile is the child's reading level (round final answer to one decimal place).
This shows that they read less frequently than 95.7% of their classmates in the same grade level.
what is percentile ?In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.
given
We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.
z = (x - μ) / σ
where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.
Inputting the values provided yields:
z = (46.2 - 85) / 22
z = -1.727
We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.
As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).
This shows that they read less frequently than 95.7% of their classmates in the same grade level.
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