We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal. AB = 8cm ; BC = 6.5 cm.
Determine the area ?We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal.
The formula for calculating the area of a circle is [pi r 2], which we should keep in mind. With respect to a rectangle, there is only one such circle.The Pythagorean theorem states that the diagonal of a rectangle with sides lengths a and b is equal to a2 + b2.
The radius is simply a2+b22 since the diagonal has a diameter.Keep this response on hand.
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
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the breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. what is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9950 and 10,250?
So, on solving the provided question, we can say that the probability will be P( -1.26 <Z<2.53) => P( Z < 2.53)
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
the probability will be
mean = 10,000
standard deviation = 500
for point a -
n = 40
u = 10,000
P( 9,900 < x < 10,200)
P( -1.26 <Z<2.53)
P( Z < 2.53)
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airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. what is the individual?
airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. then In this situation of statistics , individual is the cases are the bags or each piece of baggage.
What is a case?
In statistics, the word case is used to refer to the individual from which data is collected. For example, in a study about students' performance, the cases are each of the students.
What is the case in this situation?
Considering the administrators will need to weight and record each bag, the cases are each piece of baggage.
A. Number of bags weighing more than 75 pounds.
B. Average weight of the bags.
C. Each piece of baggage.
D. The airport administrators.
Hence airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. then In this situation of statistics , individual is the cases are the bags or each piece of baggage.
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What are the 4 solutions?
The four solutions in math include algebraic solutions, geometric solutions, numerical solutions, and analytical solutions.
1. Algebraic solutions involve solving equations with variables and operations such as addition, subtraction, multiplication, and division.
2. Geometric solutions involve visualizing shapes and solving problems related to angles, lines, and shapes.
3. Numerical solutions involve using numbers and operations such as addition, subtraction, multiplication, and division to solve problems.
4. Analytical solutions involve using logic and reasoning to solve problems. This may involve using diagrams, graphs, and other visual tools to help solve a problem.
The four solutions in math include algebraic solutions, geometric solutions, numerical solutions, and analytical solutions. Algebraic solutions involve solving equations with variables and operations, geometric solutions involve visualizing shapes and solving problems related to angles, lines, and shapes, numerical solutions involve using numbers and operations to solve problems, and analytical solutions involve using logic and reasoning to solve problems with the help of diagrams, graphs, and other visual tools.
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What is called absolute?
The exact value of a number is often what is meant when the word absolute is used in mathematics.
The absolute value of a number is often what is meant when the word absolute is used in mathematics. For mathematicians, knowing the absolute value is essential. To display a number's absolute value, vertical bars are placed on either side of the number. The absolute value on a number line denotes separation from zero.
The absolute value of a negative number is a positive number. The absolute value of one positive number is equal to that of another positive number. No matter what its sign, a number's absolute value is always its non-negative value. For instance, 5 is also the absolute value of 5, as is the absolute value of -5.
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(100 POINTS)
Multiple Qustions.
What are the Answers?
(List all the correct ones below)
Answer:
Options 3 and 4 are correct-------------------------------------
Simplify each expression and compare with the given answer:
1) 3/8 × 54 = 3/4 × 27 = 81/4 = 20 1/4
This is not matching the given answer, so FALSE2) 5/12 × 26 = 5/6 × 13 = 65/6 = 10 5/6
This is not matching the given answer, so FALSE3) 11/15 × 20 = 11/3 × 4 = 44/3 = 14 2/3,
Matching the given answer, TRUE4) 3/8 × 48 = 3 × 6 = 18
Matching the given answer, TRUE5) 7/12 × 48 = 7 × 4 = 28,
This is not matching the given answer, so FALSE[tex]y=x^{2} +4x-2[/tex]
(PLS HELP!!!)
Divide.
(6x²+19x+10) ÷ (3x+2)
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
a teacher has two large containers filled with blue, red, and green beads. he wants his students to estimate the difference in the proportion of red beads in each container. each student shakes the first container, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. the student repeats this process for the second container. one student sampled 13 red beads from the first container and 16 red beads from the second container. assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container?
Answer: Assuming the conditions for inference are met, we can use the difference in proportions of red beads in the two samples to estimate the difference in proportions of red beads in the population. The 95% confidence interval for the difference in proportions of red beads in the two containers is calculated as follows:
Difference in sample proportions = p1 - p2 = (13/50) - (16/50) = -0.03
Standard error of the difference in sample proportions = sqrt{(p1*(1-p1)/n1) + (p2*(1-p2)/n2)} = sqrt{(13/50)(37/50)/50 + (16/50)(34/50)/50} = 0.079
Margin of error = z* * standard error of the difference in sample proportions = 1.96 * 0.079 = 0.155
95% Confidence interval for the difference in proportions of red beads in the two containers = (difference in sample proportions - margin of error, difference in sample proportions + margin of error) = (-0.03 - 0.155, -0.03 + 0.155) = (-0.185, 0.125)
So, we can be 95% confident that the difference in the proportion of red beads in the two containers is between -0.185 and 0.125.
Step-by-step explanation:
given the completely factorized polynomial p=(x+2)(x-9)^4(x-14), what are the roots of p?
The roots of the polynomial are:
2, -9 (with a multiplicity of 4), and -14
What are the roots of the polynomial?Remember that for a polynomial of degree N with the roots:
{x₁, ..., xₙ}
Can be written as:
P(x)= (x - x₁)*(x - x₂)*...*(x - xₙ)
Here the polynomial given is:
P(x) =(x+2)(x-9)^4(x-14)
We can expand this as:
P(x) =(x + 2)*(x - 9)*(x - 9)*(x - 9)*(x - 9)*(x - 14)
Then the roots are:
2, -9, and -14
(where the -9 has a multiplicity of 4).
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a nursery employee wishes to plant $2$ identical golden delicious apple trees and $5$ identical bartlett pear trees in one row. how many distinct arrangements are possible?
Using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication, and Division (from Left to Right),
Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, we know that:
Golden delicious apple trees: 2
Bartlett pear tree: 5
Different arrangements that can be made are as follows:
2 * 5
10
Therefore, using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.
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four cards are chosen from a deck of 52 cards with replacement. a deck contains 13 cards each of spades, hearts, diamonds, and clubs. what is the prob
Answer:
Hi Hannah!
there's a little tiny mistake in your question
what's the probability of getting what heart spade etc
you didn't specify it
sorry for bothering but this is my favorite questions
Is there time t, for 5 < t < 10,at which the rate of change of the volume of water in the tub changes from positive to negative? Give reason for your answer
It is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.
It is not possible to determine if there is a time t, for 5 < t < 10, at which the rate of change of the volume of water in the tub changes from positive to negative without any more information. The rate of change of the volume of water in the tub is the derivative of the function representing the volume of water in the tub with respect to time. The information provided does not specify the function or the rate of change of the volume of water in the tub so it is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.
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A certain equation of the form , where a, b, and c are real numbers, has one real solution. How many non-real solutions does the equation have?
The equation has no non-real solutions.
An equation of the form ax^2 + bx + c = 0, where a, b, and c are real numbers, can have either no, one, or two solutions. The solutions can be real or non-real (complex).
If the discriminant (b^2 - 4ac) is greater than zero, the equation has two distinct real solutions.
If the discriminant is equal to zero, the equation has one real solution.
If the discriminant is less than zero, the equation has two non-real solutions (complex roots).
In this case, it is given that the equation has one real solution, so that means the discriminant equals zero (b^2 - 4ac = 0). Therefore, the equation has no non-real solutions.
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Reviewing the Sequence of Dots document below, determine the equation describing the pattern for the number of black dots, number of white dots, and the total number of dots.
The equation for the number of white dots is a(n) = 2n - 1 while the equation for the number of black dots is a(n) = (n - 1)²
The pattern for the number of black and white dots is depicted in the attached picture.
Refer to the the picture, the sequence of the white dots are:
n = 1 number of white dots = 1
n = 2 number of white dots = 3
n = 3 number of white dots = 5
n = 4 number of white dots = 7
Notice that the number of white dots form an arithmetic sequence, with:
first term = a = 1
common difference = d = 3 - 1 = 2
Hence, the equation for the nth term is:
a(n) = a + (n - 1) d
a(n) = 1 + (n - 1) x 2
a(n) = 2n - 1
Now look at the black dots.
n = 1 number of black dots = 0
n = 2 number of black dots = 1
n = 3 number of black dots = 4
n = 4 number of black dots = 9
Notice that the number of black dots is a quadratic sequence starting from 0.
We can write:
n = 1 number of black dots = 0 = (1 - 1)²
n = 2 number of black dots = 1 = (2 - 1)²
n = 3 number of black dots = 4 = (3 - 1)²
and so on. Hence, the equation of the nth term for the number of black dots is:
a(n) = (n - 1)²
The picture in your question was missing, but most likely it was like in the attached picture.
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im stuck on this question
Answer: Change per minute is 26. Water already there is 500.
Step-by-step explanation:
this table shows overall advertising revenue for the American newspaper industry (in billions of inflation-adjusted 2015 for the years 1980 to 2015.
The grouped frequency distribution data is given in the image.
What is a distribution?The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.
Given:
This table shows overall advertising revenue for the American newspaper industry (in billions of inflation-adjusted 2015 dollars) for the years 1980 to 2015.
From the given data,
we can build the grouped frequency distribution data.
And our first class should be 10-19.9.
The table is given in the attached image.
Therefore, the frequency is given in the attached image.
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calculate the percentage of data points that fall within one standard deviation of the mean (55,54, 66,38,53,56,57,66,45,65)
Answer:
70% of the data points
Step-by-step explanation:
To calculate the percentage of data points that fall within one standard deviation of the mean, you can follow these steps:
Calculate the mean of the data set: (55+54+66+38+53+56+57+66+45+65)/10 = 55
Calculate the standard deviation of the data set: √ (((55-55) ²+(54-55) ²+(66-55) ²+(38-55) ²+(53-55) ²+(56-55) ²+(57-55) ²+(66-55) ²+(65-55)²)/9) = 7.8
Determine the range for data points within one standard deviation of the mean: Mean ± 1 * standard deviation = 55 ± 1 * 7.8 = [47.2, 62.8]
Count the number of data points that fall within this range: 55, 54, 53, 56, 57, 45, and 65 fall within this range.
Calculate the percentage of data points that fall within this range: (7/10) * 100 = 70%
Therefore, 70% of the data points in the given data set fall within one standard deviation of the mean.
A shirt is on sale for 12% off. If the original price was $28, what is the sale price? $ Ontorn is having a store wide sale on all merchandise. All items
Answer:
price is now $24.64
and it was $3.36 off
Step-by-step explanation:
three candidates are running for the office of grand satrapy of vorania. the third- and second-place candidates received and votes, respectively. there were no ties. if the winner received of the total votes, what is the smallest possible value of ?
The smallest possible value is 44%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
Given that,
If only three persons are running for the office and the third-place candidate received 28 votes and the second-place candidate received 98 votes, the winner could have received only 99 votes.
In this case, the total number of votes cast would be 28 + 98 + 99 = 225 votes.
The percentage for the winning candidate would be: 99 / 225 = 44%
Therefore, the smallest possible value of x is 44%.
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Select the correct answer from each drop-down menu.
Ahmed is a school student of age 15. To support his expenses, Ahmed works in his free time. The place where he works requires him to stay at work
until 9 p.m. What exemption is considered here so that Ahmed's employer does not break any law?
FLSA lets children between 14 and 16 years of age work until 9 p.m. (April 1/June 1/March 1) between
and(StPatricks day/Memorial day/Labor day)
Answer: labour day
Step-by-step explanation:
tan40*cot50-sec40*csc50
I know the answer is -1, but I'm not sure how to get it.
[tex]\tan 40^{\circ} \cot 50^{\circ}-\sec 40^{\circ} \csc 50^{\circ}\\\\=\tan 40^{\circ} \tan 40^{\circ}-\sec 40^{\circ} \sec 40^{\circ}\\\\=\tan^2 40^{\circ}-\sec^2 40^{\circ}\\\\=-1[/tex]
a rotcaf is the number that results from adding a number and the greatest factor of the number that is less than the number. for example, the rotcaf of 9 is 9 3, or 12. what is the sum of the rotcafs of all the even numbers between 1 and 25?
234 is the sum of the rotcaf of all the even numbers between 1 and 25.To solve this question use the concept of series.
What is rotcaf?A rotcaf is the sum of the largest factors of the number that is smaller than the number and the number that is obtained by adding two numbers, the rotcaf of 9, for instance, is 9, 3, or 12.
Here given that,
even numbers between 1 and 25 which is: 2,4,6,8,10,12,14,16,18,20,22,24
for finding rotcaf:
(2 + 1) , (4 + 2), (6 + 3), (8 + 4),.....(24 + 12)
Here two series are present:
(1, 3, 5, 7,......23) and (2,4,6,8,......24)
Now, sum of the series is:
= [12 /2 {2+24}] + [12/2 {1 + 12}
= 156 + 78
= 234
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I WILL MARK BRAINLIEST PLS HELP
Answer:
Commission Pay = $2,288
Gross Pay = 4,878
Step-by-step explanation:
Amount of Commission: To calculate the amount of commission earned, multiply the sales by the commission rate. In this case, $57,200 x 4% = $2,288.
Gross Pay: To calculate the gross pay, add the salary to the commission earned. In this case, $2,590 + $2,288 = $4,878.
Solve for n.
n - 26 = -13
n =
Answer:
n = 13
Step-by-step explanation:
n - 26 = - 13 ( isolate n by adding 26 to both sides )
n = - 13 + 26
n = 13
subtract the polynomial multiple questions 100points+brainleist
1) (-x^{2} -5x-3)-(-7x^{2} -8x-8)
2) (-2x^{3}+x) -(7x-3-7x^{3})
3) (3x^{3} +3x^{2} +9)-(5x^{3} -7x^{2} +6x-9)
4) (5x^{3} +5x^{2} +5)-(6x^{3} -6x^{2} +8x-5)
5) (5x^{3} +3x^{2} +5) - (7x^{3} -9x^{2} +8x-5)
The polynomials are subtracted to give;
1. 6x²- 5x⁻³ - 8x⁻⁸
2. 5x³+ x - 7x⁻³
3. -2x³ + 10x² -6x + 18
4. 11x³ + 11x² + 8x + 10
5. -2x³ + 12x² - 8x + 10
What are algebraic expressions?These are expressions that are composed of terms, coefficients, factors, variables and constants.
They are also composed of mathematical or arithmetic operations such as;
ParenthesesDivisionAdditionMultiplicationSubtractionBracket, etcPolynomials are algebraic expression with non-negative integer exponentiation of variables.
From the information given, we have the expressions;
1.{ (-x²) - 5x⁻³} - ( -7x² - 8x⁻⁸)
collect like terms
-x² + 7x² - 5x⁻³ - 8x⁻⁸
Add like terms
6x²- 5x⁻³ - 8x⁻⁸
2. (-2x³ + x) - ( 7x⁻³ - 7x³)
collect like terms
-2x³ + 7x³ + x - 7x⁻³
add like terms
5x³+ x - 7x⁻³
3. (3x³ + 3x² + 9) - (5x³ -7x² +6x - 9)
collect like terms
3x³- 5x³ + 3x² + 7x² -6x + 9 + 9
-2x³ + 10x² -6x + 18
4.5x³ + 5x² + 5 - (-6x³ - 6x² + 8x - 5)
collect like terms
5x³ + 6x³ + 5x² + 6x² + 8x + 5 + 5
11x³ + 11x² + 8x + 10
5. 5x³ + 3x² + 5 - (7x³ - 9x² + 8x - 5)
collect like terms
5x³ - 7x³ + 3x² + 9x² - 8x + 5 + 5
-2x³ + 12x² - 8x + 10
Hence, polynomials are also described as algebraic expressions
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Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.
Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.
Answer:
29$
Step-by-step explanation:
1.60+0.75+0.89=3.24 - dollars per one kid
3.24 * 9 = 29.16 - dollars total
round 29.16 to the nearest dollar - 29$
The width of a rectangle varies inversely with the length of the rectangle. The width is 4 and the length is 12. Write the inverse variation equation to match this scenario: y = 48x y = 3/x y= 48/x y = 3x
The inverse variation equation of the rectangle is y = 48/x
The term inverse variation equation in math is defined as the relationships between variables that are represented in the form of
y = k/x
here x and y refers two variables and k is the constant value and it also states if the value of one quantity increases, then the value of the other quantity decreases.
Here we know that the width of a rectangle varies inversely with the length of the rectangle
Let us consider that x refers the width and y refers the length of the rectangle.
As we all know that the inverse proportion relationship is represented with the equation, y = k/x.
Here we know that the value of width is 4 and length is 12
Then the value of the constant is calculated as,
=> k = (4) x (12)
=> k = 48
Now, we have to write the equation that matches the scenario given, plug in the value of k = 48 into y = k/x, which is written as,
=> y 48/x
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I WILL MARK BRAINLIEST! HELPPP
Answer:
The scatter plot provided shows a relationship between the independent variable (x) and the dependent variable (y) that appears to be non-linear. The data points seem to be scattered around the graph. The best fit line would be a polynomial equation, the degree of the equation depends on the shape of the data points. It is not possible to give an exact equation of the line of best fit without knowing the data points.
(a) It is not possible to give an approximate equation of the line of best fit without knowing the data points or a more detailed information of the graph.
(b) Without a clear equation to predict values, it is not possible to predict the value of y for x = 10.
Does no solution mean all real numbers?
No, it does not mean all real numbers. No solution means that there is no value of the variable that satisfies the equation.
No solution means that there is no value of the variable that satisfies the equation. This means that no matter what value is assigned to the variable, the equation will not be true. Therefore, no solution does not mean all real numbers.
No solution means that there is no value of the variable that satisfies the equation. The equation might be a linear, quadratic, or some other type of equation, but no matter what value is assigned to the variable, the equation will not be true. Therefore, no solution does not mean all real numbers since all real numbers would include the value that would make the equation true. It is possible that all real numbers would be a solution, but no solution does not mean that all real numbers are a solution.
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when a deck of 52 cards is well shuffled, what is the probability that the four kings are all next to each other and the four queens are all next to each other?
The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is approximately 0.00000000024 or 0.000000002%.
The probability of four Kings being all next to each other in a well shuffled deck of 52 cards is:
(1/51) * (1/50) * (1/49) * (1/48)
= 0.000000000077 or 0.00000077%
The probability of four Queens being all next to each other in a well shuffled deck of 52 cards is:
(1/51) * (1/50) * (1/49) * (1/48)
= 0.000000000077 or 0.00000077%
The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is:
0.000000000077 * 0.000000000077
= 0.00000000024 or 0.000000002%
The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is very small, approximately 0.00000000024 or 0.000000002%. This is because there are many other combinations of cards that can occur in a shuffled deck.
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