Answers
Measure of the arc or angle indicated is 150.9 degrees.
Describe Arc?In geometry, an arc is a portion of the circumference of a circle or any other curved shape. It is defined by two endpoints and all the points on the curve that lie between them. An arc is usually named by its two endpoints, with a small arc symbol above them to indicate that it is an arc.
The length of an arc can be calculated using the formula:
Arc length = (central angle/360) x 2πr
where r is the radius of the circle, and the central angle is the angle subtended by the arc at the center of the circle, measured in degrees.
The measure of an arc is the degree measure of the central angle subtended by the arc. A semicircle is an arc that subtends a central angle of 180 degrees, and a full circle is an arc that subtends a central angle of 360 degrees.
Since DE and PE are chords of the circle, and they intersect at point P, we can use the intersecting chords theorem to find the length of DP. Let x be the length of DP. Then:
DP * PE = DE * PC
x * (x + PE) = ([tex]\frac{CE}{2}[/tex]) * ([tex]\frac{CE}{2}[/tex])
x² + x(PE) - [tex]\frac{CE}{2}^{\frac{2}{4} }[/tex] = 0
Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:
y² = DE² + DP² - 2 * DE * DP * cos(60)
y² = ([tex]\frac{CE}{2}[/tex])² + x^2 - ([tex]\frac{CE}{2}[/tex]) * x
Substitute this expression for y^2 into the equation for x and simplify:
[tex]x^{2} +x((\frac{CE}{2})^{2} + x^{2} -\frac{CE}{2} *x)^{0.5} -(\frac{CE}{2} ^{\frac{2}{4} } )=0[/tex]
Solve for x:
x = [tex]\frac{CE^{2} -4*(CE^{2} -3*\frac{CE}{2} ^{2} )^{0.5} }{4}[/tex]
x = [tex]\frac{3}{4} *\frac{CE^{2} }{CE^{2} -12}[/tex]
Now we can find the measure of the CD arc by using the formula for the central angle:
CD arc = [tex]2*arctan(\frac{DP}{CE})[/tex]
CD arc = [tex]2*arctan(\frac{x}{\frac{CE}{2} } )[/tex]
CD arc = [tex]2* arctan(CE^{2} -4*(CE^{2} -3*\frac{(\frac{CE}{2} ^{2})^{0.5}}{CE^{2}-12 } ))[/tex]
Simplifying this expression, we get:
[tex]CD arc=2*arctan(2*3^{\frac{1}{2} } -1)[/tex]
CD arc ≈ 150.9 degrees.
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Measure of the arc or angle indicated in the given figure is 150.9 degrees.
Describe Arc?In geometry, an arc is a portion of the circumference of a circle or other curved shape. It is defined by his two endpoints and all midpoints of the curve. Arcs are usually named after their two endpoints, with a small arc symbol above them to indicate that they are arcs.
Arc Length = (Center Angle/360) x 2πr
where r is the radius of the circle and the central angle is the angle the arc makes at the center of the circle, measured in degrees.
The arc measurement is the angle of the central angle defined by the arc. A half circle is an arc that spans a central angle of 180 degrees, and a full circle is an arc that spans a central angle of 360 degrees.
Since DE and PE are chords of the circle and intersect at P, we can use the chord rule to find the length of DP. Let x be the length of DP. Then:
DP × PE = DE × PC
x × (x + PE) = (CE/2) × (CE/2)
x² + x(PE) - [tex]\frac{CE}{2} ^{\frac{2}{4} }[/tex] = 0
Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:
y² = DE² + DP² - 2 × DE × DP × cos(60)
y² = ([tex]\frac{CE}{2}[/tex])² + x² - ([tex]\frac{CE}{2}[/tex]) × x
Substitute this expression for y² into the equation for x and simplify:
[tex]x^{2} +x((\frac{CE}{2} ^{2}) + x^{2} - \frac{CE}{2}*x)^{0.5} -[/tex] [tex]\frac{CE}{2} ^{\frac{2}{4} }[/tex] = 0
Solve for x:
x = [tex]\frac{CE^{2} - 4*(CE^{2}-3*\frac{CE}{2} ^{2})^{0.5} }{4}[/tex]
x = (3/4) × (CE²/CE²-12)
Now we can find the measure of the CD arc by using the formula for the central angle:
CD arc = 2arc tan(DP/CE)
CD arc = 2arc tan [x/(CE/2)]
CD arc = 2arc tan (CE² - 4 × (CE² - 3 × [tex]\frac{(\frac{CE}{2} ^{2}) ^{0.5} }{CE^{2}-12 }[/tex] )
Simplifying this expression, we get:
CD arc ≈ 150.9 degrees.
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Related Questions
Nathaniel would like to establish a trust fund that will provide R380 000 a year, forever, for his descendants. The trust fund will be invested very conservatively, so the expected rate of return is only 6,45%. How much money must he deposit today, to fund this gift for his descendants?
Answers
Answer:
Step-by-step explanation:
To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:
Present Value = Annual Payment / Discount Rate
In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:
Present Value = R380 000 / 0.0645
This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.
Portfolio expected return. You own a portfolio that is invested 35% in stock X, 20% in stock Y, and 45% in stock Z. The expected returns on these three stocks are 9%, 15% and 12%, respectively. What is the expected return, variance and standard deviation on the portfolio?
Answers
Answer:
To calculate the expected return on the portfolio, we use the following formula:
Expected return = (weight of stock X * expected return of stock X) + (weight of stock Y * expected return of stock Y) + (weight of stock Z * expected return of stock Z)
Expected return = (0.35 * 0.09) + (0.2 * 0.15) + (0.45 * 0.12) = 0.0321 or 3.21%
To calculate the variance of the portfolio, we use the following formula:
Variance = (weight of stock X)^2 * variance of stock X + (weight of stock Y)^2 * variance of stock Y + (weight of stock Z)^2 * variance of stock Z + 2 * weight of stock X * weight of stock Y * covariance of stocks XY + 2 * weight of stock X * weight of stock Z * covariance of stocks XZ + 2 * weight of stock Y * weight of stock Z * covariance of stocks YZ
Assuming that the stocks are uncorrelated, the covariance terms will be zero. Also, we assume that the variances of the stocks are equal to the square of their standard deviations. Therefore, we can simplify the formula to:
Variance = (weight of stock X)^2 * standard deviation of stock X^2 + (weight of stock Y)^2 * standard deviation of stock Y^2 + (weight of stock Z)^2 * standard deviation of stock Z^2
Variance = (0.35)^2 * (0.09)^2 + (0.2)^2 * (0.15)^2 + (0.45)^2 * (0.12)^2 = 0.00060167 or 0.060167%
To calculate the standard deviation of the portfolio, we take the square root of the variance:
Standard deviation = sqrt(0.00060167) = 0.0245 or 2.45%
Therefore, the expected return of the portfolio is 3.21%, the variance is 0.060167% and the standard deviation is 2.45%.
Answer:
Step-by-step explanation:
To calculate the expected return on the portfolio, we need to take the weighted average of the individual stock returns based on their proportions in the portfolio. The expected return on the portfolio can be calculated as follows:
Expected return on portfolio = (weight of stock X × expected return on stock X) + (weight of stock Y × expected return on stock Y) + (weight of stock Z × expected return on stock Z)
Expected return on portfolio = (0.35 × 9%) + (0.20 × 15%) + (0.45 × 12%)
Expected return on portfolio = 3.15% + 3.00% + 5.40%
Expected return on portfolio = 11.55%
To calculate the variance and standard deviation of the portfolio, we need to use the formula that takes into account the individual stock variances, covariances, and the weights of the stocks in the portfolio. Assuming the covariances between the stocks are zero, we can use the following formulas:
Portfolio variance = (wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2) + 2(wX * wY * σXY) + 2(wX * wZ * σXZ) + 2(wY * wZ * σYZ)
Portfolio standard deviation = sqrt(portfolio variance)
where wX, wY, and wZ are the weights of stocks X, Y, and Z in the portfolio respectively, σX, σY, and σZ are the standard deviations of returns on stocks X, Y, and Z respectively, and σXY, σXZ, and σYZ are the covariances between the returns on stocks X and Y, X and Z, and Y and Z respectively.
Since we assume the covariances between the stocks are zero, we can simplify the formulas as follows:
Portfolio variance = (wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2)
Portfolio standard deviation = sqrt[(wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2)]
Substituting the values, we get:
Portfolio variance = (0.35^2 * 0.09) + (0.20^2 * 0.15) + (0.45^2 * 0.12)
Portfolio variance = 0.0036475
Portfolio standard deviation = sqrt[(0.35^2 * 0.09) + (0.20^2 * 0.15) + (0.45^2 * 0.12)]
Portfolio standard deviation = sqrt(0.0036475)
Portfolio standard deviation = 0.06035
Therefore, the expected return on the portfolio is 11.55%, the portfolio variance is 0.0036475, and the portfolio standard deviation is 0.06035.
A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
Answers
To solve this problem, we need to standardize the drive-through time using the formula z = (x - μ) / σ, where x is the drive-through time, μ is the mean, and σ is the standard deviation. Then we can look up the area under the standard normal curve corresponding to a z-score of z using a standard normal distribution table or a calculator.
In this case, we want to find the probability that a randomly selected car spends more than 2 minutes in the drive-through, which corresponds to a drive-through time of x > 120 seconds. To standardize this value, we use:
z = (x - μ) / σ = (120 - 137.5) / 27 = -0.648
Looking up the area under the standard normal curve corresponding to a z-score of -0.648, we find:
P(z > -0.648) = 0.7406
Therefore, the probability that a randomly selected car spends more than 2 minutes in the drive-through is approximately 0.7406 or 74.06%.
b) What is the probability that a randomly selected car spends between 90 and 150 seconds in the drive-through?
To find the probability that a randomly selected car spends between 90 and 150 seconds in the drive-through, we need to standardize these values using the formula z = (x - μ) / σ, where x is the drive-through time, μ is the mean, and σ is the standard deviation. Then we can find the area under the standard normal curve between the corresponding z-scores using a standard normal distribution table or a calculator.
To standardize 90 seconds and 150 seconds, we use:
z1 = (90 - 137.5) / 27 = -1.7593
z2 = (150 - 137.5) / 27 = 0.4629
Using a standard normal distribution table or a calculator to find the area under the standard normal curve between z1 = -1.7593 and z2 = 0.4629, we get:
P(-1.7593
(I hope that helps you)
Let's say you took a sample of 445 voice-activated smart TVs. The mean rate at which these TVs need to be serviced or replaced is every 3.5 years, with a standard deviation of 0.8 years. Given a confidence level of 95%, what is the maximum error of estimate?
Answers
The maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth.
What is Standard Deviatiοn?The standard deviatiοn is a measure οf the amοunt οf variatiοn οr dispersiοn οf a set οf vaIues frοm their mean οr average. It is caIcuIated as the square rοοt οf the variance.
Tο find the maximum errοr οf estimate, we need tο use the fοrmuIa:
Maximum errοr οf estimate = z * (standard deviatiοn / √(sampIe size))
where z is the z-scοre assοciated with the given cοnfidence IeveI, standard deviatiοn is the pοpuIatiοn standard deviatiοn (0.8 years), and sampIe size is the number οf TVs sampIed (445).
At a cοnfidence IeveI οf 95%, the z-scοre is 1.96.
Substituting the vaIues in the fοrmuIa, we get:
Maximum errοr οf estimate = 1.96 * (0.8 / √(445))
= 0.092 years (rοunded tο 3 decimaI pIaces)
Therefοre, the maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth. This means that we can be 95% cοnfident that the true mean rate at which the TVs need tο be serviced οr repIaced is within 1 mοnth οf the sampIe mean οf 3.5 years.
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The graph of the polynomial f(x) is shown below. Which of the following is * 1 point
NOT a factor of f(x)?
х
•(x-2)
•(*-7)
• (x+ 1)
• (x+2)
Answers
(x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.
What is Polynomial function ?
A polynomial function is a type of mathematical function that consists of a sum of terms, where each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In other words, a polynomial function is an algebraic expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
Thank you for providing the graph of the polynomial f(x). Based on the graph, we can see that the polynomial has roots at x = -2, x = -1, x = 2, and x = 7. Therefore, (x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.
However, since there is no point on the graph where f(x) is equal to zero when x = -7, we can conclude that (-x+7) is NOT a factor of f(x).
Therefore, (x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.
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Find the area of the shaded sector of the circle
Answers
Answer:
32.67 square meters
Step-by-step explanation:
finding the area of the shaded region.
area of sector = (θ/360°) x πr²
where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.
Substituting the given values into the formula, we get:
area of sector = (60°/360°) x π(14m)²
area of sector = (1/6) x 3.14 x 196m²
area of sector = 32.67m² (rounded to two decimal places)
Therefore, the area of the section is 32.67 square meters
ILL GIVE BRAINLIEST
What is the height of the plant if less than 3 weeks have passed? Express your answer as an inequality in terms of h.
Answers
It will be at least 1 cm but less than 10 cm.
Kenisha packs 3 crates of merchandise. The crates have masses of 65 kilograms, 72 kilograms, and 42 kilograms. How many kilograms of merchandise does kenisha pack
Answers
Answer:
Step-by-step explanation:
answer 42
how to explain but the answe is 42
Set of natural numbers is denoted by letter
Answers
Answer: N
Step-by-step explanation: The set of natural numbers is represented by the letter “N”. A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ...}
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answers
Therefore , the solution of the given problem of unitary method comes out to be enable the current to travel, a connection, such as a wire or conductor, is required.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
D. In order for a current to move, there must be an energy source, a recipient, and a connection.
Current is the movement of charged ions through a conductor, most frequently electrons.
The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.
The current has a route through a recipient, which can be a machine or a circuit.
In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.
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Select the correct answer from each drop-down menu.
The area of the shaded square is
square inches. The length of the unshaded rectangle is
inches.
The estimated value of the length of the shaded square is
inches. The estimated value of the area of the unshaded rectangle is
square inches.
Answers
The completed statement with regards to the area of the square and the rectangle are;
The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.
What is the area of a square?The area of a square is the product of the side lengths which are congruent, therefore;
Area of a square = Side length, s × Side length, s = s²
The possible figure in the question includes;
A shaded square that is 125 square inches
An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches
Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.
Therefore;
The side length of the square = √(125) inches = 5·√5 inches
The estimated value of the side length of the square is; 5·√5 inches
The area of a rectangle = Length × Width
The length of the rectangle = 7·√5 inches
The width of the rectangle = 5·√5 inches
Therefore;
The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175
The estimated area of the unshaded rectangle is 175 square inches
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Please help!!
Given M || N, find the value of x.
(x+1) (7x-5)
Answers
Answer:x=23
Step-by-step explanation:
x+1+7x-5=180
8x-4=180
8x=184
x=184/8
x=23
The physical fitness score for a population of police officers at a local police station is 73, with an SD of 8 on a 100-point physical endurance scale. Suppose the police chief selects a sample of 64 local police officers from this population and records a mean physical fitness rating on this scale equal to 75. He conducts a single-sample z test to determine whether physical endurance increased for this group. Based on your outcome, what is the proper format for writing out the results for this problem?
Answers
The p-value, under the assumption that the null hypothesis is correct, is the likelihood of receiving a test statistic that is as extreme as the one that was observed.
what is null hypothesis ?A declaration or assumption that there is no significant difference or association between two or more variables or populations being studied is known as the null hypothesis in statistics. The default hypothesis that is evaluated against an alternative hypothesis is known as the null hypothesis and is frequently represented as "H0." Typically, the null hypothesis is formulated in light of prior research, theoretical predictions, or accepted wisdom. It posits that any observed differences or correlations between groups or variables are the result of chance or random variation and serves as the foundation for evaluating a hypothesis.
given
We can use a standard format that includes the following details to present the z test results:
This is a claim regarding the population parameter being tested, or the null hypothesis.
In this instance, the null hypothesis is that the population of police officers' mean physical fitness score is equal to 73.
This assertion defies the null hypothesis, according to the alternative. The alternative hypothesis in this situation is that the sample of police officers' mean physical fitness score is higher than 73.
The p-value, under the assumption that the null hypothesis is correct, is the likelihood of receiving a test statistic that is as extreme as the one that was observed.
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Determine the order of the following matrix:
[9 6 -4 8]
Answers
The order of the matrix is 2 x 2.
What is a matrix and what is meant by its order?
In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.
The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.
Determine the order of the given matrix:
In the given problem, we are asked to find the order of the matrix:
[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]
we count the number of rows and columns.
This matrix has 2 rows and 2 columns, so its order is 2 x 2.
Therefore, the order of the matrix is 2 x 2.
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?how do i do this pleas help
Answers
The angles 5 and 6 which are given in the diagram above are typical example of an adjacent angle.
What is an adjacent angle?An adjacent angle is defined as the type of angle that has a common sides which is shared by the two angles that are being compared.
A vertical angle is the type of angle that is usually opposite and they constructed by the intersection of two lines.
Therefore since a common sides exists between angle 5 and 6.
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what is the average allowance for each student?
$7,$12,$8.50,$10,$7,$8,$10.50,$11
Answers
The average allowance for each student is $9.25.
What is the average allowance for each student?To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.
Adding up the allowances:
$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74
There are 8 students, so we divide the total allowance by 8 to get:
$74 / 8 = $9.25
Therefore, the average allowance for each student is $9.25.
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OABC is a parallelogram, The coordinates of A and C are (12,0) and (5,5) respectively.
(a) Calculate the length of OC.
(b) Find the gradient of OC.
(c) Find the equation of line AB.
(d) Hence determine the coordinates of point B.
Answers
Therefore, the coordinates of point B are approximately (12.67, 0.67).
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. Equations are written using an equal sign (=) between the two expressions that are being compared. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The equation is true if the LHS is equal to the RHS. Equations are used to represent various relationships and patterns in mathematics, and are an important tool in problem-solving and mathematical modeling.
Here,
(a) To calculate the length of OC, we need to find the coordinates of point O, which is the intersection of the diagonals of the parallelogram. The midpoint of AC is:
((12+5)/2, (0+5)/2) = (8.5, 2.5)
Therefore, the equation of the line passing through the midpoint of AC and perpendicular to AC is:
y - 2.5 = -(5-0)/(5-12) (x - 8.5)
Simplifying:
y - 2.5 = 5/7 (x - 8.5)
y = 5/7 x - 1
This is the equation of the line passing through O and parallel to AB. We can see that when x = 12, y = 5/7 * 12 - 1 = 7.4. Therefore, the coordinates of O are (12, 7.4).Using the distance formula, we can now calculate the length of OC:
OC = √((12-5)² + (7.4-0²) = √(109.96) ≈ 10.49
Therefore, the length of OC is approximately 10.49 units.
(b) The gradient of OC can be found using the coordinates of points O and C:
m = (y₂ - y₁)/(x₂ - x₁) = (7.4 - 5)/(12 - 5) = 0.4/1 ≈ 0.4
Therefore, the gradient of OC is approximately 0.4.
(c) The equation of line AB can be found using the coordinates of points A and B:
m = (y₂ - y₁)/(x₂ - x₁) = (y - 0)/(x - 12)
Simplifying and substituting the coordinates of point A:
0.4 = (y - 0)/(x - 12)
0.4(x - 12) = y
Therefore, the equation of line AB is y = 0.4x - 4.8.
(d) The coordinates of point B can be found by solving the system of equations formed by the equations of lines AB and OC. Equating y in both equations:
0.4x - 4.8 = 5/7 x - 1
Simplifying and solving for x:
0.3x = 3.8
x = 12.67
Substituting x in either equation:
y = 0.4(12.67) - 4.8 ≈ 0.67
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Find the product……..
Answers
The product of the expressions are;
Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)
Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)
Step 4: 3/x + 5
How to determine the productIt is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.
From the information given, we have the fraction;
4x + 8/x² + 5x + 6 × 3x + 9/4x + 20
To determine the product, let us reduce the expressions to their lowest forms, we have;
4x + 8 = 4(x + 2)
x² + 5x + 6 = (x + 2)(x + 3)
3x + 9 = 3(x +3)
4x + 20 = 4(x + 5)
Substitute the expressions
4(x + 2)/(x + 2)(x + 3) × 3(x +3)/4(x + 5)
divide the common terms
4(x + 3) × 3(x + 3)/4(x + 5)
Divide further, we have.
3/x + 5
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Given that cos theta= 3/10 and 3pi/2 < theta < 2pi, find the exact value of each of the following:
a) sin 2theta
b) The quadrant in which the angle theta/2 is located.
B) cos theta/2
Answers
(a) The value of sin 2θ is -3√(91)/50.
(b) θ/2 is located in the third quadrant.
(c) The value of cos θ/2 is -√65/10.
What is the value of the sine and cosine functions?We know that cos θ = 3/10, so we can find sin θ using the Pythagorean identity:
sin² θ + cos² θ = 1
sin²θ + (3/10)² = 1
sin²θ = 1 - (3/10)² = 91/100
sin θ = ±√(91)/10
Since 3π/2 < θ < 2π,
we know that sin θ < 0, so sin θ = -√(91)/10.
a) To find sin 2θ, we can use the double angle formula:
sin 2θ = 2 sin θ cos θ
sin 2θ = 2 (-√(91)/10) (3/10)
sin 2θ = -3√(91)/50
b) To find the quadrant in which θ/2 is located, we first need to find θ/2:
θ/2 = (3π/2 + 2π)/2 = 5π/4
5π/4 is in the third quadrant, so θ/2 is located in the third quadrant.
c) To find cos θ/2, we can use the half angle formula:
cos θ/2 = ±√((1 + cos θ)/2)
Since 3π/2 < θ < 2π, we know that cos θ < 0,
so we take the negative square root:
cos θ/2 = -√((1 + 3/10)/2)
cos θ/2 = -√(13/20)
Simplifying the radical by dividing both numerator and denominator by 4:
cos θ/2 = -√(13)/2√5
Multiplying numerator and denominator by √5 to rationalize the denominator:
cos θ/2 = -√65/10
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30 points and brainliest!
Answers
Answer: a )The answer is 196.126.
b )
Step-by-step explanation:
a) Multiply 33.1 and 18.2= 602.62
Divide the result by 5.8:
602.62 / 5.8 = 196.126
Therefore, 33.1x18.2 / 5.8 = 196.126.
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Sunny Town is symmetric
Mean, because Sunny Town is skewed
Median, because Beach Town is skewed
Mean, because Beach Town is symmetric
Answers
Tο determine which lοcatiοn typically has the cοοler temperature, we shοuld cοmpare the median temperature οf Sunny Tοwn tο the mean temperature οf Beach Tοwn. Thus, cοrrect οptiοns are:
A) Median, because Sunny Tοwn is symmetricB) Mean, because Sunny Tοwn is skewedwhat is median?Median is a measure οf central tendency that represents the middle value in a dataset when the values are arranged in οrder οf magnitude.
When cοmparing the data tο determine which lοcatiοn typically has the cοοler temperature, the measure οf center tο use depends οn the shape οf the distributiοn οf the data.
Fοr the Sunny Tοwn data, since the histοgram is symmetric, we can use the median as a measure οf center. The median οf the Sunny Tοwn data wοuld be the value that separates the data intο twο equal halves.
Fοr the Beach Tοwn data, since the histοgram is skewed, we can use the mean as a measure οf center. The mean οf the Beach Tοwn data wοuld be the average οf all the data pοints.
Therefοre, tο determine which lοcatiοn typically has the cοοler temperature, we shοuld cοmpare the median temperature οf Sunny Tοwn tο the mean temperature οf Beach Tοwn.
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14thousands+46hundreds+13tens+9 is what number?
Answers
Answer:
18,739
Step-by-step explanation:
14 thousands = 14,000. 46 hundreds = 4,600. 13 tens = 130. 9 = 9. You add them all up and get 18,739.
Mr. Ed earns $15.50 per hour. His regular hours are 40 hours per week, and he receives
time-and-a-half overtime. Find his total pay for a week in which he works 45 hours.
Answers
Answer:
For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:
40 hours x $15.50 per hour = $620
For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:
5 hours x $15.50 per hour x 1.5 = $116.25
Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:
$620 (regular pay) + $116.25 (overtime pay) = $736.25.
Find the volume of the composite figure.
Answers
Answer:
volume = 290m
Step-by-step explanation:
box 1
[tex]vol= lwh\\=3*5*6\\=90m[/tex]
box 2
[tex]vol=lwh\\=8*5*5\\=200m[/tex]
total volume = 90+200 =290m
GIVING BRAINLIST WHOEVER GETS IT RIGHT!!!!!!!!!!!!!!!!!!!! Select the correct answer.
Sam's height is 15 centimeters less than 2 times Martha's height. If Sam is 185 centimeters tall, and Martha's height is x, the relationship between the heights can be represented by the equation 2x − 15 = 185. What is Martha's height?
Answers
Step-by-step explanation:
The equation 2x − 15 = 185 represents the relationship between Sam's and Martha's heights. We can solve for x, which represents Martha's height, by isolating x on one side of the equation:
2x − 15 = 185
Add 15 to both sides of the equation:
2x = 200
Divide both sides of the equation by 2:
x = 100
Therefore, Martha's height is 100 centimeters.
How many thousands are in 200,000
Answers
There are 200 thousands in 200,000.
PLEASEEE HELP WITH THESE THREE QUESTIONS
Answers
If the graph of a polynomial function P(x) has x-intercepts at x = -4, x = 0, x = 5, the following must be true for P(x): D. The degree of the polynomial is greater than or equal to three.
Based on the graph of the polynomial f(x), the following is not a factor: B. (x - 1).
What is a polynomial graph?In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph. Since the polynomial function with x-intercepts at x = -4, x = 0, and x = 5 cuts the x-axis at three (3) points. Therefore, the degree of this polynomial is either greater than or equal to three (3).
By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;
x = -1 ⇒ x + 1 = 0.
x = -2 ⇒ x + 2 = 0.
x = 2 ⇒ x - 2 = 0.
x = 3 ⇒ x - 3 = 0.
Therefore, (x - 1) is not a factor.
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explain the logic in fractions where 1/6+2/3+3/7 becomes 7/42+28/42+18/42
Answers
Answer:
Step-by-step explanation:
What are fractions?Fractions are parts or pieces of a complete thing.
In this problem, the fractions start out with varying denominators, and then end with the same denominator. In order to go from different denominators to the same denominator, we must find a common denominator.
What is a common denominator?A common denominator is a number that denominators of fractions can equal when multiplied by something else. Ex: 1/3 + 2/ 7 Multiples of 3: 3, 6, 9, 12, 15, 18, 21 Multiples of 7: 7, 14, 21. Both 3 and 7 have 21 in common, so this would be the common denominator.
A common denominator is needed so fractions with different denominators can be combined. To get from 6, 3, and 7 to 42, the multiples of 2, 3, and 7 must be listed.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 29, 42
Multiples of 7: 7, 14, 21, 28, 35, 42
All three numbers have 42 in common, so that is their common denominator. Whatever was done to the denominator, must be done to the numerator. Now, we must take the number that can be multiplied by the denominator to reach 42 and multiply it by the numerator.
[tex]\frac{1*7}{6*7}}[/tex]
[tex]=\frac{7}{42}[/tex]
[tex]\frac{2*14}{3*14}[/tex]
[tex]=\frac{28}{42}[/tex]
[tex]\frac{3*6}{7*6}[/tex]
[tex]=\frac{18}{42}[/tex]
So, to sum it up, when trying to add fractions with different denominators, find a common denominator by listing multiples of the denominators and multiply the numerator by the number the denominator was multiplied by to get the common denominator.
The logic in this fraction addition problem is to find a common denominator for all the fractions and then add the numerators. In this case, the common denominator is the least common multiple of the denominators, which is 42.
To convert the first fraction, 1/6, to have a denominator of 42, we need to multiply both the numerator and denominator by 7. This gives us 7/42.To convert the second fraction, 2/3, to have a denominator of 42, we need to multiply both the numerator and denominator by 14. This gives us 28/42.To convert the third fraction, 3/7, to have a denominator of 42, we need to multiply both the numerator and denominator by 6. This gives us 18/42.Now that all the fractions have a common denominator of 42, we can add the numerators to get the final answer:
[tex]\begin{aligned} \sf \dfrac{1}{6} + \dfrac{2}{3} + \dfrac{3}{7} = \dfrac{7}{42} + \dfrac{28}{42} + \dfrac{18}{42} = \bold{\dfrac{53}{42}} \end{aligned}[/tex]
Therefore, the sum of the fractions is 53/42.
I hope this helps!
Martha made 2 2/3 pounds of pasta. she divided the pasta into fourths. how much pasta is in each portion?
Answers
Step-by-step explanation:
2 2/3 = 8/3
8/3 * 1/4 = 8/12 = 2/3 pound in each portion
A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answers
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.