Answer:
To use the FOIL method to simplify the expression (2x - 1/2)^2, follow these steps:
F: Multiply the first terms in each set of parentheses:
(2x) * (2x) = 4x^2
O: Multiply the outer terms in each set of parentheses:
(2x) * (-1/2) = -x
I: Multiply the inner terms in each set of parentheses:
(-1/2) * (2x) = -x
L: Multiply the last terms in each set of parentheses:
(-1/2) * (-1/2) = 1/4
Now, combine the like terms:
4x^2 - x - x + 1/4
Simplify by combining like terms:
4x^2 - 2x + 1/4
Therefore, (2x - 1/2)^2 = 4x^2 - 2x + 1/4.
The coordinates of the points A and B are (0, 6) and (8, 0) respectively. (i) Find the equation of the line passing through A and B. Given that the line y = x + 1 cuts the line AB at the point MÄUK (ii) the coordinates of M, (iii) the equation of the line which passes through M and is parallel to the x-axis, (iv) the equation of the line which passes through M and is parallel to the y-axis.
Therefore, the equation of this line is: x = 8/7.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables, and the goal is to solve for the value(s) of the variable(s) that make the equation true.
Given by the question.
To find the equation of the line passing through points A and B, we need to determine the slope and the y-intercept of the line.
The slope of the line can be found using the formula:
slope = (change in y) / (change in x)
Using the coordinates of A and B, we have:
slope = (0 - 6) / (8 - 0) = -6/8 = -3/4
The y-intercept of the line can be found by substituting the coordinates of point A and the slope into the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope and b are the y-intercept.
Using the coordinates of point, A and the slope we just calculated, we have:
6 = (-3/4) (0) + b
b = 6
Therefore, the equation of the line passing through points A and B is:
y = -3/4 x + 6
(ii) To find the coordinates of point M where the line y = x + 1 intersects the line AB, we need to solve the system of equations:
y = -3/4 x + 6 (equation of line AB)
y = x + 1 (equation of line y = x + 1)
Substituting y = x + 1 into the equation of line AB, we have:
x + 1 = -3/4 x + 6
Solving for x, we have:
x = 8/7
Substituting x = 8/7 into the equation of line y = x + 1, we have:
y = 8/7 + 1 = 15/7
Therefore, the coordinates of point M are:
M (8/7, 15/7)
(iii) The line passing through point M and parallel to the x-axis is a horizontal line with equation y = c, where c is the y-coordinate of point M. Therefore, the equation of this line is:
y = 15/7
(iv) The line passing through point M and parallel to the y-axis is a vertical line with equation x = c, where c is the x-coordinate of point M.
To learn more about variable:
https://brainly.com/question/17344045
#SPJ9
1. Four plus a number
2. Twice Daria's age
3. Six times a number plus forty-one
4. The sum of a number and 17
5. The difference between Mary's height and Frank's height
6. The quotient of Iquan's age and 4
7. The product of Arielle's age and 50
8. Seventy-five increased by a number
9. Four hundred decreased by twice a number
Eleven ples more than a number
10.
11. Twice as many dogs
41X
12.
A number doubled plus ten
13. A variable tripled less 40
14. Twice the temperature minus 60 degrees
15. A number divided by fifteen less than 3
16. Five more than a number
17. Thirty-three less than a number
8. Twice Solomon's weight less fifteen pounds
3. The difference between sixty and twice a number
D. The factor of a variable and the coefficient four
From the given information provided, the given sentences in the form of algebraic expressions are as follows:
1. 4 + x
2. 2D
3. 6n + 41
4. x + 17
5. Mary's height - Frank's height
6. Iquan's age / 4
7. 50Arielle's age
8. 75 + x
9. 400 - 2x
10. 11 + x
11. 2d
12. 2x + 10
13. 3v - 40
14. 2t - 60
15. x/15 - 3
16. 5 + x
17. x - 33
18. 2S - 15
19. 60 - 2x
20. 4D
Question - 1. Four plus a number 2. Twice Dharia's age 3. Six times a number plus forty-one 4. The sum of a number and 17 5. The difference between Mary's height and Frank's height 6. The quotient of Aquaman's age and 4 7. The product of Arielle's age and 50 8. Seventy-five increased by a number 9. Four hundred decreased by twice a number Eleven ples more than a number 10. 11. Twice as many dogs 41X 12. A number doubled plus ten 13. A variable tripled less 40. 14. Twice the temperature minus 60 degrees 15. A number divided by fifteen less than 3 16. Five more than a number 17. Thirty-three less than a number 18. Twice Solomon's weight less fifteen pounds 19. The difference between sixty and twice a number 20. The factor of a variable and the coefficient four. Translate the following into algebraic expression.
Learn more about variable here: brainly.com/question/27894163
#SPJ4
A student answers a multiple choice examination question that offers four possible answers. Suppose the probability that the student knows the answer to the question is .8 and the probability that the student will guess is .2. Assume that if the student guesses, the probability of selecting the correct answer is .25. If the student correctly answers a question, what is the probability that the student really knew the correct answer?
If the student correctly answers a question, the probability that the student really knew the correct answer is 0.941.
The probability that the student knows the answer to the question and correctly answers it is 0.8 x 1 = 0.8. The probability that the student guesses and correctly answers the question is 0.2 x 0.25 = 0.05. The probability that the student correctly answers the question is 0.8 + 0.05 = 0.85.
The probability that the student really knew the correct answer given that they correctly answered the question is 0.8 / 0.85 = 0.941. Therefore, the probability that the student really knew the correct answer is approximately 94.1%.
Know more about probability here:
https://brainly.com/question/30034780
#SPJ11
Find the perimeter of the shape below:
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad R(\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) ~\hfill SR=\sqrt{(~~ -1- (-2)~~)^2 + (~~ 3- 7~~)^2} \\\\\\ ~\hfill SR=\sqrt{( 1 )^2 + ( -4)^2} \implies \boxed{SR=\sqrt{ 17}}[/tex]
[tex]R(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad U(\stackrel{x_2}{-1}~,~\stackrel{y_2}{5}) ~\hfill RU=\sqrt{(~~ -1- (-1)~~)^2 + (~~ 5- 3 ~~)^2} \\\\\\ ~\hfill RU=\sqrt{( 0)^2 + ( 2)^2} \implies RU=\sqrt{ 4}\implies \boxed{RU=2} \\\\\\ U(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad T(\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill UT=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 5- 5~~)^2} \\\\\\ ~\hfill UT=\sqrt{( 3)^2 + ( 0)^2} \implies UT=\sqrt{ 9}\implies \boxed{UT=3}[/tex]
[tex]T(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{7}) ~\hfill TS=\sqrt{(~~ -2- 2~~)^2 + (~~ 7- 5~~)^2} \\\\\\ ~\hfill TS=\sqrt{( -4)^2 + ( 2)^2} \implies \boxed{TS=\sqrt{ 20}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{17}+2+3+\sqrt{20} }~~ \approx ~~ \text{\LARGE 13.6}[/tex]
find number of conversion periods and rate of interest when compounded half-yearly for a sum of Rs 5000 is taken for 7 years and 9% p.a
The rate of interest when compounded half-yearly is 4.45% and there are 14 conversion periods.
Solving compounded interestThe formula for calculating the compound interest is:
A = P (1 + r/n)^(n*t)
Where:
A = Final amountP = Principal amountr = Annual interest rate (as a decimal)n = Number of times the interest is compounded per yeart = Time period (in years)In this case, P = Rs 5000, r = 9% p.a. and the interest is compounded half-yearly (i.e., n = 2).
To find the number of conversion periods, we need to multiply the number of years by the number of conversion periods per year:
Number of conversion periods = n*t = 2 * 7 = 14
So there are 14 conversion periods in 7 years.
To find the rate of interest when compounded half-yearly, we can rearrange the formula and solve for r:
A = P (1 + r/n)^(nt)
A/P = (1 + r/n)^(nt)
(1 + r/n) = (A/P)^(1/nt)
r/n = (A/P)^(1/nt) - 1
r = n[(A/P)^(1/n*t) - 1]
Substituting the given values, we get:
r = 2[(5000*(1 + 0.09/2)^(27))^(1/(27)) - 1]
= 0.0445 or 4.45%
Therefore, the rate of interest when compounded half-yearly is 4.45%.
Learn more on compound interest here: https://brainly.com/question/24924853
#SPJ1
what function is f (-2)?
The value οf f(-2) fοr this functiοn is 12.
What is functiοn ?A functiοn is a mathematical rule οr prοcess that assigns a unique οutput value tο each input value. In οrder tο evaluate a functiοn at a specific input value, we need tο knοw the functiοn itself. The functiοn can be given in different fοrms, such as an equatiοn οr a graph, and we use these fοrms tο determine the οutput value fοr a given input value.
Fοr example, if we are given the equatiοn οf a functiοn[tex]f(x) = x^2 - 3x + 2,[/tex] we can evaluate f(-2) by substituting -2 for x in the equation:
[tex]f(-2) = (-2)^2 - 3(-2) + 2 = 12[/tex]
Therefοre, the value οf f(-2) fοr this functiοn is 12. Hοwever, if we are nοt given the equatiοn οr any οther infοrmatiοn abοut the functiοn, we cannοt determine its οutput at a specific input value.
To know more about function visit :
https://brainly.com/question/11624077
#SPJ1
Complete Qustion:
How to find f (- 2 for a function?
A new car is purchased for 19700 dollars. The value of the car depreciates at
9. 25% per year. To the nearest year, how long will it be until the value of the
car is 5500 dollars?
It will take 10.4 years for the value of the car to depreciate to 5500 dollars.
The equation for calculating the number of years until the value of the car is 5500 dollars is:
y = (19700 - 5500) / 0.0925
y = 10.4 years
In order to calculate the number of years until the value of the car is 5500 dollars, we can use the equation y = (19700 - 5500) / 0.0925. This equation uses the initial value of the car (19700) and the desired value (5500), as well as the depreciation rate of 9.25% per year. By solving this equation, we can determine that it will take 10.4 years for the value of the car to depreciate to 5500 dollars.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ4
Write The Polynomial in the form at^2 + bt + c and then identify the values of a, b, and c
0
The polynomial 0 can be written in the form at^2 + bt + c as 0t^2 + 0t + 0. In this case, a, b, and c are all equal to 0.
Which pair of angles are vertical angles?
O KRC and CRH
O ERT and MRC
O MRC and KRM
O KRE and ERT
Answer:
Option B
Step-by-step explanation:
Vertical angles are a pair of angles which have the following characteristics:
(i) Equal in measurement
(ii) Located on opposite sides of two intersecting straight lines
AND
(iii) Have the same vertex
Vertical angles in this figure:
∠ERT and ∠MRC
∠KRC and ∠ERH
∠KRE and ∠CRH
Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3100. Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.
The z-score is a measure of how many standard deviations a data point is from the mean. It can be calculated using the formula
z = (x - μ) / σ,
where x is the data point, μ is the mean, and σ is the standard deviation.
a. The z-score for a backyard structure costing $2300 can be calculated as follows:
z = (2300 - 3100) / 1200 = -800 / 1200 = -0.67
b. The z-score for a backyard structure costing $4900 can be calculated as follows:
z = (4900 - 3100) / 1200 = 1800 / 1200 = 1.
c. The z-score in part (a) is -0.67, which means that the backyard structure costing $2300 is 0.67 standard deviations below the mean. The z-score in part (b) is 1.5, which means that the backyard structure costing $4900 is 1.5 standard deviations above the mean. Neither of these z-scores are extreme enough to be considered outliers, as they are both within 2 standard deviations of the mean.
d. The z-score for the backyard shed-office combination costing $13,000 can be calculated as follows:
z = (13000 - 3100) / 1200 = 9900 / 1200 = 8.25
This z-score is much larger than 2, which means that the structure costing $13,000 is more than 8 standard deviations above the mean. This is an extreme value and should be considered an outlier.
To know more about z-score refer here:
https://brainly.com/question/15016913
#SPJ11
Find the measure of angle NSR.
A)50
B)63
C)126
D)113
The measure of angle NSR.
D. angle NSR = 113 degreesHow to find the measure of the angleThe situation in the picture is when two chords intersect in a circle in this case the angle NSR is calculated using the formula
angle NSR = 1/2 (arc NR + arc QP)
Plugging in the values
angle NSR = 1/2 (176 + 50)
angle NSR = 1/2 (226)
angle NSR = 113 degrees
Learn more about angle at:
https://brainly.com/question/25770607
#SPJ!
Please help! What do I graph?
Answer:
look at image
Step-by-step explanation:
Find the equation of the line shown.
y
10
9
876
5
4
3
2
1
O
1 2 3 4 5 6 7 8 9 10
X
Answer: y=1x+6
Step-by-step explanation:
The equation of a line is y=mx+c
m is the gradient and c is the y intercept.
on the graph the line intercepts the y axis at 6- the y intercept!
The gradient is the difference in y divide by the difference in x.
(0,6) and (4,10)
10-6=4
4-0=
4
4/4 is 1! so the equation is
y=1x+6
Answer:
y = x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 10) ← 2 points on the line
m = [tex]\frac{10-6}{4-0}[/tex] = [tex]\frac{4}{4}[/tex] = 1
the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = x + 6 ← equation of line
The table gives the average number of days of rain in each month of the year. Find the mode of the given data. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Days of Rain 6 7 10 10 11 12 10 10 9 7 7 6 A. 7 B. 7 and 10 C. 9.5 D. 10
The mοde value fοr the table οf data given is οptiοn D. 10.
What is mοde?A mοde is described as the value in a grοup οf values that οccurs mοre frequently. The value that appears the mοst frequently is this οne.
The mοde is nοt necessarily unique tο a given discrete distributiοn, since the prοbability mass functiοn may take the same maximum value at several pοints x1, x2, etc. The mοst extreme case οccurs in unifοrm distributiοns, where all values οccur equally frequently.
The data is given fοr the average number οf days οf rain in each mοnth οf the year.
The mοde will the number οf days repeating itself mοre number οf times.
It can be seen that 10 is repeated 4 times amοng the data given.
Therefοre, the mοde value is 10.
To learn more about mode from the given link
https://brainly.com/question/27951780
#SPJ1
What is the relationship between the base of an exponential function and its rate of growth?
O The base of an exponential function is unrelated to its rate of growth.
O The smaller the value of the base, the greater the function's rate of growth.
O The greater the value of the base, the greater the function's rate of growth.
O For each increase in the base, the function's rate of growth doubles.
The cοrrect statement is "The greater the value οf the base, the greater the functiοn's rate οf grοwth"
What is Expοnential functiοn?An expοnential functiοn is a mathematical functiοn οf fοrm f(x) = abˣ,
where a and b are cοnstants, and x is the variable.
The base b is a pοsitive cοnstant and is typically greater than 1. The expοnent x represents the degree οf grοwth οr decay οf the functiοn.
Expοnential functiοns are cοmmοnly used tο mοdel grοwth οr decay in variοus real-wοrld phenοmena, such as pοpulatiοn grοwth, cοmpοund interest, radiοactive decay, and the spread οf disease.
When b is greater than 1, the functiοn represents expοnential grοwth. As x increases, the functiοn grοws at an increasing rate.
When b is between 0 and 1, the functiοn represents expοnential decay. As x increases, the functiοn decays at a decreasing rate.
Therefοre,
The cοrrect statement is "The greater the value οf the base, the greater the functiοn's rate οf grοwth".
Learn more about Exponential function at
https://brainly.com/question/14355665
#SPJ1
Units of Capacity
Customary
System Units
1 gallon
1 quart
1 cup
Metric System Units
3.79 liters
0.95 liters
0.237 liters
Sameer usually drinks 3 cups of coffee in the morning.
How many liters of coffee does he drink? Round your
answer to the nearest tenth.
3 cups
1
X
new units
original units
Sameer drinks
morning.
=?
=
liters of coffee in the
As given the conversion unit: 1 cup = 0.237 liters. Sameer drinks 0.71 liters of coffee.
Explain about the units of measurements?Any physical quantity can be measured by comparing it to a recognised standard, and the magnitude is almost always expressed in terms of the reference standard known as a unit.
The FPS system, which measures length, mass, plus time in feet, pounds, and seconds, is one of the three systems that also was utilised for the measurement. The MKS system, which stands for metre, kilogramme, and seconds, has replaced the CGS system in centimetre, gramme, and seconds as the one that is widely used.
Units of Capacity are given as:
System Units Metric System Units
1 gallon - 3.79 liters
1 quart - 0.95 liters
1 cup - 0.237 liters
Coffee Intake of Sameer: 3 cups
1 cup - 0.237 liters
Multiply both sides by 3.
1*3 cup - 0.237*3 liters
3 cup - 0.711 liters
Thus, Sameer drinks 0.71 liters of coffee (rounded off nearest tenth).
Know more about the units of measurements
https://brainly.com/question/777464
#SPJ1
Complete question:
Units of Capacity are given as:
System Units Metric System Units
1 gallon - 3.79 liters
1 quart - 0.95 liters
1 cup - 0.237 liters
Sameer usually drinks 3 cups of coffee in the morning. How many liters of coffee does he drink? Round your answer to the nearest tenth.
Drew triangle JKL, with a height of inches and a base of inches, and triangle XYZ, with a height of inches and a base of inches. Which triangle has the greater area?
Triangle JKL has a greater area than triangle XYZ, as it has an area of 98 square inches
To determine which triangle has the greater area, we need to use the formula for the area of a triangle, which is half the product of the base and height.
For triangle JKL, with a base of 14 inches and a height of 14 inches, we have:
Area = (14 x 14) / 2 = 98 square inches
For triangle XYZ, with a base of 20 inches and a height of 8 inches, we have:
Area = (20 x 8) / 2 = 80 square inches
Therefore, triangle JKL has a greater area than triangle XYZ, as it has an area of 98 square inches compared to 80 square inches for triangle XYZ. This is because the base and height of triangle JKL are both larger than those of triangle XYZ.
To know more about area click here:
brainly.com/question/27683633
#SPJ4
Draw triangle JKL, with a height of 14 inches and a base of 14inches, and triangle XYZ, with a height of 8 inches and a base of 20 inches. Which triangle has the greater area? in 100 words
An increasing number of consumers believe they have to look out for themselves in the marketplace. According to a survey conducted by the Yankelovich Partners for USA WEEKEND magazine, 60% of all consumers have called an 800 or 900 telephone number for information about some product. Suppose a random sample of 25 consumers is contacted and interviewed about their buying habits
The probability that 11 or more of these consumers have called an 800 or 900 telephone number for information about some product is approximately 0.326.
How is the binomial probability distribution employed in statistics? What is it?The number of successes in a certain number of independent trials that all have the same probability of success are described by the discrete probability distribution known as the binomial probability distribution. The probability of success is constant during all trials, and it is used in statistics to describe situations where there are two alternative outcomes (success or failure).
The binomial probability distribution is given as:
P(X ≥ k) = 1 - P(X < k)
Here, p = 0.60, and the sample size is n = 20.
Thus,
P(X ≥ 11) = 1 - P(X < 11)
= 1 - ∑(20 choose x) (0.6)ˣ (0.4)⁽²⁰⁻ˣ⁾ for x from 0 to 10
P(X ≥ 11) = 0.326
Hence, the probability that 11 or more of these consumers have called an 800 or 900 telephone number for information about some product is approximately 0.326.
Learn more about binomial probability distribution here:
https://brainly.com/question/30786502
#SPJ1
The complete question is:
Two families at the zoo.
The smith family of two adults and three children pay £61.
The jones family of three adults and five children pay £96.
Work out the cost of and adult ticket and the cost of a child ticket.
Answer:
adult ticket £17
child ticket £9
Step-by-step explanation:
Let the cost of an adult ticket be X and child ticket be Y
make two simultaneous equations
2X+3Y=61
3X+5Y=96
solve for each variable by either substitution or elimination method
2X+3Y=61
X=(61-3Y)/2
3[(61-3Y)/2]+5Y=96
(183-9Y)/2 + 5Y=96
183-9Y+10Y=192
Y=9
X=(61-3(9))/2
X=17
5+5+5=15pts (Quadrics) Let Q=1 be a quadric surface in 3-dimensional affine Euclidean space R^3. (See the list of reduced quadrics given in Lecture 5). Determine which of these quadrics are - regular 2-surfaces; - ruled 2-surfaces. On p.271 of the book, M. Audin mentions that all quadrics appear as ruled surfaces if one allows lines to be imaginary. What does she mean by this statement?
In 3-dimensional affine Euclidean space R³, a regular 2-surface is a surface that has a well-defined tangent plane at each point on the surface, and a ruled 2-surface is a surface that can be generated by moving a straight line (the generator) along a curve (the directrix) on the surface.
What are quadric surfaces like?For the quadric surfaces, we have:
Ellipsoid: Regular 2-surfaceHyperboloid of one sheet: Regular 2-surfaceHyperboloid of two sheets: Regular 2-surfaceCone: Not a regular 2-surface (the vertex is a singular point)Elliptic paraboloid: Ruled 2-surfaceHyperbolic paraboloid: Ruled 2-surfaceCylinder: Ruled 2-surfaceSphere: Not a regular 2-surface (the center is a singular point)Regarding the statement by M. Audin, she means that if we allow lines to be imaginary, then any quadric surface can be generated by moving a straight line (even if it is an imaginary line) along a curve on the surface.
In other words, every quadric surface can be considered a ruled surface if we allow imaginary lines. This is a consequence of the fact that any two points on a quadric surface can be connected by at least one real or imaginary line.
learn more about quadric surfaces: https://brainly.com/question/12955029
#SPJ1
5 menos que el conciente de un número y 2.
The expression "5 less than the conscious number and 2" can be written mathematically as: n - 5 = 2
What is a Math Expression?A math expression is a combination of mathematical symbols, numbers, and variables that represents a mathematical statement or calculation. It can be as simple as a single number, such as 5, or as complex as a multi-term equation, such as 3x + 4y = 12.
Expressions can include arithmetic operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions such as exponents, logarithms, and trigonometric functions.
How to solve the given expression?Where "n" represents the number in question. To find the value of "n", you can add 5 to both sides of the equation:
n - 5 + 5 = 2 + 5
This is the result:
n = 7
Therefore, the number in question is 7.
Read more about algebra here:
https://brainly.com/question/432678
#SPJ1
The question in English is:
(What is) 5 less than the conscious of a number and 2
A 15-foot ladder is leaning against a wall of a building. If the top of the ladder makes a 72° angle with the wall of the building, approximately how high above the ground is the top of the ladder?
Answer:
14.2665 feet above the ground
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's call the height of the ladder on the wall "h". Then we have:
sin(72°) = h/15
Multiplying both sides by 15, we get:
h = 15 sin(72°)
Using a calculator, we find that sin(72°) is approximately 0.9511. So:
h ≈ 15 × 0.9511
h ≈ 14.2665
Therefore, the top of the ladder is approximately 14.2665 feet above the ground.
A plant in Alamo, TN, manufactures complex transformer components that must meet specific guidelines for safety. One such component is constructed to deliver 1,000 volts of electricity. A component creates a critical safety hazard if it absorbs humidity at a level above 3%. Any components that absorb too much humidity will be destroyed. A quality control inspector uses a random sample of components to conduct a hypothesis test with H0: The humidity level absorbed is 3%, and Ha: The humidity level absorbed is more than 3%. What is the consequence of a Type II error in this context?
The company believes the humidity absorbed is more than 3% when in fact it is not. Correctly functioning components will be destroyed at great expense to the company.
The company believes the voltage delivered is more than 1,000 volts, when in fact it is not more than 1,000 volts. Correctly functioning components will be destroyed at great expense to the company.
The company believes the voltage delivered is no more than 1,000 volts, when in fact it is more than 1,000 volts. The company will sell components that absorb a dangerous level of humidity.
The company believes the humidity absorbed is not more than 3%, when in fact it is more than 3%. The company will sell components that absorb a dangerous level of humidity.
answer is D
In this case, it means that the company fails to identify components that absorb too much humidity, leading to a potential safety hazard for customers.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The consequence of a Type II error in this context is that the company believes the humidity absorbed is not more than 3%, when in fact it is more than 3%.
This means that the company will fail to detect components that absorb a dangerous level of humidity, and these components will be sold to customers, potentially causing a safety hazard. This is because the null hypothesis in this case is that the humidity level absorbed is 3%, and the alternative hypothesis is that it is more than 3%. A Type II error occurs when the null hypothesis is not rejected, even though it is false, and the alternative hypothesis is true.
Therefore, In this case, it means that the company fails to identify components that absorb too much humidity, leading to a potential safety hazard for customers.
To learn more about Algebraic expression from given link.
brainly.com/question/953809
#SPJ1
Jermaine spent $204 dollars on
shirts for his 21 employees while he
was on his vacation. Large shirts
were $12 and small shirts were $8.
How many larges did he buy?
Jermaine bought 9 large shirts for $12, and 12 small shirts for $8 for his 21 employees.
Let's represent the number of large shirts Jermaine bought as "L" and the number of small shirts as "S". We can set up a system of equations based on the information given:
L + S = 21 (equation 1, the total number of shirts is 21)
12L + 8S = 204 (equation 2, the total cost of the shirts is $204)
To solve for L, we need to eliminate S. We can do this by multiplying equation 1 by 8 and subtracting it from equation 2:
12L + 8S = 204
8L + 8S = 168 (multiply equation 1 by 8)
4L = 36
Dividing both sides by 4, we get:
L = 9
Therefore, Jermaine bought 9 large shirts for his 21 employees. We can find the number of small shirts by substituting L = 9 into equation 1:
L + S = 21
9 + S = 21
S = 12
So, by using linear equation system we find that Jermaine bought 9 large shirts and 12 small shirts for his 21 employees.
To know more about Purchase:
https://brainly.com/question/18649419
#SPJ4
In ΔABC, c = 75 cm,
�
m∠B=154° and
�
m∠C=13°. Find the length of a, to the nearest 10th of a centimeter.
The length of the side a , to the nearest 10th of a centimeter is 75cm
How to determine the valueIt is important to note that the sum triangle theorem states that the sum of the interior angles of a triangle is equal to 180 degrees.
Then, we have;
m< A + m< B+ m < C = 180
substitute the values, we have;
m < A = 180 - 154 - 13
subtract the values
m < A = 13 degrees
Using the sine rule, we have that;
sin A/a = sin B/b = sin C/c
Where; the capital letters are the angles and the small letters are the sides.
We have;
sin A/a = sin C/c
substitute the values
sin 13/a = sin 13/75
cross multiply
a = sin 13 × 75/sin 13
a = 75cm
Learn about law of sines at: https://brainly.com/question/27174058
#SPJ1
Somebody please help me with my homework
The missing angle measures are 50 degrees, 100 degrees, and 80 degrees.
x = 50, we can substitute this value into the expressions for the other two angles:
2x = 2(50) = 100
x + 30 = 50 + 30 = 80
What are angles?When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol stands for the angle. Angle is a derivative of the Latin word "Angulus."
The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the shape of the angle can alternatively be used to symbolize the angle, with the middle letter indicating the location of the angle (i.e.its vertex).
From the question:
The total of the measures of the angles in any triangle is always 180 degrees, as shown by the characteristics of triangle angles.
This knowledge allows us to construct an equation to account for the missing angle measurements:
x + 2x + 30 = 180
Combining like terms, we get:
3x + 30 = 180
Subtracting 30 from both sides, we get:
3x = 150
Dividing both sides by 3, we get:
x = 50
Knowing that x = 50, we can change the formulas for the remaining two angles to reflect this value:
2x = 2(50) = 100
x + 30 = 50 + 30 = 80
As a result, the missing angle measurements are 50, 100, and 80 degrees.
to know more about angle visit:
https://brainly.com/question/28451077
#SPJ1
HELPPP PLEASE
Line p has a slope of -3/8, Line q is perpendicular to p. What is the slope of line q?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
[tex]\frac{8}{3}[/tex]
Step-by-step explanation:
We know that
Line q's slope = [tex]-\frac{3}{8}[/tex]
AND we know that line q is perpendicular to line p.
When a line is perpendicular to another line, this means that the slope is the opposite reciprocal of the other slope.
This means that we simply have to flip our fraction and change the sign.
Thus, the slope is [tex]\frac{8}{3}[/tex]
Assume g and h are whole numbers, and g < h. Which expression has the least value?
Expression B has the least value if g and h are whole numbers, and
g < h.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Given that,
g < h
To determine which expression has the least value, we need to simplify each expression as much as possible and compare the results.
First, let's simplify expression A:
A = (h + g) * (h - g)
= h*h - g*g
Next, let's simplify expression B:
B = h*h- 2hg + g*g
Finally, let's simplify expression C:
C = h*h + 2hg + g*g
Now we can compare the expressions. We know that g < h, so g*g < h*h. Therefore, the smallest value will be produced by the expression with the smallest coefficient for the h*h term.
A has a coefficient of 1 for the h*h term, while B and C have coefficients of -2h and 2h, respectively. Since h is positive, -2h is the smallest coefficient, so expression B has the smallest value.
Therefore, expression B has the least value.
To learn more about Algebraic expression from given link.
brainly.com/question/953809
#SPJ1
PLEASE HELP ASAP!!!
Question in photo
Sam purchases a new car for $29,500. The car depreciates at a rate of 13. 25% per year. What is
the value of the car after 7 years?
If Sam purchases a new car for $29,500 and the car depreciates at a rate of 13. 25% per year, then the value of the car after 7 years is $11652.50
We can use the formula for exponential decay to find the value of the car after 7 years:
V = P × e^(-rt)
where:
V = value of the car after 7 years
P = initial price of the car
r = annual depreciation rate (as a decimal)
t = time in years
Plugging in the values we get:
V = 29500 × e^(-0.1325 × 7)
V = 29500 × e^(-0.9275)
V = 29500 × 0.395
V = $11652.50
Learn more about exponential decay here
brainly.com/question/30935879
#SPJ4