a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.
How did we get the values?a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score for the desired confidence level (1.96 for 95% confidence level)
p = proportion of beak adjustments estimated from preliminary investigation (0.3)
E = margin of error (0.1)
Plugging in the values:
n = (1.96^2 * 0.3 * 0.7) / 0.1^2
n = 38.15
Rounding up, we need at least 39 work sampling observations.
b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.
c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:
Standard = (Total time worked / Total number of beak adjustments) * 100
For the six employees summarized in the table:
Granny:
Standard = (82 / 164) * 100
Standard = 50 hours per hundred beak adjustments
Tweety:
Standard = (80 / 161) * 100
Standard = 49.69 hours per hundred beak adjustments
Item:
Standard = (200 / 185) * 100
Standard = 108.11 hours per hundred beak adjustments
Total:
Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100
Standard = 83.56 hours per hundred beak adjustments
The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:
Standard Error = Standard Deviation / √(n)
Where:
Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))
n = sample size
Using the data provided in the table, we can calculate the standard deviation and standard error as follows:
Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))
Standard Deviation = 55.88
Standard Error = 55.88 / √(6)
Standard Error = 22.83
This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.
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The complete question goes thus:
ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99
How far is the mall from the pet shop? Explain how you know
The distance of the mall from the pet shop, based on the graphic given, is 2 miles.
How to find the distance?The distance between the Pet Shop, the School, the Mall and the Park are all shown on the graphic. The intervals between the distance given is shown to be 1 / 2 miles.
The number of distance marks between the Pet Shop and the Mall is 4 marks which means that distance between the Pet Shop and the Mall would be :
= 4 x 1 / 2
= 4 / 2
= 2 miles
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The probability that a person will be helped by a certain medicine is .75. Our facility will be seeing 30 patients today. Let X count the number of patients, of those 30, that are helped by the medicine. Determine the following:
a) P (20 < or = X)
b) P (18 < or = X < 25)
c) P ( X < 16)
a) P (20 < or = X) = 0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.
b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.
c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.
The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:
P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.
a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617
b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557
c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266
Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.
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Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3
The result obtained when x^(4)-6x^(2)-x-19 is divided by x-3 using long division method is x3 - 18x2 - 9x - 57 + 19/x-3.
The question is, "Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3".
To solve this problem using long division, we need to set up the division like this:
x4 - 6x2 - x - 19
___________________ (x-3)
0
-3x3 - 18x2 - 9x - 57
Now, divide the first term of the numerator by the first term of the denominator, x4/x = x3, and write it above the division. Next, multiply the result x3 by the denominator (x-3) to get -3x3.
Now subtract -3x3 from the numerator (x4 - 6x2 - x - 19) to get -6x2 - x - 19. Divide this by the denominator (x-3) to get -18x2 - 9x - 57, and write it below the division. Now multiply the result -18x2 by the denominator (x-3) to get -54x2 - 27x - 171.
Finally, subtract -54x2 - 27x - 171 from -6x2 - x - 19 to get the remainder, -19.
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Several anthropology students are unprepared for a surprise true/false test with 23 questions, and all of their answers are guesses.
Give the range for the usual number of correct answers.
(Enter answer as an interval using square-brackets only with whole numbers.)
usual values =
The range for the usual number of correct answers is given as follows:
[7, 16]
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
p = 0.5, n = 23.
The mean and the standard deviation are given as follows:
E(X) = np = 23 x 0.5 = 11.5.S(X) = sqrt(np(1-p)) = sqrt(23 x 0.5 x 0.5) = 2.4.The usual range of correct answers is within 2.5 standard deviations of the mean, hence:
11.5 - 2 x 2.4 = 6.7. -> rounded to 7.11.5 + 2 x 2.4 = 16.3. -> rounded to 16.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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PLEASE HELP!! I don’t even know how to type that
The value of [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given equation is [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex]
[tex]\sum \:a_n+b_n=\sum \:a_n+\sum \:b_n[/tex]
By Applying the sum rule
[tex]=\sum \:_{n=1}^{400}2n-\sum \:_{n=1}^{400}1[/tex]
=2×2(400+1)/2 -400
=2×200×401−400
=16000
Hence, the value of [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.
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For the given number, (a) identify the complex conjugate and (b) determine the product of the number and its conjugate. -5-2i Part 1 of 2 The complex conjugate is
The product of the number and its conjugate is 29.
The complex conjugate of a complex number is the number with the same real part and the opposite sign of the imaginary part. In other words, if a complex number is a + bi, then its complex conjugate is a - bi.
For the given number -5 - 2i:
(a) The complex conjugate is -5 + 2i. This is because the real part is the same (-5) and the imaginary part has the opposite sign (2i instead of -2i).
(b) To determine the product of the number and its conjugate, we simply multiply them together:
(-5 - 2i)(-5 + 2i) = 25 - 10i + 10i - 4i^2
Since i^2 = -1, we can simplify this to:
25 - 4(-1) = 25 + 4 = 29
So the product of the number and its conjugate is 29.
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Convert this rational number to its decimal form and round to the nearest thousandth. 1/7=__√[?] First, let's convert the fraction into a long division problem. Hint: First enter the number on the inside of the division box. This number should be the numerator of the fraction.
0.142857.
To convert the rational number 1/7 to its decimal form and round to the nearest thousandth, let's start by converting the fraction into a long division problem.
Enter the numerator of the fraction, 1, into the division box, and then divide it by the denominator of the fraction, 7.
The result of this long division is 0.142857. Finally, round this decimal to the nearest thousandth, which gives us 0.143.
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Indigo built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box. What is the surface area, in square centimeters, of the toy box? (Lengths are 9cm, 5cm and 10cm)
The surface area, in square centimeters, of the toy box is 370 cm²
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. Surface area is measured in cm².
Given, the lengths are 9 cm, 5 cm, and 10 cm.
To calculate the surface area, the formula is2(h × W) + 2(h × L) + 2(W × L)
2 x 9 x 5 + 2 x 9 x 10 + 2 x 5 x 10
90 + 180 + 100
370
Therefore, the surface area of the box is 370 cm²
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The question is incomplete, the image of the box is attached below:
Use line direction to:
A. eliminate the imaginary cross contour lines of fabric.
B. hide the underlying form of the fabric.
C. show the undulating forms of fabric.
Answer:
C.
Step-by-step explanation:
C. show the undulating forms of fabric.
common help me with this pls
Answer:
See image attached for complete answer
Step-by-step explanation:
The attached image shows the calculation of probabilities for each branch
I believe it is self-explanatory
Since P(bus to shops) = 0.4, P(walk to shops ) = 1- 0.4 = 0.6
Since P(bus from shops) = 0.7, P(walk from shops) = 1- 0.7 = 0.3
The probabilities at the leaves of the tree(rightmost entries) show the combined probabilities of to and from
For example if she takes a bus to the shops and takes a bus from the shops, the combined probability = 0.4 x 0.7 = 0.28
If she walks to the shops and takes a bus from the shops the combined probability = 0.6 x 0.7 = 0.42
The other two probabilities can be computed the same way
The probability that she walks at least one way
= P(walking to shop) or P(walking from shop)
= sum of the probabilities in the yellow shaded boxes
= 0.12 + 0.42 + 0.18
= 0.72
Work out th june salary that was received bythe tanker driver if he woked the entire month
The total salary received by the tanker driver if he worked the entire month would be equal to Rs. 19980 .
It is already given that the tanker driver worked for 5 and a half days for 9 hours daily, except on Saturday where they worked for half a day (which means 4.5 hours) and were paid double than the daily rate. It is also known that the month of June has 30 days. So calculating the number of working days, we get approximately 4 working weeks in which 20 days are week days and 4 days are Saturdays.
Total amount earned by the tanker driver = (No. of week days worked × Total hours worked × Rate of pay per hour) + (No. of working Saturdays × Total hours worked × Rate of pay per hour on Saturday)
Total amount earned by the tanker driver = (20 × 9 × 92.50) + (4 × 4.5 × 185)
Total amount earned by the tanker driver = 16650 + 3330 = 19980
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Refer to complete question below:
The driver of the water tanker works for 5½ days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4.5 hours). The rate per hour was Rs. 92.50 and the rate of pay was doubled on Saturdays. Work out the June salary that was received by the tanker driver if he worked the entire month.
Write the equation of y=x^(2) when it is translated 8 units to the left and then 6 units downward.
The equation of y=x^(2) can be translated 8 units to the left and then 6 units downward by modifying the equation as follows:
y=(x+8)^(2)-6
This equation represents the same parabola as y=x^(2), but it has been shifted 8 units to the left and 6 units downward.
The translation of a function can be represented by modifying the equation in the form y=f(x-h)+k, where h is the horizontal shift and k is the vertical shift. In this case, h=-8 and k=-6, so the equation becomes:
y=f(x-(-8))+(-6)
y=f(x+8)-6
Substituting the original function f(x)=x^(2) into this equation gives:
y=(x+8)^(2)-6
Therefore, the equation of y=x^(2) when it is translated 8 units to the left and then 6 units downward is y=(x+8)^(2)-6.
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What is the probability of selecting a
red pencil and a green M&M?
A. 2/141
B. 2/151
C. 2/161
The probability of selecting a red pencil and a green M&M is calculated as follows:
p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The pencil and the M&M are independent events, hence we calculate the probability of each event and then multiply then, as follows:
p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].
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60 points :d
how can you do whole numbers divided by decimals?
like for example
9 divided by 0.85
sorry if this is obvious!!
Answer:
When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:
. __________
0.85 | 9.00
8.50 (0.85 goes into 9.00 one time)
-----
1.50 (subtract 8.50 from 9.00)
1.27 (0.85 goes into 1.50 one time)
-----
0.23 (subtract 0.85 from 1.50)
When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:
sql
Copy code
. __________
0.85 | 9.00
8.50 (0.85 goes into 9.00 one time)
-----
1.50 (subtract 8.50 from 9.00)
1.27 (0.85 goes into 1.50 one time)
-----
0.23 (subtract 0.85 from 1.50)
The quotient is the number above the division line, which is 10 with a remainder of 23/100. Therefore:
9 / 0.85 = 10 with a remainder of 23/100, or 10.5882 (rounded to four decimal places)
So, 9 divided by 0.85 is approximately 10.5882.
Ils Practice 3 Simplify the expression. Make all exponents pos ((-8x^(5))(x^(-3)))/(20x^(2))
The expression ((-8x⁵)(x⁻³))/(20x²) when simplified, making all exponents positive, will become -2/5.
To simplify the expression ((-8x⁵)(x⁻³))/(20x²), we need to apply the rules of exponents and simplify the coefficients.
First, let's simplify the coefficients:
-8/20 = -2/5
Next, let's apply the rules of exponents:
Product Rule: When multiplying two exponential expressions with the same base, you can add the exponents. That is, xᵃ · xᵇ = xᵃ⁺ᵇ
Quotient Rule: When dividing two exponential expressions with the same base, you can subtract the exponents. That is, xᵃ / xᵇ = xᵃ⁻ᵇ
(x⁵)(x⁻³) = x⁵⁺⁽⁻³⁾ = x²
x²/x² = x²⁻² = x⁰ = 1
So the expression simplifies to:
(-2/5)(1) = -2/5
Therefore, the simplified expression is -2/5.
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What is the answer? I don't quite get it.
(3x + 1/2) + (7x - 4 1/2)
Answer:
To simplify the expression, we can combine the like terms.
(3x + 1/2) + (7x - 4 1/2)
= 3x + 7x + 1/2 - 4 1/2 (distributing the addition)
= 10x - 4 (combining the like terms)
Therefore, (3x + 1/2) + (7x - 4 1/2) simplifies to 10x - 4.
What is JL? aaaaaaaaaaaaaaaaaa
7. Parallelogram CDEF has vertices C(3, 2), D(8, 4), E(6, -3) and F(1, -5). Its image has vertices
C'(-6, 6), D'(-1, 8), E’(-3, 1), and
F’(-8, -1). Write a rule to represent this translation.
A rule to represent this translation include the following (x, y) → (x - 9, y + 4).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.C(3, 2) → C'(-6, 6)
3 + x = -6
x = -6 - 3 = -9.
y + 2 = 6
y = 6 - 2 = 4.
Therefore, the transformation rule is (x, y) → (x - 9, y + 4)
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11. Find the measures of the numbered angles in each kite.
12. For what value of X is figure XYZA a rectangle?
By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.
What is graphs?Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.
With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.
Let's give a generic kite's angles the labels displayed in the accompanying diagram:
A-------B
/ \
D-----------C
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The path of a ball thrown from a cliff is modelled by the quadratic function h(t)=-4.9(t-1)^2+35.
From what height is the hall thrown?
Range of the function?
How long does it take for the ball to land?
Answer:
2 hours
Step-by-step explanation:
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Given the function f(x)=x+3/x-8 aind the following. (a) the
average rate of change of f on [−3,1]: (b) the average rate of
change of f on [x,x+h]:
(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1
(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)
The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.
The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1
The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)
Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).
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1. Which of the following are the
possible lengths to complete a
triangle with side lengths of 11 in.
and 14 in.?
The possible length of the third side of a triangle is l < 25
What is triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Given that, we need to find the possible lengths to complete a triangle with side lengths of 11 in. and 14 in.
We know that, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
Therefore,
11 + 14 = 25
Let the third side be l,
Therefore,
l < 25
Hence, the possible length of the third side of a triangle is l < 25
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What is (z^(2)+10z+25)/(z^(2)-3z-40) in simplest form? State any restrictions on the variable.
The expression (z²+10z+25)/(z²-3z-40) in simplest form is (z+5)/(z-8), with the restriction that z cannot be equal to 8.
The expression (z²)+10z+25)/(z²-3z-40) can be simplified by factoring both the numerator and denominator.
First, factor the numerator:
(z²+10z+25) = (z+5)(z+5)
Next, factor the denominator:
(z²-3z-40) = (z-8)(z+5)
Now, the expression can be simplified by canceling out the common factor of (z+5):
(z+5)(z+5)/(z-8)(z+5) = (z+5)/(z-8)
Therefore, the expression in simplest form is (z+5)/(z-8).
There are restrictions on the variable in this expression. The denominator cannot be equal to zero, so we must exclude any values of z that would make the denominator zero.
The denominator is (z-8), so the restriction is:
z-8 ≠ 0
Solving for z, we find that the restriction is:
z ≠ 8
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Julia is a salesperson. She sold a chandelier for $66 and earned 5% commission .How much commission didJulia earn?
Answer:
$3.30
Step-by-step explanation:
66 times 0.05
DOES ANYONE KNOW THE ANSWER PLEASE
Answer:
Step-by-step explanation:
45 points for signing up.
2.5 points for each visit [tex]=2.5v[/tex]
Needs to total 75 points.
So [tex]45+2.5v=75[/tex] is the solution.
This is shown by option [tex](D)[/tex].
Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
The triangles are similar by SAS rule.
What are Similar Triangles?Similar triangles are those triangles which have the same shape, but different size.
The corresponding angles of similar triangles are equal and the corresponding sides are proportional.
Given are two triangles ΔGNH and ΔLNM.
∠N is common to both triangles are thus equal.
So ∠N ≅ ∠N
GN / LN = 40 / (12.5 + 40) = 40/52.5 = (16×2.5) / (21×2.5) = 16/21
HN / MN = 32 / (10 + 32) = 32/42 = (16×2) / (21×2) = 16/21
Two corresponding sides are proportional.
So, we have, two corresponding sides are proportional and the corresponding included angles are equal.
This is SAS Similarity rule.
Hence the triangles are similar by SAS similarity rule.
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HELP PLEASE!!!!!!!!!!!!!!!!!!!!!
The simplified fraction is given as follows:
(2x - a)/(2x + a).
How to simplify the fraction?At the numerator, the fraction is simplified applying the least common factor as follows:
2 - (a/x) = (2x - a)/x.
At the denominator, the fraction is also simplified applying the common factor as follows:
2 + (a/x) = (2x + a)/x.
x is a common denominator to both of the fractions, hence it can be simplified, and then the simplified fraction is given as follows:
(2x - a)/(2x + a).
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Anissa is making 5
hats out of balloons. She wants the hats to be the same, and she wants to use as many balloons as possible. If she starts with 54
balloons, how many balloons will not be used?
The number of balloons which will not be used by Anissa is 4 balloons.
How many balloons will not be used by Anissa?To make all 5 hats the same, Anissa needs to use the same number of balloons for each hat.
Let us call the number of balloons she uses for each hat "x". Since she's making 5 hats, she'll use a total of 5x balloons. We know that she has 54 balloons in total, so we can set up an equation:
5x = 54
To solve for x, we can divide both sides by 5:
x = 54 / 5
x = 10.8
Since she can't use a fraction of a balloon, she'll need to use 10 balloons for each hat.
= 5 hats x 10 balloons/hat
= 50 balloons used
So Anissa will not use:
= 54 - 50
= 4 balloons.
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during the two days after a blizzard, 77% of the snow had melted. If the snow is currently 30 inches deep, how much snow fell during the snow?
By answering the above question, we may infer that Hence, during the equation blizzard, snowfall totaled about 100.43 inches.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
To begin, let's calculate the amount of snow that evaporated. If 77% of the snow melted, the quantity of snow that is left is 100% - 77%, or 23%, of what was originally there.
This can be represented as:
Snow remaining equals 0.23x.
Assume that x inches of snow were present at the start. Thus, we may construct the equation shown below:
0.23y = 30
By finding y, we obtain:
y = 30 / 0.23 ≈ 130.43
Hence, the initial snowfall measured about 130.43 inches.
We may use the difference between the present depth of snow and the original depth of snow to calculate how much snow fell during the blizzard:
130.43 - 30 = 100.43
Hence, during the blizzard, snowfall totaled about 100.43 inches.
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For f(x) = x^15 and g(x) = 15Vx, find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x)
What is (fog)(x)?
(fog)(x) = ___
Based on the calculation, we find that:
(fog)(x) = (15Vx)¹⁵
(gof)(x) = 15V(x¹⁵)
(fog)(x) ≠ (gof)(x)
Function composition can be meant as an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
To find (fog)(x), we need to substitute g(x) into f(x). This means that we will replace every x in f(x) with 15Vx. So, (fog)(x) = f(g(x)) = f(15Vx) = (15Vx)¹⁵.
Similarly, to find (gof)(x), we need to substitute f(x) into g(x). This means that we will replace every x in g(x) with x¹⁵. So, (gof)(x) = g(f(x)) = g(x¹⁵) = 15V(x¹⁵).
Now, to determine whether (fog)(x) = (gof)(x), we need to compare the two expressions.
(fog)(x) = (15Vx)¹⁵ and (gof)(x) = 15V(x¹⁵). These two expressions are not equal, so (fog)(x) ≠ (gof)(x).
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