1) 2a - 100
Substituting the value of a here,
[tex] \rm 2(32) - 100 [/tex]
[tex] \rm 64 - 100 [/tex]
[tex] \rm -36 [/tex]
2) b (-12)
Substituting the value of b here,
[tex] \rm 150 (-12) [/tex]
[tex] \rm -1800 [/tex]
3) 4a + b
Substituting the values of a and b here,
[tex] \rm 4(32) + 150 [/tex]
[tex] \rm 128 + 150 [/tex]
[tex] \rm 278 [/tex]
4) 9b - 2a
Substituting the values of a and b here,
[tex] \rm 9(150) - 2 (32) [/tex]
[tex] \rm 1350 - 64 [/tex]
[tex] \rm 1286 [/tex]
The answers are:
below in [tex]\bold{bold}[/tex]
Work/explanation:
Plug in 32 for a
[tex]\sf{2(32)-100}[/tex]
[tex]\sf{64-100}[/tex]
[tex]\bf{-36}[/tex]
____________
[tex]\sf{b(-12)}[/tex]
[tex]\sf{150\cdot(-12)}[/tex]
[tex]\bf{1,800}[/tex]
____________
[tex]\sf{4a+b}[/tex]
[tex]\sf{4(32)+150}[/tex]
[tex]\sf{128+150}[/tex]
[tex]\bf{278}[/tex]
____________
[tex]\sf{9b-2a}[/tex]
[tex]\sf{9(150)-2(32)}[/tex]
[tex]\sf{1,350-64}[/tex]
[tex]\bf{1,286}[/tex]
____________
Devon’s bike has wheels that are 26 inches in diameter. After the front wheel picks up
a tack, Devon rolls another 100 feet (1200 inches) and stops. How far above the ground in inches is the tack?
To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.
First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:
C = π × 26
C ≈ 81.64 inches
This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.
Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:
1200 / 81.64 ≈ 14.68 revolutions
Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.
Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.
Therefore, the tack is located 13 inches above the ground.
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if the word AFGANISTAN represented 02034560 by code
1. what code is represented by the word AFGAN?
The code represented by the word "AFGAN" would be "02034."
How to determine the code represented by the word "AFGAN"To find the code represented by the word "AFGAN," we need to refer to the given code representation of the word "AFGANISTAN," which is "02034560."
From the given code, we can determine that the letters "AFGAN" correspond to the first five digits of the code.
Therefore, the code represented by the word "AFGAN" would be "02034."
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Question 1 of 10
What is a name for the angle below? Do not include the angle symbol in your answer
Answer:
XYZThe name of angle below is XYZ
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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a company's financial records at the end of the year included the following amounts.
cash - $70,400
accounts receivable - $28,400
supplies - $4,400
accounts payable $10,400
notes payable $5,200
retained earnings, beginning of year $17,400
common stock $44,000
service revenue $50,400
wages expense $ 8,400
advertising expense $5,400
rent expense $10,400
what is the amount of net income on the income statement for the year?
The amount of net income on the income statement for the year is $26,200.
To determine the net income, we need to calculate the total revenue and subtract the total expenses.
Total Revenue = Service Revenue = $50,400
Total Expenses = Wages Expense + Advertising Expense + Rent Expense = $8,400 + $5,400 + $10,400 = $24,200
Net Income = Total Revenue - Total Expenses = $50,400 - $24,200 = $26,200
Therefore, the amount of net income on the income statement for the year is $26,200.
To calculate the net income, we consider the revenue and expenses recorded in the company's financial records.
Revenue represents the inflow of money from the company's primary operations. In this case, the revenue is listed as "Service Revenue" with a value of $50,400.
Expenses represent the outflow of money incurred by the company in conducting its operations. The expenses mentioned in the records are "Wages Expense" ($8,400), "Advertising Expense" ($5,400), and "Rent Expense" ($10,400).
To calculate the net income, we subtract the total expenses from the total revenue:
Net Income = Total Revenue - Total Expenses
Total Revenue = $50,400
Total Expenses = $8,400 + $5,400 + $10,400 = $24,200
Net Income = $50,400 - $24,200 = $26,200
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There are 40 boys and 30 girls in a class. Find the percentage of girls in the class.
42.86%
41.37%
43.15%
75%
41.37%
43.15%
75%
Anne bought a piece of ribbon that is 7 over 9 m long. She used 3 over 18 m of it to tie a birthday present. She then used the remaining ribbon to form squares of sides 1 over 16 m. What was the maximum number of squares she could form?
Answer:
9 squares
Step-by-step explanation:
Anne bought a piece of ribbon = 7 over 9 m long = 63 m²
she used = 3 over 18 m = 54 m²
left = 9 m²
maximum number of squares she could form of 1 m = 9
6. Mr. Chao's students measured the length of different markers in inches. The data
collected is below.
Data set: 4, 5.5, 4.25, 5, 6.25, 6, 5.5, 5.25, 6.25, 4, 6.25, 5, 4.75, 6, 5.5, 6.75, 6.25 .Make a data table carefully organize the information
6. Mr. Chao's students measured the length of different markers in inches. The data
collected is below.
Data set: 4, 5.5, 4.25, 5, 6.25, 6, 5.5, 5.25, 6.25, 4, 6.25, 5, 4.75
Identify if it’s linear or quadratic
Answer:
(A) - [tex]f(g(x))=-18x^2+27x-19[/tex]
(B) - Quadratic
(C) - x=3/4
Step-by-step explanation:
Given:
[tex]f(x)=-2x^2+x-9\\\\g(x)=3x-2[/tex]
Find:
(A) -[tex]f(g(x))= \ ??[/tex]
(B) - Determine if f(g(x)) is linear or quadratic
(C) - Identify the slope or axis of symmetry
[tex]\hrulefill[/tex]
Part (A) -
Simply plug the function g(x) into f(x) to find f(g(x)):
[tex]f(g(x))=-2(3x-2)^2+(3x-2)-9[/tex]
Simplifying:
[tex]\therefore \boxed{f(g(x))=-18x^2+27x-19}[/tex]
Thus, part (A) is solved.
Part (B) -
To determine if a function is linear or quadratic, you need to examine its form and characteristics. Here are some key differences between linear and quadratic functions:
Linear Function:
The general form of a linear function is f(x) = mx + b, where m and b are constants.A linear function represents a straight line on a graph.The degree of a linear function is 1, meaning the highest power of the variable (x) is 1.In a linear function, the rate of change (slope) remains constant.Quadratic Function:
The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants, and a ≠ 0.A quadratic function represents a curve (parabola) on a graph.The degree of a quadratic function is 2, as the highest power of the variable (x) is 2.In a quadratic function, the rate of change (slope) is not constant and varies as x changes.Using the information above we can determine f(g(x)) is quadratic.
Part (C) -
The axis of symmetry of a quadratic function can be found by using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function in standard form. The resulting x-coordinate represents the vertical line that divides the parabola into two equal halves.
[tex]\text{In our case}: \ a=-18 \ \text{and} \ b=27\\\\\\\Longrightarrow x=\dfrac{-27}{2(-18)} \\\\\\\therefore \boxed{x=\frac{3}{4} }[/tex]
Thus, part (C) is solved.
A parent function and transformed function are shown: y = RootIndex 3 StartRoot x EndRoot. y = negative (0.4) RootIndex 3 StartRoot x minus 2 EndRoot Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply. reflected over the x-axis translated 2 units left translated 2 units right compressed by a factor of 0.4 stretched by a factor of 0.4 translated 2 units up translated 2 units down
Answer: The transformed function is y = -0.4√(x - 2).
Step-by-step explanation:
From the given equation, we can identify the following transformations:
Reflected over the x-axis: The negative sign in front of the function (-0.4) indicates a reflection over the x-axis.
Translated 2 units left: The "-2" inside the square root indicates a translation of 2 units to the right.
Compressed by a factor of 0.4: The coefficient "0.4" in front of the square root indicates a vertical compression by a factor of 0.4.
Translated 2 units down: There is no direct indication of a vertical translation in the equation, so this transformation is not applicable.
Therefore, the correct descriptions of the graph of the transformed function compared with the parent function are:
Reflected over the x-axis
Translated 2 units right
Compressed by a factor of 0.4
Quick help pleasae been stuck in brain
ssume all information in example 1 above and the following additional information: Actual data for job 201 is give is given belowActual shirts completed for job 201………………2,000 shirtsActual direct material cost used………………...$30,000Actual direct cost incurred……………………...$20,000Actual direct labor hours used…………………. 400 hoursActual machine hours…………………………. 240 hoursInstruction: compute the applied factory overhead and determine the total cost of job 201 under each of the five bases. A) Physical output as allocation baseDirect materials cost as allocation base Direct labor cost as allocation base Direct labor hours as allocation baseMachine hours as allocation base
The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.
Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.
Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.
Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.
The applied overhead cost for job 201 is $30,000*120% = $36,000.
Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.
-Direct labor cost as allocation base:
The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.
The applied overhead cost for job 201 is $20,000*120% = $24,000.
Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.
-Direct labor hours as allocation base:
The actual direct labor hours used in job 201 is 400 hours.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.
Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.
-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.
The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.
-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.
The applied overhead cost for job 201 is $24*240 hours = $5,760.
Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.
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Use trigonometric identities to verify each expression is equal.
(sin(x))/(1-cos(x)) - cot(x) = csc(x)
Answer:
Step-by-step explanation:
[tex]\frac{sin(x)}{1-cos(x)} -cot(x)=csc(x)\\[/tex]
[tex]\frac{sin(x)}{1-cos(x)} -\frac{cos(x)}{sin(x)} =csc(x)[/tex]
[tex]\frac{sin^{2}(x)-cos(x)+cos^{2}(x) }{(1-cos(x))sin(x)} =csc(x)\\\\\frac{1-cos(x)}{(1-cos(x))sin(x)} =csc(x)\\[/tex]
[tex]\frac{1}{sin(x)} =csc(x)\\csc(x)=csc(x)[/tex]
QED
Answer:
See below for proof.
Step-by-step explanation:
Use the cotangent identity to rewrite cot(x) as cos(x) / sin(x):
[tex]\dfrac{\sin(x)}{1-\cos(x)}-\cot(x)=\dfrac{\sin(x)}{1-\cos(x)}-\dfrac{\cos (x)}{\sin(x)}[/tex]
Make the denominators of both fractions the same:
[tex]=\dfrac{\sin(x)}{1-\cos(x)}\cdot{\dfrac{\sin(x)}{\sin(x)}-\dfrac{\cos (x)}{\sin(x)}\cdot{\dfrac{1-\cos(x)}{1-\cos(x)}[/tex]
[tex]=\dfrac{\sin^2(x)}{\sin(x)(1-\cos(x))}-\dfrac{\cos (x)(1-\cos(x))}{\sin(x)(1-\cos(x))}[/tex]
Expand the numerator of the second fraction:
[tex]=\dfrac{\sin^2(x)}{\sin(x)(1-\cos(x))}-\dfrac{\cos (x)-\cos^2(x)}{\sin(x)(1-\cos(x))}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]=\dfrac{\sin^2(x)-(\cos (x)-\cos^2(x))}{\sin(x)(1-\cos(x))}[/tex]
[tex]=\dfrac{\sin^2(x)-\cos (x)+\cos^2(x)}{\sin(x)(1-\cos(x))}[/tex]
[tex]=\dfrac{\sin^2(x)+\cos^2(x)-\cos (x)}{\sin(x)(1-\cos(x))}[/tex]
Apply the trigonometric identity, sin²θ + cos²θ = 1, to the numerator:
[tex]=\dfrac{1-\cos (x)}{\sin(x)(1-\cos(x))}[/tex]
Factor out the common term (1 - cos(x)) from the numerator and denominator:
[tex]=\dfrac{1}{\sin(x)}[/tex]
Finally, use the cosecant identity, csc(x) = 1 / sin(x):
[tex]=\csc(x)[/tex]
Hence we have verified that the left side of the equation equals the right side.
pls help me to solve this i have forgotten how to do surds:>>
Answer:
number (a) = 4
Step-by-step explanation:
tan(x-1) ( sin2x-2cos2x) = 2(1-2sinxcosx)
The equation is proved.
G[tex]`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`[/tex]
We need to prove the given equation. Solution: Using the identity [tex]`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`[/tex]
in the given equation, we get
[tex]`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-[/tex]
[tex]2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)[/tex]
[tex](2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹[/tex]
[tex]`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-[/tex]
[tex]sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹[/tex]
`[tex]2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`[/tex]
For `LHS`, using identity
[tex]`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹[/tex]
[tex]`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-[/tex]
[tex]1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.[/tex]
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How does the multiplicity of a zero affect the graph of the polynomial function? Select answers from the drop-down menus to correctly complete the statements. The zeros of a seventh degree polynomial function are 1, 2 (multiplicity of 3), 4, and 6 (multiplicity of 2). The graph of the function will cross through the x-axis at 1 only . The graph will only touch (be tangent to) the x-axis at Choose... . At the zero of 2, the graph of the function will Choose... the x-axis.
Answer:
Step-by-step ex-plane
The zeros of a polynomial function can be used to determine how the graph behaves at those points. The multiplicity of a zero also plays an important role in shaping the graph of a polynomial function.
The graph of the seventh degree polynomial function with zeros 1, 2 (multiplicity of 3), 4, and 6 (multiplicity of 2) will cross the x-axis at 1 only. This is because the zero at 1 has a multiplicity of 1.
The graph will only touch (be tangent to) the x-axis at 2. This is because the zero at 2 has a multiplicity of 3.
At the zero of 2, the graph of the function will flatten out against the x-axis.
Therefore, the correct answers are:
- The graph of the function will cross through the x-axis at 1 only.
- The graph will only touch (be tangent to) the x-axis at 2.
- At the zero of 2, the graph of the function will flatten out against the x-axis.
A Food Marketing Institute found that 28% of households spend more than $125 a week on groceries. Assume
the population proportion is 0.28 and a simple random sample of 273 households is selected from the
population. What is the probability that the sample proportion of households spending more than $125 a week
is less than 0.27?
There is a
probability that the sample proportion of households spending more than $125 a week is
less than 0.27. Round the answer to 4 decimal places.
The probability that the sample proportion of households spending more than $125 a week is less than 0.27 is approximately 0.35.
To find the probability that the sample proportion of households spending more than $125 a week is less than 0.27, we can use the sampling distribution of sample proportions and the Central Limit Theorem.
Given:
Population proportion (p) = 0.28
Sample size (n) = 273
First, we need to calculate the standard deviation of the sampling distribution, which is known as the standard error. The formula for the standard error is:
Standard Error = sqrt((p * (1 - p)) / n)
Substituting the given values:
Standard Error = sqrt((0.28 * (1 - 0.28)) / 273)
Standard Error ≈ 0.0258
Next, we can standardize the sample proportion using the formula:
Z = (sample proportion - population proportion) / standard error
Z = (0.27 - 0.28) / 0.0258
Z ≈ -0.3886
Now, we need to find the probability that the sample proportion is less than 0.27. This is equivalent to finding the area under the standard normal distribution curve to the left of Z = -0.3886. We can use a standard normal distribution table or a statistical software to find this probability.
The probability can be rounded to 4 decimal places:
Probability = 0.35 (approximately)
Therefore, the probability that the sample proportion of households spending more than $125 a week is less than 0.27 is approximately 0.35.
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solve this equation and find the table values
The completed table is as follows:
x | y
8 | 0
9 | 3
36 | 6
8 | 2√2
8 | -2√2
To solve the equation x = y², we can substitute the values of x and find the corresponding values of y in the table.
Let's fill in the missing entries one by one:
For x = 9, we need to find y. Since x = y², we take the square root of both sides to solve for y. So, y = √9 = 3. Therefore, the corresponding value for y is 3.
For x = 36, again, we apply the square root operation to both sides, giving y = √36 = 6. Hence, the corresponding value for y is 6.
For y = 2√2, we need to find x. Squaring both sides of the equation, we have [tex]x = (2\sqrt2)^2 = 4 \times 2 = 8[/tex]. Therefore, the corresponding value for x is 8.
For y = -2√2, we follow the same process as in step 3. Squaring both sides, we get [tex]x = (-2\sqrt2)^2 = 4 \times 2 = 8[/tex]. So, the corresponding value for x is 8.
After filling in the missing entries, the completed table is as follows:
x | y
8 | 0
9 | 3
36 | 6
8 | 2√2
8 | -2√2
Please note that there can be multiple valid solutions for this equation, but this table provides one possible solution.
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PLEASE HELP, WILL GIVE BRAINLIEST
Which is the best definition of phi?
Phi is the value of the golden spiral.
Phi is a single value in the Fibonacci sequence.
Phi is the length of the golden rectangle.
Phi is the value of the golden ratio.
The best definition of phi is:
Phi is the value of the golden ratio.What is The Golden Ratio?golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or, which is approximately equal to 1.618.
Phi = 1/phi Phi = 1 + phi The latter facts together give the definition of the golden ratio: x = 1/x + 1 This equation (equivalent to x^2 - x - 1 = 0) is satisfied by both Phi and -phi, which therefore can be called the _golden ratios_.
Hence, Phi is the value of the golden ratio which is the best definition of phi.
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Please help I don’t understand this and can’t get it right!!!
Answer:
$828.53
Step-by-step explanation:
The formula is: A = P(1 + r/k)^(kt)
A = 750(1 + 0.02/12)^(12*5)
A = 750(1 + 0.00166667)^60
A = 750(1.00166667)^60
A = 750(1.104713)
A = $828.53 (rounded to the nearest cent)
So, the accumulated amount after 5 years with a 2% interest rate compounded monthly is $828.53.
What the meaning of "[tex]\bigcup X[/tex] = sup X"?
"UX = sup X," means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.
Understanding Set NotationIn set theory, the symbol "∪" denotes the union of sets. So, when we say "∪X," it represents the union of all the elements in the set X.
On the other hand, "sup X" stands for the supremum (or least upper bound) of the set X. The supremum of a set is the smallest ordinal number that is greater than or equal to all the elements in the set.
Therefore, when it is stated that "UX = sup X," it means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.
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What is the product?
2y 4y-12
y-3 2y+6
O
2
3
10
9
4y
y-3
4y
Oy+3
Right triangle LMN has vertices L(7, –3), M(7, –8), and
N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).
In this case we have a translation of 8 units to the left and 11 units upwards.
How to find the translation?To find the translation, we just need to compare the two known vertices before and after the translation.
If we have a translation of a units in the x-axis and b units in the y-axis, we will get:
T(a, b)L ---> L'
We know that L = (7, -3) and L' = (-1, 8)
Then we can write:
(7 + a, -3 + b) = (-1, 8)
Then we have two equations:
7 + a = -1 ---> a = -1 - 7 = -8
-3 + b = 8 ---> b = 8 + 3 = 11
Then we have a translation of 8 units to the left and 11 units up-.
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Complete question:
"Right triangle LMN has vertices L(7, –3), M(7, –8), and
N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).
Find the translation done"
8 Solve for C. 16 17 C= [?]° Measure of Angle C Round your final answer to the nearest tenth. Law of Cosines: c²= a'+ b² - 2ab•cosC Enter
Answer:
To solve for C, we would need to know the length of side c. Without that information, we cannot determine the value of angle C.
Step-by-step explanation:
Using this assumption, we can rewrite the equation as:
c² = 16² + 17² - 2(16)(17)·cos(C)
c² = 256 + 289 - 544·cos(C)
c² = 545 - 544·cos(C)
Answer:
C = 83.0°
Step-by-step explanation:
This triangle has three sides, with lengths of 8 units, 16 units, and 17 units. The angle formed between the sides measuring 8 units and 16 units is angle C. Angle C is opposite the side measuring 17 units.
To find the measure of angle C, we can use the Law of Cosines.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Law of Cosines}}\\\\c^2=a^2+b^2-2ab \cos C\\\\\textsf{where $a, b$ and $c$ are the sides,}\\\textsf{and $C$ is the angle opposite side $c$.}\\\end{array}}[/tex]
In this case:
a = 8b = 16c = 17C = CSubstitute the values of a, b, and c into the formula, and solve for C:
[tex]\begin{aligned}c^2&=a^2+b^2-2ab\cos C\\\\17^2&=8^2+16^2-2(8)(16)\cos C\\\\289&=64+256-256\cos C\\\\289&=320-256\cos C\\\\289-320&=320-256\cos C-320\\\\-31&=-256\cos C\\\\\dfrac{-31}{-256}&=\dfrac{-256\cos C}{-256}\\\\\dfrac{31}{256}&=\cos C\\\\\cos C&=\dfrac{31}{256}\\\\C&=\cos^{-1}\left(\dfrac{31}{256}\right)\\\\C&=83.04476981...^{\circ}\\\\C&=83.0^{\circ}\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, the measure of angle C, rounded to the nearest tenth, is:
[tex]\Large\boxed{\boxed{C=83.0^{\circ}}}[/tex]
Question 5 of 10
What is the location of the point on the number line that is of the way from
A = 31 to B=6?
OA. 21
B. 16
OC. 11
OD. 19
4
Answer:
Step-by-step explanation:
To find the location of the point that is of the way from A=31 to B=6, we need to find the midpoint of the segment AB.
The formula for finding the midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂) is:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, we have A = 31 and B = 6, so x₁ = 31 and x₂ = 6. Plugging these values into the formula, we get:
Midpoint = ((31 + 6) / 2, (y₁ + y₂) / 2)
Midpoint = (37/2, (y₁ + y₂) / 2)
We still need to find y₁ and y₂, which are the positions of A and B on the number line. Since the number line is one-dimensional, we can simply use their values:
y₁ = 31
y₂ = 6
Plugging these values into the formula, we get:
Midpoint = (37/2, (31 + 6) / 2)
Midpoint = (37/2, 37/2)
Therefore, the location of the point on the number line that is of the way from A=31 to B=6 is at a distance of 37/2 units from point A and also at a distance of 37/2 units from point B. So, the midpoint of AB is located at the point (37/2, 0).
However, since the question only asks for the location of the point on the number line, we only need to consider the x-coordinate of the midpoint, which is 37/2. This point is on the number line, which means that it is a real number. Therefore, the answer is option (A) 21.
A technician installing a new refrigeration system is using rivets to fasten sheet
metal. As he begins drilling, the drill grabs the rivet and the rivet begins to spin. Now
he can't drill out the rivet head.
What should he do?
When a technician is faced with such issue, the following options can be considered:
Apply pressure Use a carbide bit Use a lubricantApply pressure to the back of the rivet with a screwdriver or other blunt object. This will help to keep the rivet from spinning and will also help to break the seal between the rivet and the sheet metal.
Use a carbide drill bit. Carbide drill bits are more durable than standard drill bits and are less likely to break when drilling through rivets.
Use a lubricant: Lubricants can help to prevent the drill bit from grabbing the rivet and can also help to cool the drill bit.
Therefore, any of the mentioned options could be taken in such situation .
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Which of the equations below represents a line perpendicular to the x-axis?
The equation of a line perpendicular to the x-axis is x = 3
The equation of a line perpendicular to the x-axis?From the question, we have the following parameters that can be used in our computation:
The equations
By definition, the equation of a line perpendicular to the x-axis is represented as
x = k
Where
k is a real value
Using the above as a guide, we have the following:
x = 3
Hence, the equation is x = 3
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IMPORTANT! HELP!
Find the angles of intersection between the curves f(x)=x^2 and g(x)=[tex]\sqrt{x}[/tex]
Answer:
To find the angles of intersection between the curves f(x) = x^2 and g(x) = |x|, we need to find the points where the two curves intersect.
Substituting g(x) into f(x), we get:
x^2 = |x|
To solve this equation, we need to consider two cases:
Case 1: x ≥ 0
In this case, the equation simplifies to:
x^2 = x
Solving for x, we get:
x(x - 1) = 0
So x = 0 or x = 1.
Case 2: x < 0
In this case, the equation simplifies to:
x^2 = -x
Solving for x, we get:
x(x + 1) = 0
So x = 0 or x = -1.
Therefore, the points of intersection between the two curves are (-1, 1), (0, 0), and (1, 1).
To find the angles of intersection, we need to find the slopes of the two curves at each point of intersection.
At (0, 0), the slopes of both curves are 0.
At (-1, 1) and (1, 1), the slope of f(x) = x^2 is 2x, and the slope of g(x) = |x| changes direction at x = 0, so we need to consider the left and right limits separately:
At x = -1, the slope of g(x) = -1, and at x = 1, the slope of g(x) = 1.
Therefore, the angles of intersection between the two curves are:
- At (0, 0), the two curves are tangent and intersect at a right angle.
- At (-1, 1) and (1, 1), the two curves intersect at acute angles.
A robot is programmed to move along a straight-line path through two points A and B. It travels at a uniform speed that allows it to make the trip from A(0,-1) to B(1, 1) in 1 minute.
Find the robot's location, P, for each time t in minutes.
1. t=14
2. t=0.7
The robot's locations for each time t are P(14, 27) when t = 14, and P(0.7, 0.4) when t = 0.7.
To find the robot's location, P, for each time t, we can use the equation of a straight line.
Given points A(0, -1) and B(1, 1), we can calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-1)) / (1 - 0) = 2/1 = 2
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
For point A(0, -1):
y - (-1) = 2(x - 0)
y + 1 = 2x
Simplifying the equation, we get:
y = 2x - 1
Now we can substitute the values of t into the equation to find the corresponding locations of the robot, P.
For t = 14:
y = 2(14) - 1
y = 28 - 1
y = 27
So, when t = 14, the robot's location is P(14, 27).
For t = 0.7:
y = 2(0.7) - 1
y = 1.4 - 1
y = 0.4
So, when t = 0.7, the robot's location is P(0.7, 0.4).
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Find the mean for the following frequency tables. (Round your answers to one decimal place.)
(a)
Grade Frequency
49.5–59.5 2
59.5–69.5 3
69.5–79.5 7
79.5–89.5 11
89.5–99.5 5
(b)
Daily Low Temperature Frequency
49.5–59.5 52
59.5–69.5 30
69.5–79.5 15
79.5–89.5 1
89.5–99.5 0
(c)
Points per Game Frequency
49.5–59.5 14
59.5–69.5 33
69.5–79.5 15
79.5–89.5 24
89.5–99.5 2
The mean for the given frequency tables is:
(a) Grade Frequency: 48.7
(b) Daily Low Temperature Frequency: 54.5
(c) Points per Game Frequency: 54.5
To find the mean for the given frequency tables, we need to calculate the weighted average. The mean is calculated by multiplying each value by its corresponding frequency, summing up these products, and then dividing by the total frequency.
(a) Grade Frequency:
To find the mean for the grade frequency table, we need to multiply the midpoints of each class interval by their respective frequencies and then divide by the total frequency.
The midpoints are:
54.5, 64.5, 74.5, 84.5, 94.5
The frequencies are:
2, 3, 6, 11, 5
Calculating the weighted sum: (54.52) + (64.53) + (74.56) + (84.511) + (94.5*5) = 1315
Calculating the total frequency: 2 + 3 + 6 + 11 + 5 = 27
Mean = 1315 / 27 ≈ 48.7
(b) Daily Low Temperature Frequency:
Since the frequency for the 49.5–59.5 class interval is 5 and for the other intervals is 0, we can conclude that the mean will be within the range of 49.5–59.5. The mean will be the midpoint of this class interval.
Mean = (49.5 + 59.5) / 2 = 54.5
(c) Points per Game Frequency:
Similarly to part (b), since the frequency for the 49.5–59.5 class interval is 1 and for the other intervals is 0, the mean will be within the range of 49.5–59.5.
Mean = (49.5 + 59.5) / 2 = 54.5
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