Answers
Answer:
The replacement axiom (axiom scheme) is the most general form you need, essentially saying that if you have a function whose domain is a set then the image is also a set. Furthermore, the empty set can be inferred by an existence of any set at all, when combined with separation (and hence, can be inferred by replacement).
Formally speaking the replacement schema says that for every formula φ(u,v,p1,…,pn)
, fix the parameters p1,…,pn
and pick any set A
, whenever u∈A
has at most one v
for which φ(u,v,p1,…,pn)
is true, then the collection of {v∣φ(u,v,p1,…,pn),u∈A}
is also a set.
How to infer separation and pairing? Simple.
First we infer separation. Given ϕ(x)
, we simply define φ(u,v,p)
to be
φ(u,v,p)=defu=v∧u∈p∧ϕ(u)
This is a functional formula (i.e. for every u
there is at most a single v
for which φ(u,v,p)
holds) and it is easy to verify that the image of φ(u,v,a)
is indeed {x∈a∣ϕ(x)}
.
The empty set exists by separation - simply take some a
(which exists because we assume there is some set in the universe) and the function ϕ(x):=x≠x
.
As you noted, {∅,P(∅)}
exists by the Power set axiom.
Now for a given x,y
we want to have {x,y}
so we define the following φ(u,v)
as following:
φ(u,v):=(u=∅∧v=x)∨(u=P(∅)∧v=y)
Note that φ
is a functional formula, i.e. for a given u
there is only one v
for which φ(u,v)
is true. By the axiom of replacement we have now that {x,y}
is a set. Therefore the axiom of pairing holds if we assume Power set and Replacement.
Now we have two ways of looking at ZFC. Sometimes we want to prove that something is a model for ZFC and need to verify the list of axioms in which case proving both Separation and Replacement is completely redundant. At other times we want to prove certain things which are quicker when using the more specific axioms (e.g. pairing (or even ordered pairing, which can be quickly inferred from pairing itself)).
This is a sort of freedom that we allow ourselves. We add extra axioms that we don't really need. Then if we want to ensure all the axioms hold we check for the "core" of the axiomatic system, and when we want to ease on ourselves in other cases we can just use the extra axioms for our convenience.
Step-by-step explanation:
Related Questions
The manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5200 tickets were sold and the receipts totaled $38,148. The adult admission is $8.50, and the children's admission is $6.60. How many adult patrons were there?
Answers
There were 3020 adult patrons at the theater.
Let x be the number of adult patrons and y be the number of child patrons. Since 5200 tickets were sold, we have: x + y = 5200 Also, the receipts totaled $38,148.
Therefore, we have:8.5x + 6.6y = 38,148 Simplifying the first equation by solving for y: y = 5200 - x Substituting this into the second equation:8.5x + 6.6(5200 - x) = 38,148 Simplifying and solving for x: 1.9x = 5736x = 3020
Hence, there were 3020 adult patrons at the theater.
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Find the value of cos 60°+ √3 cos 30°+ sin 30°.
Find the value of tan 30°+ cot 30°+ sin 30°.
Answers
Answer:
[tex]\cos 60^{\circ}+ \sqrt{3} \cos 30^{\circ}+ \sin 30^{\circ}=\dfrac{5}{2}[/tex]
[tex]\tan 30^{\circ}+\cot30^{\circ}+\sin30^{\circ}=\dfrac{3+8\sqrt{3}}{6}[/tex]
Step-by-step explanation:
Question 1To find the value of the given trigonometric expression, we can use the unit circle to first find the values of cos 60°, cos 30° and sin 30°.
In the unit circle, the cosine of the angle is the x-coordinate of a point on the circle, and the sine of the angle is the y-coordinate of that point.
Therefore, reading from the unit circle (attached):
[tex]\boxed{\begin{minipage}{2.3 cm}$\cos 60^{\circ}=\dfrac{1}{2}$\\\\\\$\cos 30^{\circ}=\dfrac{\sqrt{3}}{2}$\\\\\\$\sin 30^{\circ}=\dfrac{1}{2}$\\\end{minipage}}[/tex]
Substitute these values into the expression and solve:
[tex]\begin{aligned}\cos 60^{\circ}+ \sqrt{3} \cos 30^{\circ}+ \sin 30^{\circ}&=\dfrac{1}{2}+\sqrt{3} \cdot \dfrac{\sqrt{3}}{2}+\dfrac{1}{2}\\\\&=\dfrac{1}{2}+\dfrac{3}{2}+\dfrac{1}{2}\\\\&=\dfrac{1+3+1}{2}\\\\&=\dfrac{5}{2}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 2Use the following trigonometric identities to rewrite tan 30° and cot 30° in terms of sine and cosine.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric identities}\\\\$\tan x=\dfrac{\sin x}{\cos x}$\\\\\\$\cot x=\dfrac{\cos x}{\sin x}$\\\\\end{minipage}}[/tex]
[tex]\tan 30^{\circ}+\cot30^{\circ}+\sin30^{\circ}=\dfrac{\sin30^{\circ}}{\cos30^{\circ}}+\dfrac{\cos30^{\circ}}{\sin30^{\circ}}+\sin30^{\circ}[/tex]
Now use the unit circle to find the values of sin 30° and cos 30°:
[tex]\boxed{\begin{minipage}{2.3 cm}$\sin 30^{\circ}=\dfrac{1}{2}$\\\\\\$\cos 30^{\circ}=\dfrac{\sqrt{3}}{2}$\\\end{minipage}}[/tex]
Substitute these values into the expression and solve:
[tex]\begin{aligned}\tan 30^{\circ}+\cot30^{\circ}+\sin30^{\circ}&=\dfrac{\sin30^{\circ}}{\cos30^{\circ}}+\dfrac{\cos30^{\circ}}{\sin30^{\circ}}+\sin30^{\circ}\\\\&=\dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}+\dfrac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}+\dfrac{1}{2}\\\\&=\dfrac{1}{2}\cdot\dfrac{2}{\sqrt{3}}+\dfrac{\sqrt{3}}{2}\cdot\dfrac{2}{1}+\dfrac{1}{2}\\\\&=\dfrac{1}{\sqrt{3}}+\dfrac{\sqrt{3}}{1}+\dfrac{1}{2}\\\\&=\dfrac{1 \cdot \sqrt{3}}{\sqrt{3}\cdot \sqrt{3}}+\dfrac{\sqrt{3}}{1}+\dfrac{1}{2}\\\\\end{aligned}[/tex]
[tex]\begin{aligned}&=\dfrac{\sqrt{3}}{3}+\dfrac{\sqrt{3}}{1}+\dfrac{1}{2}\\\\&=\dfrac{\sqrt{3}\cdot 2}{3\cdot 2}+\dfrac{\sqrt{3}\cdot 6}{1\cdot 6}+\dfrac{1\cdot 3}{2\cdot 3}\\\\&=\dfrac{2\sqrt{3}}{6}+\dfrac{6\sqrt{3}}{6}+\dfrac{3}{6}\\\\&=\dfrac{2\sqrt{3}+6\sqrt{3}+3}{6}\\\\&=\dfrac{8\sqrt{3}+3}{6}\\\\&=\dfrac{3+8\sqrt{3}}{6}\end{aligned}[/tex]
Jordan bought if radio for $120 he paid for it with 2 dollars and 5 dollar bill if there are a total of 30 coins and bills. how many two dollar coins were there and how many five dollars bills worth?
Answers
There are 10 two-dollar coins and 20 five-dollar bills.
Let's assume the number of two-dollar coins as "x" and the number of five-dollar bills as "y."
According to the given information, Jordan bought the radio for $120, and he paid using 2-dollar coins and 5-dollar bills. We can express this information as an equation:
2x + 5y = 120
We also know that the total number of coins and bills is 30:
x + y = 30
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
We can start by solving the second equation for x:
x = 30 - y
Now substitute this expression for x in the first equation:
2(30 - y) + 5y = 120
Simplify:
60 - 2y + 5y = 120
Combine like terms:
3y = 60
Divide both sides by 3:
y = 20
Now substitute this value of y back into the equation x = 30 - y:
x = 30 - 20
x = 10
Therefore, there are 10 two-dollar coins and 20 five-dollar bills.
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Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.
Answers
(a) The slope of the curve at point P is 1300.
(b) The equation tangent the line at P is y = 1300x + 5.
What is the slope of the curve at P?(a) The slope of the curve at P is calculated as follows;
Sope refers to the steepness or inclination of a line on a graph. It measures the rate of change between two points on the line.
The given curve equation;
y = -5 - 5x²
The slope of the curve is calculated as;
dy/dx = -10x
The point P is given as P = (5, - 130)
slope, dy/dx = -10x = -10(-130) = 1,300
(b) The equation tangent the line at P is given as;
y = mx + c
y = 1300x + 5
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Answer:
[tex]\textsf{(a)} \quad \textsf{The\;slope\;of\;the\;curve\;at\;$P$\;is\;$\boxed{-50}$\:.}[/tex]
[tex]\textsf{(b)} \quad \textsf{The\;equation\;of\;the\;tangent\;line\;at\;$P$\;is\;$\boxed{y = -50x + 120}$\:.}[/tex]
Step-by-step explanation:
The derivative of a function gives us the slope of the tangent line at any given point on the graph.
Differentiate y = -5 - 5x² using the following rules of differentiation.
[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}y&=-5-5x^2\\\\\implies \dfrac{\text{d}y}{\text{d}x}&=0-2 \cdot 5x^{2-1}\\\\\dfrac{\text{d}y}{\text{d}x}&=-10x\end{aligned}[/tex]
To find the slope of the curve at the given point P(5, -130), substitute x = 5 into the derivative of the function:
[tex]\text{Slope}=-10(5)=-50[/tex]
To find the equation of the tangent line, substitute the found slope m = -50 and the given point (5, -130) into the point-slope form of a linear equation and simplify:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\\implies y-(-130)&=-50(x-5)\\y+130&=-50x+250\\y&=-50x+120\end{aligned}[/tex]
Therefore, the equation of the tangent line at P is y = -50x + 120.
Focus Question #4 + Rita can choose from 2 membership options at a movie rental store. Option A has a yearly fee of $40 and every movie rental costs $3. Option B has a yearly fee of $150 for unlimited movie rentals at no additional cost. How many movies would Rita need to rent in order for Option B to be cheaper than Option A?
Answers
Rita would need to rent at least 37 movies in a year for Option B to be cheaper than Option A.
To determine the number of movies Rita would need to rent for Option B to be cheaper than Option A, we can set up an equation and solve for the unknown variable.
Let's assume Rita rents "x" number of movies in a year.
For Option A:
Yearly fee = $40
Cost per movie rental = $3
Total cost for Option A = Yearly fee + (Cost per movie rental * Number of movie rentals)
Total cost for Option A = $40 + ($3 * x) = $40 + $3x
For Option B:
Yearly fee = $150
Cost per movie rental = $0 (unlimited movie rentals)
Total cost for Option B = Yearly fee + (Cost per movie rental * Number of movie rentals)
Total cost for Option B = $150 + ($0 * x) = $150
We want to find the number of movies (x) at which Option B becomes cheaper than Option A. So we can set up the inequality:
$150 < $40 + $3x
Now, we can solve the inequality:
$150 - $40 < $3x
$110 < $3x
Dividing both sides of the inequality by $3:
($110 / $3) < ($3x / $3)
Approximately 36.67 < x
Since the number of movies must be a whole number, we round up to the nearest whole number:
x ≥ 37
Therefore, Rita would need to rent at least 37 movies in a year for Option B to be cheaper than Option A.
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What is the area?
Ty
Answers
The area of the composite figure in this problem is given as follows:
284.5 mm².
How to obtain the area of the figure?The figure in this problem is composed as follows:
Rectangle of dimensions 10 mm and 18 mm.Triangle of base 19 mm and height 11 mm.The area of the rectangle is given as follows:
18 x 10 = 180 mm².
The area of the triangle is given as follows:
0.5 x 19 x 11 = 104.5 mm².
Then the total area is given as follows:
180 + 104.5 = 284.5 mm².
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Don’t understand need answer
Answers
a.) If the trial is in Japan, the probability that all the defendants will be found guilty would be = 0.95.
The probability if the trials where in the United States would be = 0.60.How to calculate tye probability of the given events?To calculate tye probability of the given events, the formula that should be used would be given below as follows:
Probability = possible outcome/sample space.
If the trial is in Japan the possible outcome = 95%
The sample space = 100%
The probability = 95/100 = 0.95
If the trial is in United States the possible outcome = 60%
The sample space = 100%
The probability = 60/100 = 0.60
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2 The graph of y=f(x) is shown below.
Which expression defines f(x)?
1) 2x
2) 5(2^x)
3) 5(2^x/2)
4) 5(2^2x)
Answers
Based on the given graph, the expression that best defines f(x) is option 2) 5(2^x). It aligns with the exponential growth pattern shown in the graph.
To determine the expression that defines f(x) based on the given graph, we need to analyze the behavior and characteristics of the graph.
Looking at the options provided:
2x: This expression represents a linear function with a constant slope. However, the given graph does not exhibit a linear pattern or a constant slope, so this option is not a suitable representation for f(x).
5(2^x): This expression represents an exponential function with a base of 2 and a vertical scaling factor of 5. The graph shows an exponential growth pattern that aligns with this expression, so it is a plausible representation for f(x).
5(2^x/2): This expression represents an exponential function with a base of 2, but it includes a division by 2 in the exponent. This modification would alter the growth rate of the function and result in a different graph shape compared to what is shown. Thus, this option does not match the given graph.
5(2^2x): This expression represents an exponential function with a base of 2 and an exponent of 2x. The graph of f(x) does not exhibit a quadratic growth pattern, so this option does not accurately represent the given graph.
Based on the analysis, option 2) 5(2^x) is the most suitable expression that defines f(x) based on the given graph.
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In the figure below, h || l and j || K. Find the values of x and z
Answers
Answer: The value of z = 32 , x = 103
Step-by-step explanation: As given h || l and j || k .
we can say (3z - 19) = 77
solving the above equation we get:
3z = 77 + 19
3z = 96
z = 32
Now , The sum of 77 + x = 180
solving this equation we get:
x = 180 - 77
x = 103
√x
f(x)=
2x²+x-1
value(s) can "x" be?).
A
X=-1
which answer is the most accurate? Hint: think of the answer in terms of domain (what
B
Answers
The domain of the function f(x) = 2x² + x - 1 is -1 ≤ x and x ≥ 1/2
What is a domain of a function?The domain of a function is the number of valid input to the function.
Given the quadratic function f(x) = 2x² + x - 1, we want to find the values x can be, that is its domain. We proceed as follows
For x to have valid values, then f(x) ≥ 0.
So, 2x² + x - 1 ≥ 0
Factorizing, we have that
2x² + x - 1 ≥ 0
2x² + 2x - x - 1 ≥ 0
2x(x + 1) - (x + 1) ≥ 0
(2x - 1)(x + 1) ≥ 0
⇒ 2x - 1 ≥ 0 or x + 1 ≥ 0
⇒ 2x ≥ 1 or x ≥ - 1
⇒ x ≥ 1/2 or x ≥ - 1
So, we determine the values of x for which (2x - 1)(x + 1) ≥ 0
So, when x < -1
(2(-2) - 1)(-2 + 1)
(-4 - 1)(-1)
(-5)(-1)
5 > 0
when -1 ≤ x < 1/2
Let x = 0
(2(0) - 1)(0 + 1) ≥ 0
(0 - 1)(1) ≥ 0
(-1)(1) ≥ 0
-1 < 0
when x > 1/2
Let x = 1
(2(1) - 1)(1 + 1)
(2 - 1)(2)
(1)(2)
2 ≥ 0
Since f(x) ≥ 0 for -1 < x and x > 1/2
The domain of the function is -1 ≤ x and x ≥ 1/2
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Question #2
Find the measure of UK
T
99
O
U
87 R
S
K
Answers
Answer:
UK = 75°
Step-by-step explanation:
the measure of the chord- chord angle TRS is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
∠ TRS = [tex]\frac{1}{2}[/tex] (TS + UK) , that is
87° = [tex]\frac{1}{2}[/tex] (99 + UK) ← multiply both sides by 2 to clear the fraction
174° = 99° + UK ( subtract 99° from both sides )
75° = UK
A student earned grades of 84, 78, 84, and 72 on her four regular tests. She earned a grade of 78 on the final exam and 86 on her class projects. Her combined homework grade was 87. The four regular tests count for 40% of the final grade, the final exam counts for 30%, the project counts for 10%, and homework counts for 20%.What is her weighted mean grade? Round to one decimal place
Answers
Answer and Step-by-step explanation:
To calculate the student’s weighted mean grade, we need to find the average of her four regular test grades and then multiply each component of her grade by its respective weight.
The average of her four regular test grades is (84 + 78 + 84 + 72) / 4 = 79.5.
Her weighted mean grade is calculated as follows:
Weighted mean grade = (0.4)(79.5) + (0.3)(78) + (0.1)(86) + (0.2)(87) = 31.8 + 23.4 + 8.6 + 17.4 = 81.2
So, her weighted mean grade is approximately 81.2 when rounded to one decimal place.
1.1
Q(-4; 2)
R(7:-1)
P (-2;-4)
Figure 1.1: Triangle PQR in a Cartesian plane
Prove that PQR is right-angled.
Please help
Answers
Legs = 122.10 "rounded"
Hypotenuse= 122.10 "Exact cannot be rounded"
Distance
PQ = 5.66
PR=9.49
QR= 11.05
squared that all then add the PQ and PR if the sum of that two is equal to hypotenuse it is prove
we squared 11.05, 5.66, 9.49
hope that helps
The function h(x) = (x+4)³ can be expressed in the form f(g(x)) where f(x) = x³, and g(x) is defined
below:
g(x)=
Answers
To express the function [tex]\displaystyle\sf h(x) = (x+4)^{3}[/tex] in the form [tex]\displaystyle\sf f(g(x))[/tex], where [tex]\displaystyle\sf f(x) = x^{3}[/tex] and [tex]\displaystyle\sf g(x)[/tex] is the inner function, we need to determine [tex]\displaystyle\sf g(x)[/tex].
Notice that [tex]\displaystyle\sf h(x)[/tex] is the cube of [tex]\displaystyle\sf (x+4)[/tex]. This suggests that [tex]\displaystyle\sf g(x)[/tex] is equal to [tex]\displaystyle\sf x+4[/tex].
So, [tex]\displaystyle\sf g(x) = x+4[/tex].
Now, to express [tex]\displaystyle\sf h(x)[/tex] as [tex]\displaystyle\sf f(g(x))[/tex], we substitute [tex]\displaystyle\sf g(x) = x+4[/tex] into [tex]\displaystyle\sf f(x) = x^{3}[/tex]:
[tex]\displaystyle\sf h(x) = f(g(x)) = f(x+4) = (x+4)^{3}[/tex].
Therefore, [tex]\displaystyle\sf h(x)[/tex] can be expressed as [tex]\displaystyle\sf f(g(x))[/tex], where [tex]\displaystyle\sf f(x) = x^{3}[/tex] and [tex]\displaystyle\sf g(x) = x+4[/tex].
what does a two column proof do
Answers
In simple term, it is used to prove a logical argument true.
Which tab is used to access the Compact and Repair option in Access 2016?
External Data
Create
Database Tools
File
Answers
Step-by-step explanation:
In Access 2016, the "Database Tools" tab is used to access the Compact and Repair option. To compact and repair a database, you can follow these steps:
Open Access 2016.
Open the desired database.
Click on the "Database Tools" tab in the ribbon at the top of the screen.
In the "Database Tools" tab, you will find a section called "Database Tools" with various options.
Look for the "Compact & Repair Database" button within this section.
Click on the "Compact & Repair Database" button.
Access will prompt you to select the database file you want to compact and repair. Choose the appropriate file and click "Compact."
By following these steps, you can access the Compact and Repair option in Access 2016 using the "Database Tools" tab.
Step-by-step explanation:
The Compact and Repair option in Access 2016 can be accessed through the "Database Tools" tab.
if a room is 15 feet long and 12 feet wide and a scale drawing of the room is 10 inches by 8 inches, what is the scale of inches in the drawing to inches in the actual room?
Answers
Answer:
1:18
Step-by-step explanation:
There are 12 inches in 1 foot.
The room is 15ft × 12ft.
Convert 15ft to inches:
15ft × 12in/ft = 180in
Convert 12ft to inches:
12ft × 12in/ft = 144in
So the room is 180 × 144 and that is represented by 10×8
10 represents 180 and
8 represents 144.
Simplifying or reducing as you fractions can help you find the ratio.
drawinginches/real inches
10/180 = 1/18
also (should be the same)
8/144 = 1/18
The ratio is 1/18, can also be written 1:18,
or in words
1 to 18.
Answer:hi I think it's 12 but I mightbewrong .
Fill in the blanks below in order to justify whether or not the mapping shown represent a function
Answers
The mapping shown does not represents a function
How to determine if the mapping is a functionFrom the question, we have the following parameters that can be used in our computation:
The mapping
From the mapping, we have the following ordered pairs
(1, 7), (8, 3), (8, -1) and (3, 0)
The above ordered pair is not a function
This is so because the input value 8 have different output values 3 and -1
i.e. it would not pass the vertical line test when represented on a graph
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choose a number between 61-107 multiple of 4,8,16
Answers
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 355 grams and a standard deviation of 12 grams. Find the weight that corresponds to each event
highest 30 percent
middle 70 percent
highest 90 percent
lowest 20 percent
Answers
Step-by-step explanation:
To find the weight corresponding to each event, we can use the properties of the normal distribution and the given mean and standard deviation.
Highest 30 percent:
To find the weight that corresponds to the highest 30 percent, we need to find the z-score that represents the 30th percentile. Using a standard normal distribution table or a calculator, we find that the z-score for the highest 30 percent is approximately 0.524. We can then use the z-score formula to find the corresponding weight:
z = (x - mean) / standard deviation
0.524 = (x - 355) / 12
Solving for x:
x - 355 = 0.524 * 12
x - 355 ≈ 6.29
x ≈ 361.29 grams
Therefore, the weight corresponding to the highest 30 percent is approximately 361.29 grams.
Middle 70 percent:
The middle 70 percent represents the range from the 15th percentile to the 85th percentile. Using the z-score formula, we find the z-scores for these percentiles: -1.036 and 1.036. We can then calculate the corresponding weights:
For the 15th percentile:
-1.036 = (x - 355) / 12
x - 355 = -1.036 * 12
x ≈ 342.55 grams
For the 85th percentile:
1.036 = (x - 355) / 12
x - 355 = 1.036 * 12
x ≈ 367.43 grams
Therefore, the weight corresponding to the middle 70 percent is approximately between 342.55 grams and 367.43 grams.
Highest 90 percent:
To find the weight that corresponds to the highest 90 percent, we need to find the z-score that represents the 90th percentile. The z-score is approximately 1.282. Using the z-score formula:
1.282 = (x - 355) / 12
Solving for x:
x - 355 = 1.282 * 12
x ≈ 370.18 grams
Therefore, the weight corresponding to the highest 90 percent is approximately 370.18 grams.
Lowest 20 percent:
To find the weight that corresponds to the lowest 20 percent, we need to find the z-score that represents the 20th percentile. The z-score is approximately -0.841. Using the z-score formula:
-0.841 = (x - 355) / 12
Solving for x:
x - 355 = -0.841 * 12
x ≈ 344.69 grams
Therefore, the weight corresponding to the lowest 20 percent is approximately 344.69 grams.
problem.
The graph of f(x) = -(x+5)³-3 can be obtained from the graph of y =
reflecting the graph through the Select an answer B, then shifting the graph Select an answer
unit(s) and Select an answer
unit(s).
Which of the following is the graph of f(x) = (x+5)³-3?
Answers
The graph of f(x) = (x+5)³-3 can be obtained by reflecting the graph of y = -B through the x-axis and shifting it 0 units horizontally and 0 units vertically.
To obtain the graph of f(x) = (x+5)³-3 from another function, we need to go through a series of transformations.
Let's break down the steps to achieve this:
Reflection:
The reflection of a function across the x-axis can be obtained by multiplying the function by -1.
Thus, the initial function B, which when multiplied by -1 gives -(x+5)³-3, is y = (x+5)³-3.
Shifting:
To shift the graph, we need to determine the direction and distance of the shift.
The term "unit(s)" indicates that we are dealing with a shift by a certain number of units.
Since the question does not provide specific values for the shift, we'll consider shifting by "c" units horizontally and "d" units vertically.
Therefore, the graph of f(x) = (x+5)³-3 is obtained from the initial function B by reflecting it across the x-axis and then shifting it c units horizontally and d units vertically.
By following these steps, we achieve the desired transformation. It's important to note that without specific values for the shifts, we cannot determine the exact position of the graph.
The shifts can be positive or negative, indicating movement to the right or left, up o down, respectively, but the specific magnitude depends on the values assigned to c and d.
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A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. The brick has a density of 2.7 grams per cubic centimeter. Find the mass of the brick to the nearest gram.
Answers
The mass of the brick to the nearest gram is 2474 grams.
To find the mass of the brick, we need to calculate its volume and then multiply it by its density.
The volume of a rectangular prism is given by the formula V = length × width × height. In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches. So, we have:
V = 8 inches × 3.5 inches × 2 inches
V = 56 cubic inches
Since we need to convert the volume to grams, we also need to convert inches to centimeters. One inch is equal to 2.54 centimeters. Therefore, the volume in cubic centimeters is:
V = 56 cubic inches × (2.54 cm/in)^3
V ≈ 915.6496 cubic centimeters
Now, we can calculate the mass using the formula:
Mass = Volume × Density
Mass = 915.6496 cubic centimeters × 2.7 grams per cubic centimeterMass ≈ 2473.9072 grams
Rounding to the nearest gram, the mass of the brick is approximately 2474 grams.
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628 hamburgers and cheese burgers sold on Tuesday their were 72 fewer cheese burgers sold than hamburger how many were sold on Tuesday
Answers
Answer: 350 hamburgers and 278 cheeseburgers
Step-by-step explanation:
Let's denote the number of hamburgers sold on Tuesday as 'H' and the number of cheeseburgers sold as 'C'.
According to the information given, we have two pieces of information:
The total number of hamburgers and cheeseburgers sold on Tuesday is 628:
H + C = 628
There were 72 fewer cheeseburgers sold than hamburgers:
C = H - 72
We can solve this system of equations to find the values of H and C.
Substituting the second equation into the first equation, we get:
H + (H - 72) = 628
2H - 72 = 628
2H = 628 + 72
2H = 700
H = 350
Now we can substitute the value of H back into the second equation to find C:
C = H - 72
C = 350 - 72
C = 278
Therefore, on Tuesday, 350 hamburgers and 278 cheeseburgers were sold.
Question #9
Find the measure of the indicated angle.
161°
H
73° E
195°
Answers
Answer:
sorry i try but cannot get correctly
sorry
In 2022, Elaine paid $2,280 of tuition and $740 for books for her dependent son to attend State University this past fall as a freshman. Elaine files a joint return with her husband.
What is the maximum American opportunity tax credit that Elaine can claim for the tuition payment and books in each of the following alternative situations?
Note: Leave no answer blank. Enter zero if applicable.
Required:
Elaine's AGI is $85,500.
Elaine's AGI is $171,000.
Note: Round your intermediate calculations to the nearest whole dollar amount.
Elaine's AGI is $212,000.
Answers
The maximum American opportunity tax credit that Elaine can claim for the tuition payment and books is: $667.50
How to find the tax credit?Assuming that Elaine's son goes to a qualifying university, then the AOTC covers expenses like tuition, books, supplies and materials.
The first $2,000 are fully deductible, and then you can deduct up to 25% of the next $2,000.
Total maximum deduction possible = $2,500 per year.
Since Elaine's AGi is $174,500, she will not be able to claim the full deduction. If their AGI had been below $160,000, then Elaine could have claimed $2,000 + (25% x $1,920) = $2,480
Since the AOTC phases out evenly, then Elaine's reduction = $2,500 x ($14,500 / $20,000) = $1,812.50
Elaine will be able to claim $2,480 - $1,812.50 = $667.50
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On 1 January 2014 Alex had a motor vehicle with an original cost of $17000 on which depreciation of $6800 had been provided.
On 1 April 2014 he bought a new vehicle, costing $24 000. He sold the old one and received a cheque for $9400.
Alex provides depreciation on motor vehicles at the rate of 40% per annum on the reducing (diminishing) balance basis. He allows a full year’s depreciation in the year of purchase and none in the year of disposal.
Required
Prepare the accumulated depreciation account and motor vehicle disposal account for the year ended 31 December 2014. Balance the account(s) where necessary and bring down the balance(s) on 1 January 2015.
Answers
Answer:
Depreciation: 24,000 x 40% x 9/12 (From April to December) =7,200
pls see attached image
A spoke of a bicycle wheel is 14cm. What will be the distance of one turn of the wheel?
a) 88cm
b) 88cm²
c) 616cm
Answers
Answer:
a) 88 cm
Step-by-step explanation:
The spoke is 14 cm
⇒ radius = 14
Distance in one turn is the circumference of the circle
⇒ d = 2πr
= 2*3.14*14
= 87.92
≈ 88
a circle has a diameter of 28 cm, what would be the quadrants perimeter?
Answers
The perimeter of a circle's quadrants with a diameter of 28 cm would be 22 cm.
1. The diameter of a circle is a straight line passing through the center and touching two points on the circumference.
2. Given that the diameter is 28 cm, we can find the radius by dividing the diameter by 2: 28 cm / 2 = 14 cm.
3. The perimeter of a circle is the total distance around its circumference. We can find the circumference using the formula C = 2πr, where C is the circumference and r is the radius.
4. Plugging in the radius we found earlier, the circumference of the circle is C = 2π(14 cm).
5. Simplifying the equation, we get C = 28π cm.
6. However, we only need to find the perimeter of one quadrant of the circle, which is a quarter of the full circumference.
7. To find the perimeter of the quadrant, we divide the circumference by 4: (28π cm) / 4 = 7π cm.
8. Approximating the value of π to 3.14, the perimeter of the quadrant is approximately 7(3.14) cm.
9. Calculating the approximate value, the perimeter of the quadrant is 21.98 cm.
10. Rounding to the nearest whole number, the perimeter of the quadrant is approximately 22 cm.
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If a cube has volume 125cm³, find the height of the cube.
Answers
Answer:
height = 5 cm
Step-by-step explanation:
a cube has congruent sides (s)
the volume (V) of a cube is calculated as
V = s³
given V = 125 , then
s³ = 125 ( take cube root of both sides )
[tex]\sqrt[3]{s^3}[/tex] = [tex]\sqrt[3]{125}[/tex] = [tex]\sqrt[3]{5^3}[/tex]
s = 5
then height = 5 cm
The point below lies o the terminal side of angle O. Find the sine, cosine and tangent of each. (-0.866,0.5)
Answers
The sine of angle O is 0.5, the cosine of angle O is -0.866, and the tangent of angle O is approximately -0.577.
To find the sine, cosine, and tangent of an angle given a point on its terminal side, we can use the coordinates of the point and apply trigonometric definitions. Let's solve this step by step:
The given point is (-0.866, 0.5). Let's denote the angle formed with the positive x-axis as angle O.
1. Finding the hypotenuse:
The hypotenuse can be found using the Pythagorean theorem:
hypotenuse = √((-0.866)^2 + (0.5)^2)
= √(0.75 + 0.25)
= √1
= 1
2. Finding the sine:
The sine of angle O can be found by dividing the y-coordinate of the point by the hypotenuse:
sine(O) = y-coordinate / hypotenuse
= 0.5 / 1
= 0.5
3. Finding the cosine:
The cosine of angle O can be found by dividing the x-coordinate of the point by the hypotenuse:
cosine(O) = x-coordinate / hypotenuse
= -0.866 / 1
= -0.866
4. Finding the tangent:
The tangent of angle O can be found by dividing the y-coordinate by the x-coordinate:
tangent(O) = y-coordinate / x-coordinate
= 0.5 / -0.866
≈ -0.577
Therefore, the sine of angle O is 0.5, the cosine of angle O is -0.866, and the tangent of angle O is approximately -0.577.
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