The formula hu; vi d t .u/t .v/ defines an inner product on v because it is linear equation in u and v, symmetric, and positive definite.
The formula hu; vi d t .u/t .v/ defines an inner product on v because satisfies all of the requirements of an inner product. Specifically, it is linear in both u and v, meaning that ah; vi bh; vi for any scalar a and any two vectors u, v. This means that it is distributive over addition, so hu b c; v i d hu b; v i C hc; v i. It is also symmetric, so hu; v i d hv; ui, which is necessary for hu; ui to be considered a valid inner product. Finally, it is positive definite, meaning that hu; ui d k uk2 0 for all vectors u 6 d 0. This means that for any two vectors u, v, the inner product of hu; vi d t .u/t .v/ is a valid inner product on the vector space v.
Proof: Let u, v ∈ V .
1.hau b; v i d t .au b/t .v/ d at t .u/t .v/ bt t .v/ d ah; vi bh; vi
2. hu; vi d t .u/t .v/ is linear in v :
h u; av b i d t .u/t .av b/ d at t .u/t .v/ bt t .u/t .v/ d ah; vi bh; vi
3. hu; vi d t .u/t .v/ is symmetric:
h u; v i d t .u/t .v/ d t .v/t .u/ d hv; ui
4. hu; vi d t .u/t .v/ is positive definite:
h u; u i d t .u/t .u/ d k t .u/ k2 d k uk2 0 for all u 6 d
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t on rn . 14. let t be a one-to-one linear transformation from a vector space v into rn . show that for u, v in v , the formula hu; vi d t .u/t .v/ defines an inner product on v .
NO LINKS!!
A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes ) and T is the temperature (in degrees Celsius).
t T
0 81
5 69
10 60.5
15 54.2
20 49.3
25 45.4
30 42.6
a. Subtract the room temp. from each of the temp. in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T-24). An exponential model for the data (t, T-24) is T-24 = 54.4(0.964)^t. Solve for T.
T=
Graph the model. Compare the result with the plot of the original data.
b. Use a graphing utility to plot the points (t, ln(T-24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T-24) = at + b, which is equivalent to e^(ln(T-24)) = e^(at+b). Solve for T, and verify that the result is equivalent to the model in part (b). Round all numerical values to 3 decimal places).
T=
c. Fit a rational model to the data. Take the reciprocals of the y-coordinates of the revised data points to generate the points. (t, 1/(T-24))
Use a graphing utility to graph these points and observe that they appear to be linear. Use the regression feature of a graphing utility to fit a line to these data. The resulting line has the form 1/(T - 24) = at + b.
Solve for T. (Round all numerical values to 4 decimal places). Use a graphing utility the rational function and the original data points.
T=
Part (a)
Given data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T\\\cline{1-2}0 & 81\\\cline{1-2}5 & 69\\\cline{1-2}10 & 60.5\\\cline{1-2}15 & 54.2\\\cline{1-2}20 & 49.3\\\cline{1-2}25 & 45.4\\\cline{1-2}30 & 42.6\\\cline{1-2}\end{array}[/tex]
where,
t = time in minutesT = temperature in CelsiusIt's unfortunate that T is used twice for these variables. It might cause some confusion.
This is what happens when we subtract 24 from each temperature.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T-24\\\cline{1-2}0 & 57\\\cline{1-2}5 & 45\\\cline{1-2}10 & 36.5\\\cline{1-2}15 & 30.2\\\cline{1-2}20 & 25.3\\\cline{1-2}25 & 21.4\\\cline{1-2}30 & 18.6\\\cline{1-2}\end{array}[/tex]
The graph of each set of points is shown in figure A. I used GeoGebra to make the graph.
The first set of data points are in red. The second set in blue. Notice the set of blue points is the result of shifting the red points 24 units down.
The green exponential model is also shown as the curve through the set of red points.
The green regression exponential model doesn't go through each point perfectly. Rather it tries to get as close as possible.
To go from
T-24 = 54.4(0.964)^t
to
T = 54.4(0.964)^t + 24
we simply add 24 to both sides. This means there isn't much to show in terms of steps when solving for T.
=======================================================
Part (b)
Use spreadsheet technology or something like GeoGebra to generate this data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & ln(T-24)\\\cline{1-2}0 & 4.043051\\\cline{1-2}5 & 3.806662\\\cline{1-2}10 & 3.597312\\\cline{1-2}15 & 3.407842\\\cline{1-2}20 & 3.230804\\\cline{1-2}25 & 3.063391\\\cline{1-2}30 & 2.923162\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
Then plot each of those points on the same xy grid. Use technology of your choice to determine the regression line is roughly
y = -0.03723x + 3.99739
So we can say
ln(T-24) = -0.03723t + 3.99739
the right hand side fits the format at + b where
a = -0.03723b = 3.99739both of which are approximate.
Then,
e^(ln(T-24)) = e^(at+b)
T-24 = e^(at+b)
T-24 = e^(-0.03723t + 3.99739)
T-24 = e^(-0.03723t)*e^(3.99739)
T-24 = e^(-0.03723t)*54.45583
T-24 = 54.45583*e^(-0.03723t)
T = 54.45583*e^(-0.03723t) + 24
T = 54.456*e^(-0.037t) + 24
Let's verify that this is equivalent to the model found in part (a).
T = 54.456*e^(-0.037t) + 24
T = 54.456*(e^(-0.037))^t + 24
T = 54.456*(0.963676)^t + 24
T = 54.5*(0.964)^t + 24
which is very close to the model mentioned in part (a). There's some slight rounding error. That's to be expected in problems like this.
-----------------------------
Answer: T = 54.456*e^(-0.037t) + 24
See figure B for the graph. Like with the other regression curve, this straight line doesn't go through all of the points. It tries to get as close as possible.
=======================================================
Part (c)
Refer to the 2nd table mentioned in part (a).
We'll apply the reciprocal to each item in the column labeled T-24.
For instance, the item 57 becomes 1/57 = 0.017544 approximately.
This is what the data table looks like:
[tex]\begin{array}{|c|c|} \cline{1-2}t & 1/(T-24)\\\cline{1-2}0 & 0.017544\\\cline{1-2}5 & 0.022222\\\cline{1-2}10 & 0.027397\\\cline{1-2}15 & 0.033113\\\cline{1-2}20 & 0.039526\\\cline{1-2}25 & 0.046729\\\cline{1-2}30 & 0.053763\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
The set of points and regression line are shown in figure C1. This line does not go through all of the points. Like with the others, it tries to get as close as possible to each point.
Use technology to determine the equation of the regression line is approximately:
y = 0.00121x + 0.01613
Which tells us that
1/(T-24) = 0.00121t + 0.01613
Let's solve for uppercase T.
1/(T-24) = 0.00121t + 0.01613
T-24 = 1/(0.00121t + 0.01613)
T = 1/(0.00121t + 0.01613) + 24
T = 1/(0.0012t + 0.0161) + 24
which is the approximate final answer.
Figure C2 shown below represents the original data points (t, T) in red. The blue curve is y = 1/(0.0012x+0.0161)+24, which is the rational regression curve we just found. This curve tries its best to get as close as possible to each red point.
Compare the regression curves of figure A and figure C2. We have a very close tie in terms of which curve does a better job of fitting the original data.
pls help me with both of these questions
The number of times a large popcorn without butter is sold is, 49.
The conditional relative frequency of no.of Item2 sold given that
50% off is 0.27.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
The number of times a large popcorn without butter is sold is,
= 49.
The total no. of items that is 50% off is (12 + 20 + 32) = 74.
The no. of Item2 which is 50% off is 20.
So, The conditional relative frequency of no.of Item2 sold given that 50% off is,
= 20/74.
= 0.27.
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the surface area of a sphere is 320 square centimeters what is the radius of the square
The radius of the sphere of surface area 320 cm² is 5.04 cm.
What is a radius?A radius is defined as half of a diameter. The unit of radius is meter.
To calculate the radius of the sphere, we use the formula below.
Formula:
r = √(A/4π)....................... Equation 1Where:
r = Radius of the sphereA = Surface area of the sphereπ = PieFrom the question,
Given:
A = 320 cm²π = 3.14Substitute these values into equation 1
r = √[320/(3.14×4)]r = √(25.48)r = 5.04 cmHence, the radius of the sphere is 5.04 cm.
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In 1950, a U.S. population
model
was y = 151. (1.013)^t-1950 million
people, where t is the year. What did
the model predict the U.S. population
would be in the year 2000?
In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.
What is population model ?Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).
The model was given as y=151x(1.013)^t-1950
where the future time t = 2000
Then we can substitute the given year 2000 as the value of 't'
then we will have y=[151x(1.013)^(2000-1950)] = 288 million
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need help with all these
Answer:
|
|
|
∆∆∆∆∆∆∆∆∆∆∆∆∆∆
Step-by-step explanation:
get better
Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results:
9. The conditional distribution for preferred cookie brand among males (in percents) is given by which of the following?
A. A: 27%; B: 19%; C: 25%; D: 29%
B. A: 4%; B: 6%; C: 13%; D: 15%
C. A: 11%; B: 16%; C: 34%; D: 39%
D. A: 23%; B: 13%; C: 11%; D: 14%
E. A: 38%; B: 21%; C: 19%; D: 22%
They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
Ida made four brands A , B , C and D
Mostly students like A brand 11% , B brand 16% , C brand 34% and D brand 39%
So this is best brand like by students male and female
They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.
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A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 18% per hour. He will check on the bacteria every 3 hours. How many bacteria will he find in 3 hours? Round your answer to the nearest whole number.
Answer:
The answer is approximately 770 bacteria after 3 hours.
(Factoring Algebraic Expressions MC)
x3y2 is the result of the expression employing the common factor (x - 6y).
What is Mathematical expression?Here,
The sentence is,
x⁴y² - 6x³y³
We must use the common factor to solve.
Mathematical expression refers to the combining of numbers and variables utilizing the operations addition, subtraction, multiplication, and division.
Now,
The sentence is,
x⁴y² - 6x³y³
The common factor is used to solve as,
6x3y3 - x4y2 equals x*x*x*y*y - 6*x*x*x*y*y.
= x³y² (x - 6y) (x - 6y)
Consequently, x3y2 is the value of the expression employing the common factor (x - 6y).
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QUESTION ISDOWN BELOW
The Answers to the Question are solved below.
What is Cube root?A number's cube root is the factor that we multiply three times to get that number.
The symbol for cube root is 3 cube root of, end cube root(∛) .
Given:
1. [tex]5^{-2[/tex]
Using Exponents
[tex]a^{-m[/tex] = 1 / [tex]a^m[/tex]
So, [tex]5^{-2[/tex] = 1/5² = 1/25.
2. z+ 5= 12
z= 12-5
z= 7
3. Pythagorean triplet: m²-1, 2m, m²+1
2m= 6
m=3
and, m²-1 = 9-1= 8
and, m²+1 = 9+1= 10
3. Cube root of 64 = ∛64= ∛(4 x 4 x 4)= 4
4. 4z+ 3= 6+ 2z
2z = 3
z= 3/2
5. a- b+ ab, b- c + bc, c- a +ac
Adding: (a- b+ ab) + (b- c + bc) + (c- a +ac)
= ab+ bc+ ac
6. -1 x -2/5
= 2/5
The Multiplicative inverse = -5/2
7. y+3 = 10
y=7
8. 10³= 10 x 10 x 10= 1000
9. [tex]3^{-2[/tex]
= 1/3²
= 1/9
10. Volume = Base Area x height
900 = 180 h
h= 900/180
h = 5
11. 16 as sum of 4 add number
= 1 + 3 + 5 + 7
12. 78 x 82
(80- 2)(80+ 2)
= 80² - 2²
= 6400 - 4
= 6396
13. 2/3 x 100
= 200/3 %
14. (ab- bc)+ (bc - ca) + (ca- ab)
= [tex](-4)^5[/tex] ÷ [tex](-4)^8[/tex]
= [tex](-4)^{5-8}[/tex]
= [tex](-4)^{-3[/tex]
15. 4p² - 9q²
= (2p)² - (3q)²
= (2p - 3q) (2p + 3q)
16. 2y-1 = 14- y
3y= 15
y= 5
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Lines PQ and BC are parallel.
What is the value of x ?
Answer:
x = 40
Step-by-step explanation:
since lines PQ and BC are parallel , then
∠ BCQ and ∠ AQP are corresponding angle and are congruent , that is
∠ BCQ = 80°
the sum of the 3 angles in Δ ABC = 180° , then
x + 80 + 60 = 180
x + 140 = 180 ( subtract 140 from both sides )
x = 40
Solve for x using the quadratic formula: x² - 6x + 9 = 0
X=
-b± √b²-4ac
2a
Ox=6
Ox=3
Ox=1
Ox=0
Answer:
[tex] \huge{ \boxed{x = 3}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 6x + 9 = 0[/tex]
Using the quadratic formula that's,
[tex] \bold{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}} \\ [/tex]
Comparing the equation to the general form of a quadratic equation ( ax² + bx + c), we have.
[tex]a = 1 \\ b = - 6 \\ c = 9[/tex]
Substituting the values into the formula we have.
[tex]x = \frac{- ( -6) \pm \sqrt{( - {6})^{2} - 4(1)(9) } }{2(1)} \\ x = \frac{6 \pm \sqrt{36 - 36} }{2} \\ x = \frac{ 6 \pm\sqrt{0} }{2} \\ x = \frac{6}{2} \: \: \: \: \: \\ \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
We have the final answer as
x = 3
If the opposite corners of the rectangle ABCD are A (5, 3) and C (10, 1) and the equation of side BC is x-2y=8, find the equations of the other three sides. You must show your work and explain why you are doing it. (Note: opposite side of a rectangle are parallel and consecutive sides are
perpendicular)
Answer:
Equation of side AB:
We know the coordinates of A and B, so we can use the point-slope form to create the equation of the line:
y - 3 = (3/5)(x - 5)
y - 3 = 3/5x - 15/5
5/3y - 15/3 = x - 5
5/3y - x = -15/3 + 5
5/3y - x + 15/3 = 5
5/3y - x + 15/3 = 0
Equation of side AB: 5/3y - x + 15/3 = 0
Equation of side DC:
We know the coordinates of C and D, so we can use the point-slope form to create the equation of the line:
y - 1 = (2/5)(x - 10)
y - 1 = 2/5x - 20/5
5/2y - 10 = x - 10
5/2y - x = -10
5/2y - x - 10 = 0
Equation of side DC: 5/2y - x - 10 = 0
Equation of side BD:
We know the equation of side BC (x - 2y = 8) and that consecutive sides are perpendicular, so we can use the slope-intercept form to find the equation of line BD:
Slope of BC = -2/1
Slope of BD = -1/-2 = 1/2
y = (1/2)x + b
We can use the coordinates of B to find b:
1 = (1/2)(8) + b
2 = 4 + b
b = -2
Equation of side BD: y = (1/2)x - 2
Step-by-step explanation:
Digits a, b, and c can be chosen to make the following
multiplication work. What is the 3-digit number abc.
a b c
� 2 4
1 c b a 2
Answer:
1
Step-by-step explanation:
Anne Richards purchased two slippers at one price and three pajamas at another price. Let s = the price of each slipper and p = the price of each pajama. Each slipper
cost $12. How much did each pajama cost if the total purchase price was $120?
Each pajama cost $. (Simplify your answer.)
Answer:
[tex]E[/tex]ach pajama costs $32
Step-by-step explanation:
So, the said person bought:
2 slippers at a price, 3 pajamas at another price. (The prices are unknowns, s, and p)
Each slippers cost $12
We are to find the cost of each pajama, where the total purchase price is $120
With the given conditions, we formulate an equation: 2s + 3p = 120
Since s = 12, we replace for the value of s in the equation. s becomes 2 × 12 = 24.
The new equation is then: 24 + 3p = 120, where we are to find the value of p.
Collect like terms: 3p = 120 - 24 → 3p = 96
Divide both sides of the equation by 3 to find the value of p: 3p/3 = 96/3 → p = 32
Therefore, the price of each pajama is $32
I hope this helpsPLS HELP ASAP pic attached
The slope and y-intercept, or the points, should be used to graph the line. Slope: 3 y-intercept: (0, 1 )
How to find the Calculation?g ( x ) = − 3 x − 1
Create an equation using the function.
y = − 3 x − 1
Calculate the slope and y-intercept using the slope-intercept form.
Less steps by tapping...
In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.
y = m x + b
With the use of the formula y = m x + b, determine the values of m and b.
m = − 3 b = − 1
m is the line's slope, and is the value of the y-intercept.
B. Slope: 3 Y-intercept: (0, 1 )
Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.
Less steps by tapping...
Assign the x and y values to a table.
x y
0 − 1
1 − 4
The slope and y-intercept, or the points, should be used to graph the line.
Slope: 3 y-intercept: (0, 1 )
x y
0 1
1 4.
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Solve Please and Thank U
The solution to the systems are (1, 1), (-3, -1), (1, -2), (2, -1), (7, -1) and (-2, 2)
How to determine the solution to the system?System 1
In this case, the system of equations is given as
y = -3x + 4
y = 3x - 2
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, 1)
So, the solution is (1, 1)
System 2
In this case, the system of equations is given as
y = x + 2
x = -3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, -1)
So, the solution is (-3, -1)
System 3
In this case, the system of equations is given as
4x + y = 2
x - y = 3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, -2)
So, the solution is (1, -2)
System 4
We have
y = 4x - 9
y = x - 3
Substitute y = 4x - 9 in y = x - 3
4x - 9 = x - 3
Evaluate the like terms
3x = 6
So, we have
x = 2
Recall that:
y = x - 3
So, we have
y = 2 - 3
y = -1
So, the solution is (2, -1)
System 5
We have
x + 7y = 0
2x - 8y = 22
Make x the subject in x + 7y = 0
x = -7y
Substitute x = -7y in 2x - 8y = 22
-14y - 8y = 22
Evaluate the like terms
-22y = 22
So, we have
y = -1
Recall that:
x = -7y
So, we have
x = -7(-1)
x = 7
So, the solution is (7, -1)
System 6
We have
-7x + 2y = 18
6x + 6y = 0
Make x the subject in 6x + 6y = 0
x = -y
Substitute x = -y in -7x + 2y = 18
7y + 2y = 18
Evaluate the like terms
9y = 18
So, we have
y = 2
Recall that:
x = -y
So, we have
x = -2
So, the solution is (-2, 2)
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If tan x = 3/4 find sin x and cos x.
Step-by-step explanation:
tan(x) = sin(x)/cos(x) = 3/4
in the trigonometric triangle sin(x) and cos(x) are the legs, and the radius is the Hypotenuse, the baseline (opposite of the 90° angle).
so, we can use Pythagoras to find the radius.
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
let's stay integer.
if sin(x) is equivalent to 3, and cos(x) to 4, then what is the radius ?
3² + 4² = c²
9 + 16 = c²
25 = c²
c = radius = 5
so,
3 = sin(x) × 5
4 = cos(x) × 5
sin(x) = 3/5 = 0.6
cos(x) = 4/5 = 0.8
The value of sin x is 3/5 and the value of cos x is 4/5.
What are trigonometry ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given that tan x = 3/4.
The tangent of an angle is the ratio of height to the base of the right triangle.
Here the height of the triangle is 3 and the base is 4.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the base and height.
Thus,
hypotenuse = √(3² + 4²)
hypotenuse = 5.
The sine of an angle is the ratio of height to the hypotenuse.
Sin x = Height/ hypotenuse
sin x = 3/5
The cosine of an angle is the ratio of the base to the hypotenuse.
cos x = base/ hypotenuse
cos x = 4/5
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What is the value of sin0 given that (-3,4) is a point on the terminal side of 0?
I need help asap i don’t get it
∠SWV is congruent to ∠TWU because vertically opposite angle.
Define congruent.If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence. Two triangles are said to be congruent if their two sides and their included angle are the same in both of them. Congruence appears to be based on the concept of a "rigid body," which may be transported from one location to another without affecting the internal relationships between its components.
Given
∠SWV ≅ ∠TWU
Vertically opposite angle
∠SWV is congruent to ∠TWU because vertically opposite angle.
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DUE SOON! PLEASE SHOW HOW YOU KNOW! THIS IS A SSA SITUATION BUT NOT SURE HOW TO FIND OUT HOW MANY TRIANGLES ARE POSSIBLE!
This is a SAS situation, only one triangle is possible. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
In triangle ΔABC, the angle ∠A is 22°. And the measure of the side BC is 18.9 cm and the measure of the side AC is 15.1 cm.
To fix a triangle, the known dimensions of the triangle should be three which one must be a side.
This is a SAS circumstance, just a single triangle is conceivable. Then the right choice is C.
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How is 25 to 5 and 10 to 2 equivalent ratios
Answer:
They are equivalent ratios because if you multiply 10 to 2 by 2.5 you get 25 to five
Answer:
equals 25
Step-by-step explanation:
is it correct? i will brinlist to who answer first
I don't see the full picture but your answer should look like this:
4ab+(-12ab)+9ab+(-5ab)
= 4ab-12ab+9ab-5ab
= (4-12+9-5)ab
= -4ab
Three students that share a townhouse find that their electric bill for October is $2.23 less than the September bill. The
total of both bills is $292.43, and each bill is split evenly among the roommates. How much did each owe in September?
Answer:
$47.48
Step-by-step explanation:
Let x = the amount owed Sept.
x + x - 2.23 = 292.43 Combine like terms
2x -2.23 = 292.43 Add 2.23 to both sides
2x - 2.23 + 2.23 = 292.43 + 2.23
2x = 294.66 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{294.66}{2}[/tex]
x = 147.33 this is the bill for September
Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.
Total:
147.33 + 145.10 = 292.43
292.43 ÷ 3 = 97.48 This is what each will owe rounded to the nearest penny.
I need help with the statement and the reasons
Explanation:
You can make use of the properties of parallel lines to prove ∠ACB≅∠DAC.
Statement . . . . Reason
2. ∠DAB +∠ABC = 180° . . . . definition of a right angle
3. AD║BC . . . . consecutive interior angles are supplementary
4. ∠ACB≅∠DAC . . . . alternate interior angles are congruent
How do I solve this?
Answer:
Area = 5π/2 in^2
Perimeter = 3π + 2 in
Step-by-step explanation:
A=area of a circle. P=Perimeter of a circle
F=Area of first semi-circle
T=Area of Figure
Solve for Area:
A=πr^2
F=A/2
A=π(2)^2 ==> solve for A
A=4π
F=(4π)/2
F=2π ==> this is for the first semi-circle
S=Area of second semi-circle
S=(πr^2)/2
S=(π(2/2)^2)/2 ==> the radius is half the diameter, and the diameter is 2 in
S=(π(1)^2)/2
S=π/2
T=F+S ==> The total area is the area of both semi-circles
T=2π + π/2 ==> plugin 2π for F and π/2 for S
T = 4π/2 + π/2 ==> common denominators
T = 5π/2 in^2
Now solve for perimeter
P = 2πr.
q = perimeter of first semi-circle
q = P/2
q = 2πr/2
q = 2π(2)/2 ==> plugin 2 for r
q = 2π
R = Perimeter of second semi-circle
R = 2π(1)/2 ==> we calculated that the radius of the semi-circle is half of the
radius of the first semi-circle
R = 2π/2 ==> simplify
R = π
Also, add in side length DC into the perimeter as it is part of the perimeter.
E = Entire perimeter of figure
E = q + R + DC
E = 2π + π + 2
E = 3π + 2 in
Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon? A. 0.2 B 1/0.2 C. 0.2^8 D 0.2 (0.8)^7
E. 0.8 (0.2)^7
The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.
How to calculate probability of needing to catch 8 fish to get the first salmon?
Given that he probability of fishing a salmon in a certain river is 20% i.e. 0.2. Now, the probability of not getting a salmon will be
1 - probability of not getting salmon = 1 - 0.2 = 0.8.
So, the first fish should be salmon and the others should not be salmon. So, the required probability of independent events can be calculated as,
P =0.2×0.8×0.8×0.8×0.8×0.8×0.8×0.8×0.8
P = 0.2× (0.8)^7
Hence,the probability of needing to catch 8 fish to get the first salmon is 0.2 (0.8)^7.
The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.
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Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.
What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.
The 95% confidence interval for this population proportion is (0.10, 0.23).
What is a confidence interval?A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.
Sample size n = 125
number of people who planned to take an extended vacation = 21
sample proportion p = 21/125 = 0.168
Confidence level = 0.95
significance level α = 1-0.95 = 0.05
Z score =[tex]Z_{\alpha 2}[/tex] = Z(0.05) = 1.96, from Z table.
The confidence interval for population proportion is-
p±[tex]Z_{\alpha 2}[/tex] x √{p(1-p)}/n =0.168±1.96 x 0.168 x √{(1-0.168)}/125
=0.168±1.96 x 0.0334
=0.168±0.0655
=(0.1025, 0.2335)
=(0.10, 0.23)
Therefore, the confidence interval is (0.10, 0.23).
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Suppose that the function h is defined, for all real numbers, as follows.
=hx +−12x24 ≠if x2
−2 =if x2
Find h−3, h2, and h4.
The function h is defined, for all real numbers h(-3) = -1/2 , h(2) = -2 and h(4) = -4.
What is a function ?
When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x. Mathematicians refer to functions as mapping or transformations.
The given function,
h(x) = -1/2 x^2 + 4 if x≠ 2
-2 if x=2
So, h(-3) = -1/2 (-3)^2 + 4
= - 9/2 + 4
= -1/2
h(2) = -2 ( given )
h(4) = -1/2 (4)^2 + 4
= -8 + 4
= -4 .
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A recent survey found that about 73.2% of all gasoline purchases at a certain service station chain are paid with a credit or debit card. If 250 gasoline purchases completed at this chain are randomly selected, find the probability that at most 195 of those purchases are paid with a credit or debit card. • Use Excel to find the probability, rounding your answer to four decimal places.
The probability that at most 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 ) is 0.9625..
We have given that,
Sample size , n=250
Sample proportion, p= 73.2% = 0.732
np = 183
n(1-p) = 67
both np & n(1-p) values are greater than 5, So normal approximation is applicable
mean, µ = np = 183
std. dev, σ = √np(1-p) =√250×0.732 ×(1-0.732) =7.0031
we have to calculate probability that at most 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 )
= P( X < 195.5 )
= P((x - µ) / σ < (195.5 -183)/ 7.0031)
= P( Z < 1.78 )
= 0.9625
Required probability using Excel function ,
Excel command: =NORM.S.DIST(z,1)
= Norm.S.DIST(1.78,1)
= 0.9625
Hence, required probability is 0.9625..
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Why did he write (x+4), even though the root
is at negative 4?
The reason behind this is that when the negative root goes from the RHS to LHS, its sign gets converted, and it appears like (x + 4).
What is the quadratic equation?A 2nd equation in x is known as a quadratic function. Ax2 + bx + c = 0 is the quadratic equations in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.
As per the given information in the question,
The root obtained is -4 or,
We can also write this thing as,
x = -4
So, when -4 will come to the LHS the sign will be converted to positive, and then it can be written as (x + 4).
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