The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.
In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).
Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).
So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
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Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) g(x) = 8- x / 8+ 7 ; g(2), g(-8), g(1/2), g(a), g(a – 8), g(x^2 - 8) g(2) = 6/10 g(-8) = UNDEFINED g(1/2) = (8-(1/2) / 8+(1/2))
g(a) = (8-a) – (8+a)
g(a-8) = _________
g(x^2 – 8) = ________
The function values.
To evaluate the function g(x) = 8 - x / 8 + 7 at the indicated values, we need to substitute the values into the function and simplify.
g(2) = 8 - 2 / 8 + 7 = 6 / 15 = 2 / 5
g(-8) = 8 - (-8) / 8 + 7 = 16 / 15 = 16 / 15
g(1/2) = 8 - (1/2) / 8 + 7 = (15.5) / 15 = 31 / 30
g(a) = 8 - a / 8 + 7 = (15 - a) / 15
g(a - 8) = 8 - (a - 8) / 8 + 7 = (16 - a) / 15
g(x^2 - 8) = 8 - (x^2 - 8) / 8 + 7 = (16 - x^2) / 15
So, the function values are:
g(2) = 2 / 5
g(-8) = 16 / 15
g(1/2) = 31 / 30
g(a) = (15 - a) / 15
g(a - 8) = (16 - a) / 15
g(x^2 - 8) = (16 - x^2) / 15
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Find the equation of the curve with gradient function 3x2+5x4 that passes through (1,8)
The equation of the curve that passes through the point (1, 8) and has the gradient function 3x² + 5x⁴ is y = x³ + x⁵ + 6
In this problem, we are given the gradient function 3x² + 5x⁴ and the point (1, 8) through which the curve passes. To find the equation of the curve, we need to integrate the gradient function and add the constant of integration. Let's start by integrating 3x² + 5x⁴:
∫(3x² + 5x⁴)dx = x³ + x⁵ + C
where C is the constant of integration.
Now we have the general equation of the curve, but we need to find the specific value of C that will give us the curve that passes through the point (1, 8). We can do this by plugging in the values of x and y into the equation:
8 = 1³ + 1⁵ + C
8 = 1 + 1 + C
C = 6
Therefore, the equation of the curve is:
y = x³ + x⁵ + 6
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equation be multiplied? What will be the result after completing the multiplication? 7x+3y=-8 4x-y=-13
65x + 17y = -108 is the result of completing the multiplication 7x+3y=-8 4x-y=-13 of two equations together.
To find the result of multiplying these two equations, we need to use the distributive property. The distributive property states that a(b + c) = ab + ac. In this case, we can distribute the 7 and the 4 across the equations:
7(7x + 3y) = 7(-8)
4(4x - y) = 4(-13)
Simplifying these equations gives us:
49x + 21y = -56
16x - 4y = -52
Now, we can combine like terms:
65x + 17y = -108
This is the result of multiplying the two equations together. We can check our work by plugging in values for x and y and seeing if the equation holds true. For example, if x = 1 and y = 2, then the equation becomes:
65(1) + 17(2) = -108
65 + 34 = -108
99 = -108
This is not true, so we know that our answer is correct.
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Question 4(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.
cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.6 feet and a height labeled 4.4 feet
23.35 cubic feet
35.92 cubic feet
71.84 cubic feet
93.4 cubic feet
The volume of the Cylinder is 24.11 cubic feet.
What is Volume?Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.
The radius of the cylinder is half the diameter of the circular base, so:
r = 2.6/2 = 1.3 feet
The volume of the cylinder is given by:
V = πr²h
Substituting the values given:
V = 3.14 × 1.3² × 4.4 ≈ 24.11 cubic feet
Rounding to the nearest hundredth:
V ≈ 24.11 cubic feet
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50 points
At a financial conference, the 750 attendees were given the choice of turkey, ham, both, or neither on the sandwich in their sack lunch. Seventy-five of the attendees chose neither and 250 chose both. If a total of 450 people had ham on their sandwiches, use the given Venn diagram to determine how many people had turkey on their sandwiches.
475
525
225
300
The number of people who had turkey on their sandwiches is 475.
option A.
What is the number of people who had turkey on sandwiches?
Let's define the following;
A be the number of people who chose turkey,
B be the number of people who chose ham,
C be the number of people who chose both, and
D be the number of people who chose neither.
From the problem statement, we know that:
D = 75 (75 attendees chose neither)
C = 250 (250 attendees chose both)
B = 450 (450 attendees chose ham)
We want to find A (the number of attendees who chose turkey).
We can start by using the formula for the number of elements in the union of two sets:
|A U B| = |A| + |B| - |A n B|
where;
|A| and |B| denotes the number of elements in set A, set B and A n B denotes the intersection of sets A and B.Applying this formula to the problem, we get:
750 - D = A + B - C
750 - 75 = A + 450 - 250
675 = A + 200
A = 475
Therefore, 475 attendees chose turkey on their sandwiches. The answer is (A) 475.
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How many solutions exist for 1/1-x^2=-|3x-2|+5
A. 1
B. 2
C. 3
D. 4
23 POINTS!
Answer:
4 !!!!
Step-by-step explanation:
f (x) = 1/1-x2 g (x) = -(3 x -2 ) - 5 then the number of solutions if the number of intersections of f(x) and g (x) i drew a graph and there was 4 intersections so thats how i got this answer
I hope i was right
There are two solutions to the equation 1/(1 - x²) = -|3x - 2| + 5.
What is Equation?An equation is a statement that shows that two mathematical expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponents.
We can start by considering the case where the expression inside the absolute value is non-negative, i.e., 3x - 2 ≥ 0, which implies x ≥ 2/3. In this case, the equation becomes:
1/(1 - x²) = 3x - 2 + 5
1/(1 - x) = 3x + 3
Multiplying both sides by 1 - x², we get:
1 = (3x + 3)(1 - x²)
3x³ + x² - 3x - 2 = 0
This equation has one real root.
The root is approximately x = 0.727.
Next, we consider the case where the expression inside the absolute value is negative, i.e., 3x - 2 < 0, which implies x < 2/3. In this case, the equation becomes:
1/(1 - x²) = -(3x - 2) + 5
Simplifying this equation, we get:
1/(1 - x) = -3x + 3
1 = (-3x + 3)(1 - x²)
3x³ - x² - 3x + 2 = 0
This equation also has one real root, which we can find using the same methods as before. The root is approximately x = -0.727. \
Therefore, there are two solutions to the equation 1/(1 - x²) = -|3x - 2| + 5.
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Simply these expressions 2*x*3*y
The value of the expression is A = 6xy
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the expression be represented as A
Now , the value of A is
A = 2 ( x ) ( 3 ) ( y )
On simplifying the equation , we get
A = ( 2 ) (3 ) ( xy )
A = 6xy
Therefore , the value of A is 6xy
Hence , the expression is A = 6xy
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Which one of the following equations could describe the graph above?
A. V=1.5x+2) - 3
B. V=3-1
= (-3)* +
О с.
C.
-5-4-3-2-1-1 2 3 4 5 6 7 8
V=
+6
An equation that could describe the graph below include the following: A. y = (1/2)^x + 6.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value or y-intercept.x represents time.b represents the slope or rate of change.Generally speaking, When the base value or y-intercept (a) is less than one (1), the graph of an exponential function increases exponentially to the left. Additionally, the smaller the value of y-intercept (a), the steeper the slope (b) of the line.
By critically observing the graph of this exponential function, we can logically deduce that it was vertically shifted up by 6 units.
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Find the measure of angle E.
Answer:
m∠E = 57º
Step-by-step explanation:
We can use the isosceles triangle theorem to determine that angle E is congruent to angle D, since side DF is congruent to side EF.
This means that:
m∠E = m∠D
m∠E = (4x + 1)º
Now, we can solve for x using the fact that the interior angles of a triangle sum to 180º.
m∠D + m∠E + m∠F = 180º
↓ substituting the given angles measures (in terms of x)
(4x + 1)º + (4x + 1)º + (5x - 4)º = 180º
↓ grouping like terms
(4x + 4x + 5x)º + (1 + 1 - 4)º = 180º
↓ combining like terms
13xº - 2º = 180º
↓ adding 2º to both sides
13xº = 182º
↓ dividing both sides by 13º
x = 14
With this x value, we can now solve for m∠E using its definition in terms of x.
m∠E = (4x + 1)º
↓ plugging in solved x value
m∠E = (4(14) + 1)º
m∠E = (56 + 1)º
m∠E = 57º
the data is given for 62 students in certain class regarding their mathematics marks out of 100.take the classes 0-10,10-20..and prepare frequency distribution table and cumulative frequency table more than or equal to type 55,60,81,90,45,65,45,52,30,85,20,10,75,95,09,20,25,39,45,50,78,70,46,64,42,58,31,82,27,11,78,97,07,22,27,36,35,40,75,80,47,69,48,59,32,83,23,17,77,45,05,23,37,38,35,25,46,57,68,45,47,49.from the prepared table answer the following question 1.
The frequency and cumulative frequency distribution tables for the given data are below in the solution part.
What is the cumulative frequency of the data?Cumulative frequency is used to calculate the number of observations in a data collection that is above (or below) a specific value.
The data is provided for 62 students in a certain class in terms of their maths marks out of 100.
55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
The frequency distribution table for the given data is as follows:
Class Frequency
(Marks obtained) (No. of students)
0 - 10 4
10 - 20 3
20 - 30 8
30 - 40 9
40 - 50 13
50 - 60 6
60 - 70 5
70 - 80 6
80 - 90 5
90 - 100 3
N = 62
The cumulative frequency table more than or equal to the type for the given data is as follows:
Class Frequency Cumulative frequency
(Marks obtained) (No. of students)
0 - 10 4 62
10 - 20 3 58
20 - 30 8 55
30 - 40 9 47
40 - 50 13 38
50 - 60 6 25
60 - 70 5 19
70 - 80 6 14
80 - 90 5 8
90 - 100 3 3
N = 62
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please help me its so confusing
The total surface area of the cube is 3.84 m². The solution has been obtained by using the area of cube.
What is area of a cube?The total surface area of a given cube is said to be equal to the sum of all the surface areas of the cube's faces, according to the definition of surface area. Given that the cube has six faces, its total surface area will be equal to the sum of its six faces.
We are given a cube with side length 0.8 metres.
We know that total surface area of a cube is given by 6a².
Now, by substituting a = 0.8 in the formula, we get
⇒Total surface area of cube = 6 (0.8)²
⇒Total surface area of cube = 6 (0.64)
⇒Total surface area of cube = 3.84 m²
Hence, the total surface area of the cube is 3.84 m².
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Triangle ABC is similar to triangle DEF. The length of BC¯¯¯¯¯ is 44 cm. The length of DE¯¯¯¯¯ is 14 cm. The length of EF¯¯¯¯¯ is 22 cm.
What is the length of AB¯¯¯¯¯?
Enter your answer in the box.
Answer:
28cm
Step-by-step explanation:
[tex] \frac{44}{22} \times 14 = 28[/tex]
For f(x) = x^15 and g(x) = 15Vx, find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x)
What is (fog)(x)?
(fog)(x) = ___
Based on the calculation, we find that:
(fog)(x) = (15Vx)¹⁵
(gof)(x) = 15V(x¹⁵)
(fog)(x) ≠ (gof)(x)
Function composition can be meant as an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
To find (fog)(x), we need to substitute g(x) into f(x). This means that we will replace every x in f(x) with 15Vx. So, (fog)(x) = f(g(x)) = f(15Vx) = (15Vx)¹⁵.
Similarly, to find (gof)(x), we need to substitute f(x) into g(x). This means that we will replace every x in g(x) with x¹⁵. So, (gof)(x) = g(f(x)) = g(x¹⁵) = 15V(x¹⁵).
Now, to determine whether (fog)(x) = (gof)(x), we need to compare the two expressions.
(fog)(x) = (15Vx)¹⁵ and (gof)(x) = 15V(x¹⁵). These two expressions are not equal, so (fog)(x) ≠ (gof)(x).
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p please help I have no clue.
Answer:
11 meters, 4.1 centimeters
Step-by-step explanation:
If for every centimeter it equals 2 meters, we can use this expression to solve for the width of the building in real-life:
5.5 × 2 = 11Therefore, the width of the building is 11 meters in real life.
If the real-life height of the building is 8.2 m tall, then we can use this expression:
8.2 ÷ 2 = 4.1We multiplied the first time, so why are we dividing now?Because we were given the drawings width the first time, we needed to multiply by 2 to get the real-life height in meters. But now that we are given the real-life height, we now need to divide by 2 to get the height of the drawing in centimeters.
Therefore, the width, in meters, of the building in real life is 11 meters, and the height of the drawing is 4.1 centimeters.
Two cheeseburgers and one small order of fries contain a total of 1420 calories. Three cheeseburgers and two small orders of fries contain a total of 2290 calories. Find the caloric content of each item.
One cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Two cheeseburgers and one small order of fries contain a total of 1420 calories.
Three cheeseburgers and two small orders of fries contain a total of 2290 calories.
let the number of Calories in one cheeseburgers be x and in one fries be y.
So, the system of Equation is:
2x + y = 1420
3x + 2y= 2290
solving the above two equation
x= 550 and y= 320
So, one cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
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A Markov chain model for the growth and replacement of trees assumes that there are "four" distinct stages of growth based on the age and size of the tree. The stages are young, medium size, large size and old, and the transition period considered is 6 years. At the end of this period, a tree either remains in the same state, moves to another higher state or gets replaced by a young tree. In each period, 20% of the young trees remain young, 70% become medium size and the rest become large size. Medium size trees remain medium, become large or replaced by young trees with probabilities 0.4, 0.5 and 0.1, respectively. In a period, it is equally likely that a large tree remains as large tree, becomes an old tree or replaced by a young tree. Old trees get replaced by young trees in 6 years with probability p, 0.5 < p < 1.
a) Write down the transition probability matrix of the Markov chain.
b) Find the proportion of old trees that will be in old state after 12 years.
c) Suppose a forest, after a bush fire, starts with all young trees. If p = 0.8, what proportion of the trees in the forest will be old after 18 years?
a) The transition probability matrix of the Markov chain is:
| 0.2 0.7 0.1 0 |
| 0.1 0.4 0.5 0 |
| 0.333 0 0.333 0.333 |
| 1-p 0 0 p |
b) The proportion of old trees that will be in old state after 12 years is 0.613.
c) If a forest starts with all young trees and p = 0.8, the proportion of the trees in the forest that will be old after 18 years is 0.413.
a) The transition probability matrix of the Markov chain is given by:
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
b) The proportion of old trees that will be in old state after 12 years can be found by multiplying the transition probability matrix by itself twice (since each period is 6 years and we want to find the proportion after 12 years).
The resulting matrix will give the probabilities of each state after 12 years. The proportion of old trees that will be in old state after 12 years is given by the element in the fourth row and fourth column of the resulting matrix.
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.293 | 0.49 | 0.293 | 0.123|
| 0.207 | 0.35 | 0.357 | 0.086|
| 0.311 | 0.233 | 0.311 | 0.311|
| 0.407 | 0.14 | 0.14 | 0.613|
The proportion of old trees that will be in old state after 12 years is 0.613.
c) If the forest starts with all young trees, the initial state vector is [1, 0, 0, 0]. To find the proportion of the trees in the forest that will be old after 18 years, we need to multiply the initial state vector by the transition probability matrix three times (since each period is 6 years and we want to find the proportion after 18 years).
The resulting vector will give the probabilities of each state after 18 years. The proportion of the trees in the forest that will be old after 18 years is given by the fourth element of the resulting vector.
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.407 | 0.49 | 0.293 | 0.123|
| 0.311 | 0.35 | 0.357 | 0.086|
| 0.407 | 0.233 | 0.311 | 0.311|
| 0.607 | 0.14 | 0.14 | 0.413|
The proportion of the trees in the forest that will be old after 18 years is 0.413.
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simplify each expression 5x^2 / 10x^3 - 15x
Step-by-step \frac{1}{2} x^{5} - 15x
find the sine of angle C in this triangle.
The sine of angle C is √30/10.
Trigonometric ratios:Trigonometric ratios are mathematical expressions used to relate the angles and sides of a right-angled triangle.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
are the fundamental ratios in a right-angle triangle
where
"Opposite" refers to the side opposite to the angle.
"Adjacent" refers to the side adjacent to the angle.
"Hypotenuse" refers to the longest side of the right-angled triangle
Here we have
A right-angle triangle DCB
Where DC = 10 units, CB = √70
From trigonometric ratios,
Sin θ = Opposite side/ Hypotenuse
Sin C = DB/CD
By the Pythagorean theorem
=> DC² = CB² + DB²
=> (10)² = (√70)² + DB²
=> 100 = 70 + DB²
=> DB² = 100 - 70
=> DB = √30
Sin C = √30/10
Therefore,
The sine of angle C is √30/10.
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Solve for the Area of the shaded region in each circle. 5. r=16in 6. r=22m Solve for the Arc Length of the following circles 2. r=3 m , angle=150°
1. angle= 315° , r=8 cm Solve for the Area of the Sector in each circle 3. angle=150° , r=19 4. angle=60°, r=10 in
Area of sector = (60°/360)*pi*(10 in)^2 = 25.13 in^2.
To solve for the Area of the shaded region in each circle, use the formula Area of circle = pi*r^2. For circle 5, Area of circle = pi*(16in)^2 = 201.06 in^2. For circle 6, Area of circle = pi*(22m)^2 = 1520.53 m^2.
To solve for the Arc Length of the following circles, use the formula Arc Length = (angle/360)*(2*pi*r). For circle 2, Arc Length = (150°/360)*(2*pi*3 m) = 11.78 m. For circle 1, Arc Length = (315°/360)*(2*pi*8 cm) = 21.99 cm.
To solve for the Area of the Sector in each circle, use the formula Area of sector = (angle/360)*pi*r^2. For circle 3, Area of sector = (150°/360)*pi*(19)^2 = 133.04. For circle 4, Area of sector = (60°/360)*pi*(10 in)^2 = 25.13 in^2.
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Can someone help? I have tried this problem the other day and I didn't get it right.
Answer:
x = 9[tex]\sqrt{\frac{1}{2}}[/tex]
Step-by-step explanation:
the base angles are both 45°, so both legs of the isosceles triangle = x
9² = x² + x² = 2x² Pythagorean theorem
x² = 9²/2
x = √(9²/2) = 9√(1/2)
20 points pls hurry and mark brainly
14C. Every store employee gets an additional 10% off the already discounted price. If an employee buys an item with an original price of $40, how much will the employee pay? Show your work or explain in words how did you get the answer.
Answer: The employee payed $36 for the item.
Step-by-step explanation:
Take $40 and since the employee gets a 10% discount
do $40 times 10% and you get 4
so take 4 away from the $40
40-4=36
Kate buys a greeting card for 3.79. She then buys 4 postcards that all cost the same amount. The total cost is 5.11. How much is each postcard? Show your work.
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32÷4=.33
Use the relationships in the diagrams below to solve for the given variable. Justify your solution with a definition or theorem.
In the parallelogram given the value for the variable x is deduced as 25°.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
According to the properties of a parallelogram, the vertically opposite angles of a parallelogram is always equation.
The first angle measures 2x + 50°.
The second angle measures 3x + 25°.
They both are placed vertically opposite to each other.
So, the equation will be -
2x + 50° = 3x + 25°
Collect the like terms -
2x - 3x = 25° - 50°
- x = - 25°
x = 25°
Therefore, the value of x is obtained as 25°.
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vow solve this equation for r. (r-3.5)(4)=(r)((9)/(4)) 4r-14=(9)/(4)r -14=-(7)/(4)r 8=r
From the given equation the value of r is 8.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
To solve this equation for r, we need to isolate r on one side of the equation. First, we add 14 to both sides of the equation:
4r-14+14 = (9/4)r+14
4r = (9/4)r+14
Then, we subtract (9/4)r from both sides:
4r - (9/4)r = (9/4)r+14 - (9/4)r
(5/4)r = 14
Finally, divide both sides of the equation by (5/4) to isolate r:
r = 14/(5/4) = 8
Therefore, the value of r is 8.
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Does someone mind helping me with this problem? Thank you!
Answer:
832
Step-by-step explanation:
The first step is to add 1 + 0.65 which is 1.65. Then you do 1.65 times itself 7 times which equals 33. You multiply 33 • 25 which is 832.
A die is rolled ten times. What is the probability that a prime
number will be rolled every time?
The probability of rolling a prime number every time
The probability of rolling a prime number on a single die is 3/6 or 1/2, since there are three prime numbers (2, 3, 5) out of six possible outcomes.
To find the probability of rolling a prime number ten times in a row, we need to multiply the probabilities together. This is because each roll is independent of the others, so the probability of rolling a prime number on each roll is the same.
So the probability of rolling a prime number ten times in a row is:
(1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 1/1024
Therefore, the probability of rolling a prime number every time a die is rolled ten times is 1/1024.
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Which of the following sets represents the solution of the equation below?
-3/2x² = x+1
The solution set is: [tex]$\left{\frac{-1+\sqrt{5}}{3}, \frac{-1-\sqrt{5}}{3}\right}$[/tex]
Option (D) is correct.
What is a quadratic equation?
A quadratic equation is a type of equation in algebra that can be written in the form of ax^2 + bx + c = 0, where x is the unknown variable, and a, b, and c are constants with a not equal to zero
The equation is:
[tex]$-\frac{3}{2}x^2 = x + 1$[/tex]
We can rewrite this equation as:
[tex]$-\frac{3}{2}x^2 - x - 1 = 0$[/tex]
To solve for x, we can use the quadratic formula:
[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]
Where a = -3/2, b = -1, and c = -1. Substituting these values into the quadratic formula, we get:
[tex]$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(-\frac{3}{2})(-1)}}{2(-\frac{3}{2})}$[/tex]
Simplifying this expression, we get:
[tex]$x = \frac{1 \pm \sqrt{5}}{3}$[/tex]
Therefore, the solution set is:
[tex]$\left{\frac{-1+\sqrt{5}}{3}, \frac{-1-\sqrt{5}}{3}\right}$[/tex]
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Logan invested $3,800 in an account paying an interest rate of 5½ % compounded
continuously. Qasim invested $3,800 in an account paying an interest rate of 6¹/8%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Logan's money to double than for Qasim's money to double?
9.63 years are required for $390 to become $660. A charge for borrowing money or other assets is called an interest.
What is Compound Interest?Compound interest simply indicates that the interest paid on a savings account, loan, or investment grows exponentially over time rather than linearly.
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Here, A = Amount,
P = Principal Amount
r = Rate of interest
n = Number of times interest is charged in a year
t = number of years
Given ,Here Principal Amount is $390, the rate of interest is 5.5%(0.055),
the number of times the interest is charged in a year (n=4),
and the final amount is $660,
therefore, number of years will be equal to,
[tex]660 = 390(1 + \frac{0.055}{4} )^{4*t}[/tex]
[tex]\frac{660}{390} = (1.01375)^{4*t}[/tex]
[tex]1.6923 = (1.01375)^{4*t}[/tex]
[tex]log_{1.01375}1.6923 = 4t[/tex]
[tex]4t = 38.5234[/tex]
[tex]t = 9.63[/tex]
Hence, number of years it will take for $390 to become $660 is 9.63 years.
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v. Use elementary row operation to transfer the augmented matrix to echelon form. Solve by back substitution also explain the type of solution. 3x + 2x, +4x4 – x4 =13 -2x + x + 5 x =5
The given system of equations is:
3x + 2y + 4z - w = 13
-2x + y + 5z = 5
We can write this system in the form of an augmented matrix as:
| 3 2 4 -1 | 13 |
| -2 1 5 0 | 5 |
To transform this matrix to echelon form, we perform the following elementary row operations:
Add 2 times the first row to the second row:
| 3 2 4 -1 | 13 |
| 0 5 13 -2 | 31 |
Divide the second row by 5 to obtain a leading 1:
| 3 2 4 -1 | 13 |
| 0 1 13/5 -2/5 | 31/5 |
Subtract 4 times the second row from the first row:
| 3 0 -6/5 3/5 | 9/5 |
| 0 1 13/5 -2/5 | 31/5 |
Multiply the second row by 6/5 and add it to the first row:
| 3 0 0 16/5 | 57/5 |
| 0 1 13/5 -2/5 | 31/5 |
The matrix is now in echelon form. Using back substitution, we can solve for the variables:
From the second row, we have:
y + (13/5)z - (2/5)w = 31/5
y = (2/5)w - (13/5)z + 31/5
Substituting y in the first row, we have:
3x + 2[(2/5)w - (13/5)z + 31/5] + 4z - w = 57/5
3x + (4/5)w - (26/5)z = 2/5
Solving for x, we have:
x = (2/15)w + (26/15)z - 2/15
So the solution is:
x = (2/15)w + (26/15)z - 2/15
y = (2/5)w - (13/5)z + 31/5
z = z
w = w
This is a parametric solution, as we have one free variable (z) and can express the other variables in terms of it. Therefore, the system has infinitely many solutions.
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Value added tax is added at 15% for goods and services In South Africa. What will be the selling of a laptop that costs R4200 before VAT
If the VAT in South Africa is 15%, then selling price of the laptop after the VAT is R4830 .
The cost price of the laptop before the VAT is R4200,
The VAT percent on goods and services is = 15%,
In order to calculate the selling price of the laptop that costs R4200 before VAT is added at 15% in South Africa, we can use the following formula:
⇒ Selling Price = Cost Price + (Cost Price × VAT )
Substituting the values,
We get,
⇒ Selling Price = R4200 + (R4200 × 0.15)
⇒ Selling Price = R4200 + R630
⇒ Selling Price = R4830
Therefore, the selling price of the laptop, including 15% VAT, will be R4830.
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