Answer: x2 - 4 = 0 and 4x2 = 16
Step-by-step explanation:
Factorize the following polynomials:
1) 54x²+42x³ - 30x4
What kind of angle is
∠mah?
What is the value of x?
What is the measure of
∠mat ?
What is the measure of
∠tah ?
So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.
What is the source of this answer and define a graph?(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]
(B) (2x+4)+(3x+1) = 90
5x+5 = 90
x= 17
(C) 2x+4 = 2×17 + 4 = 38°
(D) 3X + 1 = 3 × 17 + 1 = 52°
A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.
A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.
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The base of the right prism shown is a right triangle.
1. Name two lines parallel to AD.
2. Name a line skew to DE.
3. State the number of base edges.
4. State the number of lateral faces.
5. Find the base area,
6. Find the lateral area.
7. Find the volume.
Two lines parallel to AD are BF and CE.
Two lines skew to DE are EF and DF.
The number of base edges is three: DE, EF, and DF.
The number of lateral faces is three: ABDF, BCEF, and ACDE.
The base area is 6 square units.
The lateral area is 72 square units.
The volume is 36 cubic units.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
1. Name two lines parallel to AD.
BF, CE
2. Name a line skew to DE.
EF, DF
3. State the number of base edges.
DE, EF, DF
4. State the number of lateral faces.
3, Which are ABDF, BCEF, ACDE.
5. Find the base area,
the base of a prism is ΔDEF,
DE = AC = 3,
EF = BC = 4,
DF = 5
A = √(s(s-a)(s-b)(s-c))
s = (3 + 4 + 5)/2 = 6
A = √(s(s-a)(s-b)(s-c))
A = √(6(6-3)(6-4)(6-5))
A = √(6(3)(2)(1))
A = √36
A = 6
6. Find the lateral area.
the lateral area would be the sum of the area of the four rectangular faces.
A = lb
ABDF
A1 = 5* 6 = 30,
BCEF,
A2 = 4 * 6 = 24
ACDE
A3 = 3 *6 = 18
lateral area = 30 + 24 + 18
= 72
7. Find the volume.
The volume of a prism can be calculated by multiplying the area of the base by the height of the prism. Therefore, the formula for the volume of a prism is:
V = Bh
Where V is the volume, B is the area of the base, and h is the height of the prism.
V = 6 * 6 = 36
hence,
Two lines parallel to AD are BF and CE.
Two lines skew to DE are EF and DF.
The number of base edges is three: DE, EF, and DF.
The number of lateral faces is three: ABDF, BCEF, and ACDE.
The base area is 6 square units.
The lateral area is 72 square units.
The volume is 36 cubic units.
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PLSS HELP IMMEDIATELY
The continuous compounding rate earned by the investment is given as follows:
8.022%.
How to model continuous compounding?The balance of an account after t years, using continuous compounding, is modeled by the equation presented as follows:
A(t) = A(0)e^{kt}.
In which:
A(0) is the initial amount.k is the continuous compounding rates.For this problem, the parameters are given as follows:
A(11) = 58, A(0) = 24, t = 11.
Hence the rate is obtained as follows:
24e^(11k) = 58
e^(11k) = 58/24
11k = ln(58/24)
k = ln(58/24)/11
k = 8.022%.
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The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1600. Find the doubling period. Find the population after 70 minutes. When will the population reach 10000?
. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
a. Bert gets a Jack and Ernie rolls a five.
b. Bert gets a heart and Ernie rolls a number less than six.
c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
d. Bert gets a red card and Ernie rolls a fifteen.
e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.
What is probability, exactly?The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.
Here,
a.
P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)
= (4/52) * (1/12)
= 1/78
b.
P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)
= (13/52) * (5/12)
= 65/624
c.
P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)
= (12/52) * (6/12)
= 1/4
d.
P(Bert gets a red card and Ernie rolls a fifteen) = 0
e.
Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:
A regular 52-card deck contains 48 cards that are not Jacks,
so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.
On a 12-sided dice with 11 possible outcomes,
Ernie rolls a non-12th-number (1, 2, 3, etc.).
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if k(x) =3x, then f'(x)=?
Which geometric term describes ∠ T A G ?
Answer:
angle
Step-by-step explanation:
since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!
Answer: i know it is acute
Write an equation for the polynomial graphed below
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
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What are answers to these questions?
1. f is concave up on the intervals = ?
2. f is concave down on the intervals = ?
3. The inflection points occur at x = ?
f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(42x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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The f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?
An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(4x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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Given F(x) = 4x - 8 and g(x) = -3x + 1, what is (f - g)(x)?
A) 7x-9
B) 7x - 7
C) x-9
D) x - 7
Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.
What is function?In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.
Here,
To find (f - g)(x), we need to subtract g(x) from f(x), so we get:
(f - g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f - g)(x) = (4x - 8) - (-3x + 1)
Simplifying the expression by distributing the negative sign, we get:
(f - g)(x) = 4x - 8 + 3x - 1
Combining like terms, we get:
(f - g)(x) = 7x - 9
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What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = [tex]\frac{168}{7}[/tex] = 24
Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
+
X
Ś
The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
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Given that sin 0 = 20/29 and that angle terminates in quadrant III, then what is the value of tan 0?
The value of Tanθ is 20/21.
What is Pythagorean Theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: sinθ = -20/29 and that angle terminates in quadrant III.
We have to find the value of tanθ.
Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Sinθ = Perpendicular/hypotenuse
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Adjacent = - √Hypotenuse² - perpenducualr²
Replace the known values in the equation.
Adjacent = -√29² - (-20)²
Adjacent = -21
Find the value of tangent.
Tanθ = Perpendicular/base
Tanθ = -20/(-21)
Hence, the value of Tanθ is 20/21.
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0\left\{-10\le x\le10\right\}
Describe the transformations (vertical translation, horizontal translation, and dilation/reflection) from the parent function that happened to these formulas
The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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See the photo below
This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:
[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]
This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.
The problem involves some algebraic manipulation and the use of the linearity of the integral.
It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.
See the attached for the full solution.
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find the radius of a cylinder if the volume is 2,035.75 in^3 and the height is 3 times the radius. use the formula V= pi r^2h
The radius of the cylinder is approximately 6.75 inches.
How to calculate volume of cylinder?We can use the formula for the volume of a cylinder to solve this problem:
[tex]V = \pi r^2h[/tex]
We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:
[tex]V = \pi r^2(3r)[/tex]
Simplifying this expression, we get:
V = 3π[tex]r^3[/tex]
To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:
V/(3π[tex]r^2[/tex]) = r
Substituting the given value for V, we have:
2,035.75/(3π[tex]r^2[/tex]) = r
Multiplying both sides by 3πr^2, we get:
2,035.75 = 3π[tex]r^3[/tex]
Dividing both sides by 3π, we have:
[tex]r^3[/tex] = 2,035.75 / (3π)
Taking the cube root of both sides, we get:
r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]
Using a calculator, we find that:
r ≈ 6.75 inches
Therefore, The cylinder has a radius of about 6.75 inches.
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KPI Payouts are: Prepaid Ring-out Only: $ 1.00 Prepaid Activation: $ 2.00 Accessories: 1.5 Equipment Protection: $ 1.00 You can make $ and ring it out at the POS. % when you activate a prepaid device with equipment protection
If no accessories are sold, $3 will be paid out. In the event that accessories are sold, the compensation is $2.00 plus $1.00 plus 1.5 percent of their worth.
Based on the information given, the KPI payouts are:
$1.00 for each Prepaid Ring-out Only
$2.00 for each Prepaid Activation
1.5% of the value of each Accessories sale
$1.00 for each Equipment Protection sale
We need to know the values of the prepaid activation and equipment protection in order to compute the payment for activating a prepaid device with equipment protection. Assume that the equipment protection is worth $Y and the prepaid activation is worth $X.
The following would be the total payment for activating a prepaid device with equipment protection:
Payout = $2.00 (for activation) + $1.00 (for equipment protection) + 1.5% (of the value of accessories sold)
If no accessories are sold, the payout would be:
Payout = $2.00 + $1.00
= $3.00
If accessories worth $Z are also sold, the payout would be:
Payout = $2.00 + $1.00 + 1.5% of $Z
= $2.00 + $1.00 + 0.015Z
So the payout for activating a prepaid device with equipment protection depends on the value of the accessories sold.
Therefore, If no accessories are sold, the payout is $3.00. If accessories are sold, the payout is $2.00 + $1.00 + 1.5% of the value of the accessories sold.
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The diameter of a circle is 38 feet.what is the circles circumfrence. Use 3.14 for pi
Answer:
The circumference of the circle is 119.32 ft.
Step-by-step explanation:
The circumference of a circle can be solved through the formula:
C = πd
where d is the diameter
Given: d = 38 ft
π = 3.14
Solve:
C = πd
C = 3.14 (38 ft)
C = 119.32 ft
I need helppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x1 is a,
x2 is 0,
y1 is 0 and
y2 is b. Fitting those into the formula where they belong:
[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and
[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]
Since a negative squared is a positive, then
[tex]d=\sqrt{a^2+b^2}[/tex]
which is the second choice down.
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?
Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.
Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:
(x1, y1) = (35, 16.83)
(x2, y2) = (52, 18.87)
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27
Using point-slope form with the first point, we get:
y - y1 = m(x - x1)
y - 16.83 = 0.27(x - 35)
Simplifying, we get:
y = 0.27x + 7.74
Therefore, the monthly cost for 39 minutes of calls is:
y = 0.27(39) + 7.74 = $18.21
Step-by-step explanation:
Find the final amount of a $750 investment after 15 years at 8% interest compounded semiannually, quarterly and daily.
With given compound interest, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or the interest earned on both the principal and any previously accrued interest. In other words, interest is computed not only on the original amount of money but also on any past interest gained. The interest generated on the cumulative interest can compound exponentially, resulting in enormous growth of an investment or loan sum over time. Compound interest is computed using a formula that takes the principle amount, interest rate, and compounding frequency into consideration.
Now,
To find the final amount of the investment, we can use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
where:
A = final amount
P = principal (initial investment)
r = annual interest rate
n = times the interest is compounded per year
x = time in years
For semiannual compounding, n = 2 and x = 15:
A = 750(1 + 0.08/2)²*¹⁵= $2,067.87
For quarterly compounding, n = 4 and x = 15:
A = 750(1 + 0.08/4)⁴*¹⁵ = $2,094.28
For daily compounding, n = 365 (assuming no leap years) and x = 15:
A = 750(1 + 0.08/365)³⁶⁵*¹⁵ = $2,101.62
Therefore, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.
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Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
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Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
verbal phrase can be represented by 7.16.
What is the verbal phrase?Part A:
The verbal phrase can be represented by the following expression:
[tex]2.19g + 0.59[/tex]
Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex] .
Part B:
To evaluate the expression when [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:
[tex]2.19g + 0.59[/tex]
[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]
[tex]= 6.57 + 0.59[/tex]
[tex]= 7.16[/tex]
Therefore, the correct answer is [tex]7.16.[/tex]
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The given question is incomplete. the complete question is given below:
Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros
The two consecutive natural numbers whose sum of squares is 181 are 9 and 10
Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:
x² + (x+1)² = 181
Expanding the equation:
x² + x² + 2x + 1 = 181
Combining like terms:
2x² + 2x - 180 = 0
Dividing both sides by 2:
x² + x - 90 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -90
x = (-1 ± √(1 + 360)) / 2
x = (-1 ± √(361)) / 2
x = (-1 ± 19) / 2
We discard the negative value, as it does not correspond to a natural number:
x = 9
Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.
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The five number summary of a dataset was found to be:
45, 52, 56, 63, 66
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
Identifying the outliers in the summaryTo determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
IQR = Q3 - Q1
Where
Q1 = 52
Q3 = 63
So, we have
IQR = 63 - 52
IQR = 11
An observation is considered an outlier if it is:
Below Q1 - 1.5 × IQR
Above Q3 + 1.5 × IQR
Substituting the values, we get:
Below 52 - 1.5 × 11 = 35.5
Above 63 + 1.5 × 11 = 79.5
Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
The range is the best measure of variability for this data, and its value is 4.
Which of the following is the best measure of variability for the data, and what is its value?The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).
The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:
Range = Maximum value - Minimum value = 4 - 0 = 4
Therefore, the range is the best measure of variability for this data, and its value is 4.
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7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I
The control group for the experiment would be option C: some plants will receive no sunlight.
What is control group for experiment ?The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.
Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.
Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.
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PLEASE HELP
Find the Area
2cm
___cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
1. Find radius:
If diameter is 2, divide it by 2 to get radius = 1
2. Find formula:
A=πr^2
3. Plug in:
A = π(1)^2
4. Solve (multiply):
A = π(1)^2:
3.14159265359
Or
3.14 cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
r=2
2/2=1
A=[tex]\pi[/tex](1)^2
=[tex]\pi[/tex]1
≈3.14x1
≈3.14cm^2
Find each arc length. Round to the nearest tenth.
If FG = 27 yd, find the length of FED.
mFED= yards
(30 points) will give brainiest for effort
The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.
What is an arc length?The length of a section of a circle's circumference is known as an arc length.
The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.
To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:
m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)
m(EGD) = 360° - 80° - 47° - 90°
m(EGD) = 143°
The formula for arc length is:
Arc length = (central angle / 360) x (2πr)
We can use this information to find the radius of the circle:
FG = 2r
27 yd = 2r
r = 13.5 yd
Now we can use the formula for arc length to find the length of arc FED:
Arc length FED = ((∠FED) / 360) x (2πr)
We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):
∠(FED) = 360° - ∠(EGD)
∠(FED) = 360° - 143°
∠(FED) = 217°
Plugging in the values, we get:
Arc length FED = (217° / 360) x (2π x 13.5 yd)
Arc length FED = (0.6028) x (84.78 yd)
Arc length FED = 51.11 yd
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