The absolute maximum of f(x) = 4x / (x² + 1) on the interval [-4,0] occurs at x = 2 and the absolute minimum occurs at x = -4.
To find the absolute extrema, we first find the critical points by setting the derivative of f(x) equal to zero:
f'(x) = (4(x² + 1) - 8x²) / (x² + 1)² = 0
Simplifying, we get:
4 - 4x² = 0
x² = 1
x = ±1
Since x = -4 and x = 0 are also endpoints of the interval, we evaluate f(x) at these five points:
f(-4) = -8/17
f(-1) = -4/5
f(0) = 0
f(1) = 4/5
f(2) = 8/5
Thus, the absolute maximum occurs at x = 2, where f(x) = 8/5, and the absolute minimum occurs at x = -4, where f(x) = -8/17.
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In δmno, m = 540 inches, n = 330 inches and o=600 inches. find the measure of ∠o to the nearest 10th of a degree
The measure of ∠O in ΔMNO is approximately 41.5°.
To find the measure of ∠O, we can use the Law of Cosines in ΔMNO, with sides M = 540 inches, N = 330 inches, and O = 600 inches. The Law of Cosines states:
O² = M² + N² - 2MN * cos(∠O)
Rearrange the equation to solve for cos(∠O):
cos(∠O) = (M² + N² - O²) / (2MN)
Substitute the values:
cos(∠O) = (540² + 330² - 600²) / (2 * 540 * 330)
cos(∠O) ≈ -0.7944
Now, find the angle using the inverse cosine function:
∠O ≈ arccos(-0.7944) ≈ 141.5°
Since ∠O is an obtuse angle, we need to find its supplement to the nearest 10th:
180° - 141.5° ≈ 38.5°
Thus, the measure of ∠O is approximately 38.5°.
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In the figure, AABC and ADEF are similar. what’s the scale factor from AABC to ADEF?
Answer:
3
Step-by-step explanation:
We can see that in figure ABC, line segment AB is 5 ft.
We can also see that in figure DEF, line segment DE is 15 ft.
How did we get from 5 to 15?
We multiplied by 3, so the scale factor is 3.
Hope this helps! :)
1.2.1 determine this family's annual medical aid tax credit,
(3)
1.2.2 this amount is deducted from annual tax payable. calculate this
family's monthly income tax after this tax credit
determine the zulu family's actual percentage tax paid of their monthly
.
taxable income.
(3)
[18]
2:
value added tax (vat)
15% vat is payable on all goods and services, except for sanitary pads, fresh
produce and a few other staple food items. we will assume that 1.0% of
To determine this family's annual medical aid tax credit, we need to consider their medical aid expenses for the year. Medical aid expenses are expenses related to medical services that are not covered by the government or medical insurance.
This family can claim a tax credit of up to R310 per month for the main member and the first dependent, and R209 per month for each additional dependent. This tax credit is only applicable to registered medical schemes and is deducted from the tax payable.
In addition to medical aid expenses, this family will also need to consider the 15% VAT payable on all goods and services, except for sanitary pads, fresh produce, and a few other staple food items. This means that if this family spends R10,000 on goods and services, they will need to pay an additional R1,500 in VAT.
However, the good news is that they won't have to pay VAT on their fresh produce and staple food items. This will help to reduce their overall expenditure on food, which is an essential expense for every family.
In conclusion, while this family will need to pay VAT on most goods and services, they can claim a tax credit for their medical aid expenses. Additionally, they won't have to pay VAT on fresh produce and staple food items, which will help to reduce their overall food expenditure.
By carefully managing their expenses and taking advantage of tax credits and exemptions, this family can ensure that they are able to provide for their essential needs while also managing their financial obligations.
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PLEASE HELP! The graph of a rational function is shown below. Write the equation that represents this function.
THANK YOU.
Based on the following observations, we can write the equation of the rational function as: f(x) = (x + 1)/(x - 1)
What is rational function?A rational function is a type of mathematical function that is defined as the ratio of two polynomial functions.
In other words, it is a function that can be expressed as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) is not the zero polynomial.
To find the equation of the rational function represented by the given graph, we need to analyze the behavior of the graph and identify its key features. given below are the steps:
Look at the behavior of graph as x approaches infinity and negative infinity. The graph appears to have horizontal asymptotes at y = -1 and y = 1. This suggests that the function has a degree of 1 in both the numerator and denominator.
Identify any vertical asymptotes. The graph have vertical asymptote at x = 1. This suggests that the denominator of the function has a factor of (x - 1).
Look for any x-intercepts or y-intercepts.The graph's x-intercept and y-intercept are both at x = -1 and 1, respectively. This suggests that the numerator of the function has a factor of (x + 1) and that the function has a constant term of 1 in the numerator.
This function has a degree of 1 in both the numerator and denominator, a vertical asymptote at x = 1, and horizontal asymptotes at y = -1 and y = 1. It also has an x-intercept at x = -1 and a y-intercept at y = 1, which match the features of the graph given.
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An exponential function is given by the equation y=3x. Using the points x and x+1, show that the y-values increase by a factor of 3 between any two points separated by x2−x1=1. (4 points)
The given exponential function satisfies the property of increasing by a factor of 3 between any two points separated by x2−x1=1.
An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is any real number. The base a is typically a number greater than 1, and the function grows or decays rapidly depending on whether a is greater than or less than 1.
Exponential functions are commonly used to model processes that exhibit exponential growth or decay, such as population growth, radioactive decay, and compound interest. They also arise in various areas of mathematics and science, including calculus, probability theory, and physics.
We are given the exponential function [tex]y=3^x.[/tex]
Let x1 be any value of x, then the corresponding y-value is [tex]y1=3^{(x_1)[/tex]
Let x2=x1+1 be the next value of x, then the corresponding y-value is [tex]y2=3^x2=3^(x1+1)=3*3^x1.[/tex]
So, we can see that y2 is 3 times y1, which means the y-values increase by a factor of 3 between any two points separated by x2−x1=1.
Therefore, the given exponential function satisfies the property of increasing by a factor of 3 between any two points separated by x2−x1=1.
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I NEED HELP ON THIS ASAP!! PLEASE, IT'S DUE TODAY!!!! I WILL GIVE BRAINLIEST!
Step-by-step explanation:
A, 7^(x+3) = 823, 543
7^(x+3) = 823, 543
7^(x+3) = 7^7 ....... write in the power form which it's base must be 7 in order to equalify the power
x+3 = 7
x = 4
B, 4^ -4x = 4^-8
4 ^ -4x = 1/65, 536
4^ -4x = 1/4^8 ........ write in the power form
4^ -4x = 4^-8
-4x = -8 ..... write equality among the power cause it's base is same
x=2
C, 1/(6^(x-5) ) = 1296
1/(6^(x-5) ) = 1296
6^-(x-5) = 1296
6^-(x-5) = 6^4........ write in the power form
-(x-5) = 4
-x + 5 = 4
-x = -11
x = 1
D, 1/3^x+7 = 1/243
1/3^x+7 = 1/243
3 ^ -(x+7) = 3^-5 .... write in the power form
-(x+7) = -5
-x-7 = -5
-x = 2
x= -2
Find the direction angles of the vector. (Round your answers to one decimal place.)
u = (-1, 9, -6)
The direction angles of the vector u = (-1, 9, -6) are approximately -6.1°, 64.8°, and -75.2° for the x, y, and z axes, respectively.
The direction angles of a vector are the angles that the vector makes with the positive x, y, and z axes. To find the direction angles of the vector u = (-1, 9, -6), we can use the formulas:
cosθx = u_x/||u||, cosθy = u_y/||u||, and cosθz = u_z/||u||
where θx, θy, and θz are the angles that u makes with the x, y, and z axes, respectively, and ||u|| is the magnitude of u, given by:
||u|| = √(u_x² + u_y² + u_z²)
Substituting the values of u, we have:
||u|| = √((-1)² + 9² + (-6)²) = √118
cosθx = -1/√118 ≈ -0.183, cosθy = 9/√118 ≈ 0.551, and cosθz = -6/√118 ≈ -0.366
Taking the inverse cosine of each of these values, we get:
θx ≈ -6.1°, θy ≈ 64.8°, and θz ≈ -75.2°
Therefore, the direction angles of the vector u are approximately -6.1°, 64.8°, and -75.2° for the x, y, and z axes, respectively.
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Given that quadrilateral PQRS is a parallelogram, how can you prove that it is also a rectangle?
A. Use the distance formula to find the length of both diagonals to see if they are congruent.
B. Find the slopes of all sides to determine if the angles are right angles.
C. Both A and B are valid.
D. None of these
Given that quadrilateral PQRS is a parallelogram, you can prove that it is also a rectangle by A: Use the distance formula to find the length of both diagonals to see if they are congruent and B: Find the slopes of all sides to determine if the angles are right angles. Therefore, the correct option is C: C. Both A and B are valid.
To prove that PQRS is a rectangle, we need to show that all angles are right angles.
Option A: Using the distance formula, we can find the lengths of both diagonals, PR and QS. If PR and QS are congruent, then we know that opposite sides of the parallelogram are congruent and parallel (since PQRS is a parallelogram). If we can also show that PR and QS intersect at a 90-degree angle, then we have proven that PQRS is a rectangle.
Option B: Finding the slopes of all sides can help us determine if the angles are right angles. If the product of the slopes of adjacent sides is -1, then we know that the sides are perpendicular (since the slope of a line perpendicular to another line is the negative reciprocal of its slope). If we can show that all adjacent sides have slopes that multiply to -1, then we have proven that PQRS is a rectangle.
Both options A and B can be used to prove that PQRS is a rectangle, so the correct answer is C.
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I Need Help quick please look at the photo, and the table you have to figure out if the numbers in the table represent a linear, quadratic, or a exponential function and you have to write the function that models the data in the time. And if anyone helps me give me the correct answer please and thank you
Answer:
The data in the table represent an exponential function.
[tex]y = 2( {3}^{x} )[/tex]
In a major urban area, the percentage of male drivers between the ages of 19 and 29 who did not regularly use their seatbealts was 28%
(a) Identifying the population, parameter, sample, and statistic for a study on the percentage of male drivers between the ages of 19 and 29 who did not regularly use seatbelts before and after a campaign.
(b) Stating the null and alternative hypotheses for a significance test on whether the percentage of male drivers not using seatbelts has decreased after the campaign.
(a) Population: All male drivers between the ages of 19 and 29 in the major urban area.
Parameter: The percentage of male drivers between the ages of 19 and 29 in the major urban area who do not regularly use seatbelts after the radio and television campaign and stricter enforcement by the local police.
Sample: 100 male drivers between the ages of 19 and 29 who were polled.
Statistic: The percentage of male drivers between the ages of 19 and 29 in the sample who did not wear their seatbelts, which is 24%.
(b) The null hypothesis is that the percentage of male drivers between the ages of 19 and 29 who do not regularly use seatbelts in the major urban area has not decreased after the radio and television campaign and stricter enforcement by the local police.
The alternative hypothesis is that the percentage of male drivers between the ages of 19 and 29 who do not regularly use seatbelts in the major urban area has decreased after the radio and television campaign and stricter enforcement by the local police.
Mathematically, the hypotheses can be stated as follows:
H0: p >= 0.28
Ha: p < 0.28
where p is the proportion of male drivers between the ages of 19 and 29 who do not regularly use seatbelts in the major urban area after the radio and television campaign and stricter enforcement by the local police.
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The question is -
In a major urban area, the percentage of male drivers between the ages of 19 and 29 who did not regularly use seatbelts was 28%. After a major radio and television campaign and stricter enforcement by the local police, researchers want to know if the percentage of male drivers between the ages of 19 and 29 who did not regularly use seatbelts has decreased. They polled a random sample of 100 males between the ages of 19 and 29 and find the percentage who didn’t wear their seatbelts was 24%.
(a) Identify the population, parameter, sample, and statistic.
(b) State appropriate hypotheses for performing a significance test.
Find the volume of the largest right cylinder that fits in a sphere of radius 4
The volume of the largest right cylinder that fits in a sphere of radius 4 is 128π cubic units.
How to find the volume?To find the volume, we need to understand that the cylinder that fits inside a sphere will have its height (h) equal to the diameter of the sphere (2r), and the cylinder's radius (r') will also be equal to the sphere's radius (r).
We can use the formula for the volume of a cylinder: V = π[tex]r^2^h[/tex], where π is pi (approximately 3.14), r is the radius, and h is the height.
Since the cylinder's height is equal to the sphere's diameter, which is 2r, the height of the cylinder is 2r. Therefore, we can write the volume of the cylinder as:
V = πr²(2r)
Simplifying this expression, we get:
V = 2π[tex]r^3[/tex]
To find the maximum volume of the cylinder that fits inside a sphere of radius 4, we need to maximize the volume by finding the maximum value of r. Since the radius of the cylinder is equal to the radius of the sphere, we have:
r = 4
Substituting this value into the formula for the volume of the cylinder, we get:
V = 2π[tex](4)^3[/tex]
V = 128π
Therefore, the volume of the largest right cylinder that fits in a sphere of radius 4 is 128π cubic units.
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Q4 (6 points) Use Mean value theorem to prove va + 3 1. Using methods other than the Mean Value Theorem will yield no marks. (Show all reasoning). Hint: Choose a > 1 and apply MVT to f(x) = V6x +3 - x - 2 on the interval [1.a) +
Using the Mean Value Theorem, we have proven that √(6a+3) < a + 2 for all a > 1.
To prove √(6a+3) <a + 2 for all a > 1 using the Mean Value Theorem, we will begin by defining a function f(x) as:
f(x) = √(6x+3)
We can see that f(x) is a continuous and differentiable function for all x > -1/2.
Now, let's choose two values of a, such that a > 1 and b = a + h, where h is a positive number. By the Mean Value Theorem, there exists a value c between a and b such that
f(b) - f(a) = f'(c)(b-a)
where f'(c) is the derivative of f(x) evaluated at c.
Now, let's evaluate the derivative of f(x) as:
f'(x) = 3/(√(6x+3))
Thus, we can write
f(b) - f(a) = f'(c)(b-a)
√(6(a+h)+3) - √(6a+3) = f'(c)h
Dividing both sides by h and taking the limit as h → 0, we get
lim h→0 (√(6(a+h)+3) - √(6a+3))/h = f'(a)
Now, we can evaluate the limit on the left-hand side using L'Hopital's rule
lim h→0 (√(6(a+h)+3) - √(6a+3))/h = lim h→0 [3/(√(6(a+h)+3)) - 3/(√(6a+3))] = 3/(2√(6a+3))
Therefore, we have
f'(a) = 3/(2√(6a+3))
Now, we can use this value to rewrite the inequality as
√(6a+3) - (a + 2) < 0
Multiplying both sides by 2√(6a+3) and simplifying, we get
3 < 4a + 2√(6a+3)
Subtracting 4a from both sides and squaring, we get
9 < 16a^2 + 16a + 24a + 12
Simplifying, we get
0 < 16a^2 + 40a + 3
This inequality holds for all a > 1, so we have proved that
√(6a+3) < a + 2 for all a > 1.
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The given question is incomplete, the complete question is:
Use Mean value theorem to prove √(6a+3) <a + 2 for all a > 1. Using methods other than the Mean Value Theorem will yield
The target to the right is in your backyard. What is the probability of hitting the bulls eye (center circle) when you shoot an arrow? The radius of the bulls eye is 2ft and the radius of the target is 6ft. (Use 3. 14 for pi)
The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.
Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.
The area of the bull's eye can be calculated as follows:
Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet
The area of the entire target can be calculated as follows:
Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet
Therefore, the probability of hitting the bull's eye can be calculated as:
Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%
So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.
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a = 10 m, b = 6 m and c = 9 m for the triangle shown below.
Work out the value of x rounded to 1 d.p.
In the given diagram, the value of x in the right triangle is approximately 14.7
Solving right triangles: Calculating the value of xFrom the question, we are to calculate the value of x in the given diagram.
In the given diagram, we have two right triangles.
First, we will calculate the value of the side joining the two triangles.
Let the side joining the two triangles be d
Thus,
From the Pythagorean theorem, we can write that
d² = a² + b²
d² = 10² + 6²
d² = 100 + 36
d² = 136
Now, in the other triangle
Also, using the Pythagorean theorem, we can write that
x² = c² + d²
x² = 9² + 136
x² = 81 + 136
x² = 217
x = √217
x = 14.7309
x ≈ 14.7
Hence, the value of x is approximately 14.7
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A positive integer is 40 more than 29 times another. Their product is 10116 . Find the two integers.
A positive integer is 40 more than 29 times another. Their product is 10116 these two integers are 19 and 571.
In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers can be used to represent quantities such as counting numbers, temperatures, or scores in a game.
How to determine the two integers?Let's call the two integers x and y, where x is the larger integer and y is the smaller integer.
From the problem, we know that:
x = 29y + 40 (equation 1)
xy = 10116 (equation 2)
We can substitute equation 1 into equation 2 to get:
(29y + 40)y = 10116
Expanding and simplifying:
29[tex]y^{2}[/tex]+ 40y - 10116 = 0
We can use the quadratic formula to solve for y:
y = (-40 ± √([tex]40^{2}[/tex] - 429(-10116))) / (2×29)
y = (-40 ± √308576) / 58
y ≈ 18.95 or y ≈ -12.3
Since y is a positive integer, we can round up to 19.
Now we can use equation 1 to find x:
x = 29y + 40
x = 29(19) + 40
x = 571
Therefore, the two integers are 19 and 571.
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At a large university, 15% of students are left-handed. A psychology professor selects a random sample of 10 students and records L = the number of left-handed students in the sample. Starting on line 1 of the random-number table, how many left-handed students occur in the first trial of the simulation if we let 00-14 represent left-handed students?
The number of left-handed students in the first trial of the simulation can be found by following the above steps and counting the occurrences of two-digit numbers within the 00-14 range on line 1 of the random-number table.
To find out how many left-handed students occur in the first trial of the simulation, you'll need to follow these steps,
1. Identify the probability range for left-handed students, which is 00-14 as you've mentioned.
2. Start on line 1 of the random-number table.
3. Read each two-digit number on the line and check if it falls within the range 00-14.
4. Count the number of times a number within the 00-14 range appears in the first 10 two-digit numbers (since you're selecting a random sample of 10 students).
5. The count of numbers within the 00-14 range represents the number of left-handed students in the first trial of the simulation.
By doing the aforementioned processes and counting the occurrences of two-digit numbers between the ranges of 00 and 14 on line 1 of the random-number table, it is possible to determine the number of left-handed pupils in the simulation's first trial.
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HELP ME UNDERSTAND THIS
The estimated areas of each curve are listed below:
Case 1: A = 12.75
Case 2: A = 12.5
How to estimate the area of the function by use of rectangles and triangles
In this problem we must estimate the area above the x-axis and under a curve by using sums of rectangles and triangles according to the following expression:
A = {∑ [MIN (f(xₙ₋₁), f(xₙ))] + 0.5 · ∑ [MAX (f(xₙ₋₁), f(xₙ)) - MIN (f(xₙ₋₁), f(xₙ))]} · Δx, for n = {1, 2, 3, ..., N}
Where:
A - AreaN - Number of blocks.Case 1
A = (3.5 + 3.5 + 1.5) · 1 + 0.5 · (3.5 + 0.75 + 0.75 + 2 + 1.5) · 1
A = 8.5 + 0.5 · 8.5
A = 12.75
Case 2
A = (1 + 3 + 4) · 1 + 0.5 · (1 + 2 + 1.5 + 0.5 + 4) · 1
A = 8 + 4.5
A = 12.5
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I Need help with this problem
Lori went to the grocery store and bought 7 1/2 of a pounds of vegetables. Kale made up 1⁄5 of Lori's vegetables. How many pounds of kale did Lori buy?
The amount in pounds of kale Lori bought is 1 1/2 pounds.
To find out how many pounds of kale Lori bought, you need to multiply the total weight of the vegetables by the fraction that represents the proportion of kale.
In this case, you can calculate the amount of kale as follows:
(7 1/2) * (1/5)
First, convert the mixed number 7 1/2 to an improper fraction:
(7 * 2 + 1) / 2 = 15/2
Now multiply the two fractions:
(15/2) * (1/5)
Multiply the numerators together and the denominators together:
(15 * 1) / (2 * 5) = 15 / 10
Now, simplify the fraction:
15 ÷ 5 / 10 ÷ 5 = 3 / 2
So, Lori bought 3/2 or 1 1/2 pounds of kale from the grocery store. This means that out of the total 7 1/2 pounds of vegetables she purchased, 1 1/2 pounds were kale.
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HELP (100 POINTS AND BRAINLIEST)
Answer:
Using the Distance Formula:
EG =√((-a - b)^2) + (0 - c)^2)
=√((a + b)^2 + c^2)
FH =√((-b - a)^2 + (c - 0)^2)
=√((a + b)^2 + c^2)
So EG = FH.
The sum of the numerator and denominator of the fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.
Let the fraction be x/y.
We know that x + y = 12, and that (x) / (y + 3) = 12.
Multiplying both sides of the second equation by (y + 3), we get:
x = 12(y + 3)
Substituting this into the first equation, we get:
12(y + 3) + y = 12
Expanding and simplifying, we get:
13y + 36 = 12
Subtracting 36 from both sides, we get:
13y = -24
Dividing both sides by 13, we get:
y = -24/13
Substituting this value of y into the equation x + y = 12, we get:
x - 24/13 = 12
Multiplying both sides by 13, we get:
13x - 24 = 156
Adding 24 to both sides, we get:
13x = 180
Dividing both sides by 13, we get:
x = 180/13
Therefore, the fraction is 180/13 divided by -24/13, which simplifies to -15/2.
Evaluate the limit using L'Hospital's rule
lim (e^x + 2x - 1)/2x
To evaluate the limit using L'Hospital's rule, we need to take the derivative of both the numerator and denominator separately until we get a determinate form. We have:
lim (e^x + 2x - 1) / (2x)
Taking the derivative of the numerator:
lim (e^x + 2) / 2
Taking the derivative of the denominator:
lim 2
Since we now have a determinate form, we can evaluate the limit by plugging in the value of x. We get:
(e^x + 2) / 2
As x approaches infinity, e^x also approaches infinity, so the limit diverges to positive infinity. Therefore, the limit does not exist.
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Jaleesa deposited $4,000 in an account that pays 4% interest compounded annually. Which expression can be used to find the value of her investment at the end of 6 years?
4,000. Times 1. 4. Times 6.
4,000. Times. 0. 4. To the sixth power.
4,000. Times. 1. 4. To the sixth power.
4,000. Plus. 4,000. Times 0. 4. Times. 6
The correct expression is 4,000 times. 1. 4 to the sixth power.
The formula for the future value of an investment with annual compounding interest is:
A = P(1 + r)ⁿ
A = future value
P = principal amount
r = annual interest rate expressed as a decimal
n = number of years.
In this case, Jaleesa deposited $4,000 at an annual interest rate of 4% (0.04 as a decimal) and the investment is compounded annually for 6 years. So the expression that can be used to find the value of her investment at the end of 6 years is:
A = 4,000(1 + 0.04)⁶
Simplifying the expression, we get:
A = 4,000(1.04)⁶
Therefore, the correct expression is 4,000 times. 1. 4 to the sixth power.
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3. Represent and Connect A jar has 20 marbles: 6 black, 4 brown, 8 white, and 2 blue. Julie draw
a marble from the jar.
a. What is the sample space?
b. What is the probability Julie will draw a white marble?
c. Which is more likely to happen, drawing a black marble or drawing either a brown
or blue marble?
d. Using this jar of marbles, what event has a probability of 0?
The event that has a probability of 0 is selecting a yellow marble
Other probabilities are listed below
Identifying the sample space and the probabilitiesThe items in the jar are given as
6 black, 4 brown, 8 white, and 2 blue.
These items are the sample space of this event
Hence, the sample space is 6 black, 4 brown, 8 white, and 2 blue.
For the probability Julie will draw a white marble, we have
P(White) = White/Total
So, we have
P(White) = 8/20
Simplify
P(White) = 2/5
For the event that is more likely to happen, we have
P(black marble) = 6/20
P(brown or blue marble) = (4 + 2)/20
P(brown or blue marble) = 6/20
The probabilities are equal
So, both events have equal likelihood
The event that has a probability of 0 could be the probability of selecting a yellow marble
This is because the jar has no yellow marble
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This graph represents a quadratic function. The graph shows a downward parabola vertex at (0, 9) and passes through (minus 4, minus 7), (minus 3, 0), (3, 0), and (4, minus 7). What is the value of a in this function’s equation? A. 2 B. 1 C. -1 D. -2
Answer:
Based on the given information, we can conclude that the graph represents a quadratic function. The vertex of the parabola is located at (0, 9) and the function passes through several points including (-4, -7), (-3, 0), (3, 0), and (4, -7).
To find the equation of the function, we need to determine the value of "a" in the equation f(x) = ax^2 + bx + c. Since the vertex is located at (0, 9), we know that the x-coordinate of the vertex is 0. Therefore, we can use the vertex form of the equation, which is f(x) = a(x - 0)^2 + 9, or simply f(x) = ax^2 + 9.
Next, we can use one of the given points to solve for "a". Let's use the point (-3, 0).
0 = a(-3)^2 + 9
0 = 9a - 9
9 = 9a
a = 1
Therefore, the value of "a" in the equation of the function is B. 1.
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A cable rigging must be run from the ground through the top of a guidepost 10 feet high, and continue in a straight line to the face of a building that stands 20 feet from the post along the ground.
(a) How high up the building should the cable be attached if the area of the right triangle formed by the cable, ground, and building is to be minimized?
(b) If the length of the cable is to be minimized, what angle θ should it make with the face of the building?
(a) To minimize the area of the right triangle formed by the cable, ground, and building, we need to minimize the length of the cable. To do this, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the cable, a is the distance from the guidepost to the point where the cable is attached to the building, and b is the distance from that point to the ground.
Since we want to minimize c, we can differentiate the equation with respect to a and set the derivative equal to zero:
dc/da = 2a/c = 0
Solving for a, we get a = c/2. This means that the point where the cable is attached to the building should be halfway up the building, or 10 feet high.
(b) To minimize the length of the cable, we can use the principle of least action, which states that the path taken by the cable is the one that minimizes the integral of the tension along the cable.
Assuming that the tension in the cable is constant, we can use the law of sines to find the angle θ:
sin θ / 20 = sin (90° - θ) / c
where c is the length of the cable.
We want to minimize c, so we can differentiate the equation with respect to θ and set the derivative equal to zero:
d(c)/d(θ) = -20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * dc/d(θ) = 0
Solving for dc/d(θ), we get:
dc/d(θ) = 20c * tan(θ)
Substituting this into the original equation, we get:
-20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * 20c * tan(θ) = 0
Simplifying, we get:
cos(θ) / sin(θ) = tan(θ)
Solving for θ, we get:
θ = 45°
Therefore, to minimize the length of the cable, it should make an angle of 45° with the face of the building.
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A professional athlete wants to tile his bedroom in solid gold. Each square tile will be 16
inches long and 1/4 inches thick. If the density of gold is 11. 17 ounces per cubic inch and
the price of gold is $1,303. 80 per ounce, how much will each tile cost? Round your
answer is the nearest dollar.
To calculate the cost of each tile, we need to first determine the volume of each tile. The length and width of the tile are given as 16 inches, and the thickness is given as 1/4 inches, which can be converted to 0.25 inches. Therefore, the volume of each tile is 16 x 16 x 0.25 = 64 cubic inches.
Next, we need to determine the weight of gold in each tile. Since the density of gold is 11.17 ounces per cubic inch, the weight of gold in each tile is 64 x 11.17 = 715.68 ounces.
Finally, we can calculate the cost of each tile by multiplying the weight of gold by the price of gold per ounce. The price of gold is given as $1,303.80 per ounce, so the cost of each tile is 715.68 x $1,303.80 = $933,526.78. Rounded to the nearest dollar, each tile will cost $933,527.
In summary, each square tile made of solid gold and measuring 16 inches long and 1/4 inches thick will cost approximately $933,527. This cost is based on the density of gold, which is 11.17 ounces per cubic inch, and the price of gold, which is $1,303.80 per ounce.
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Ben is 140 cm tall. Fareed is 1090 mm tall. Who is taller? How much taller?
Answer:
Ben is 31 cm taller
Step-by-step explanation:
1090mm is 109 cm
Subtract Fareeds height from Bens:
140-109=31
Hope this helps!
PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
AngleSideSide because it's bad
but also, if you had an angle, a side and a side
For your example: let's say CD≅AS
You could change the angle of S or D and the parameters of the triangle would still be true. Because you can change something and still have AngleSideSide be true, would make them not congruent any more.
11. April shoots an arrow upward at a speed
of 80 feet per second from a platform 25
feet high. The pathway of the arrow can
be represented by the equation h =-
16t2 + 80t + 25, where h is the height
and t is the time in seconds. What is the
maximum height of the arrow? [3]
The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.
The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.
To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.
To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.
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