The hypothetical value of the sum of the geometric series is 1
How to determine the hypothetical value of the progressionThe first term that we have in this progression is given as 1/2. Next we have to find the common ratio that lies between the values.
The sum of the infinite geometric series can be gotten by
a / (1 -r)
where a is the first term in the series = 1/2
r is the common ratio of the progression = 1/2
we would have to input the values. such that we would have:
1/2 / (1- 1/2)
(1/2) / (1/2)
= 1
The sum of the series is 1.
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100 POINTS PLEASE HELP!!!
The coordinate plane below represents a community. Points A through F are houses in the community.
graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.
Part A: Using the graph above, create a system of inequalities that only contains points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (7 points)
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A. (5 points)
Part C: Erica wants to live in the area defined by y < 7x − 4. Explain how you can identify the houses in which Erica is interested in living. (2 points)
Answer:
[tex]\sf A) \quad \begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}[/tex]
B) see below
C) points C, E and F
Step-by-step explanation:
Given points:
A = (-5, 5)B = (-4, -2)C = (2, 1)D = (-2, 4)E = (2, 4)F = (3, -4)Part AA system of inequalities is a set of two or more inequalities in one or more variables.
To create a system of inequalities that only contains C and F in the overlapping shaded region, create a linear equation where points C, F and E are to the right of the line and a linear equation where points C, F, A, B and D are to the left of the line.
The easiest way to do this is to find the slope of the line that passes through points C and F, then add values to move the lines either side of the points.
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{y_F-y_C}{x_F-x_C}=\dfrac{-4-1}{3-2}=-5[/tex]
Therefore:
[tex]\sf y = -5x + 5[/tex] → points C, F and E are to the right of the line.
[tex]\sf y=-5x+12[/tex] → points C, F, A, B and D are the left of the line.
Therefore, the system of inequalities that only contains points C and F in the overlapping shaded regions is:
[tex]\begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}[/tex]
To graph the system of inequalities:
Plot 2 points on each of the lines.Draw a dashed line through each pairs of points.Shade the intersected region that is above the line y > -5x + 5 and below the line y < -5x + 12.Part BTo verify that the points C and F are solutions to the system of inequalities created in Part A, substitute the x-values of both points into the system of inequalities. If the y-values satisfy both inequalities, then the points are solutions to the system.
Point C (2, 1)
[tex]\implies \sf x=2 \implies 1 > -5(2)+5 \implies 1 > -5\quad verified[/tex]
[tex]\implies \sf x=2 \implies 1 < -5(2)+12\implies 1 < 2 \quad verified[/tex]
Point F (3, -4)
[tex]\implies \sf x=3 \implies -4 > -5(3)+5 \implies -4 > -10\quad verified[/tex]
[tex]\implies \sf x=3 \implies -4 < -5(3)+12\implies -4 < -3 \quad verified[/tex]
Part CMethod 1
Graph the line y = 7x - 4 (making the line dashed since it is y < 7x - 4).
Shade below the dashed line.
Points that are contained in the shaded region are the houses in which Erica is interested in living: points C, E and F.
Method 2
Substitute the x-value of each point into the given inequality y < 7x - 4.
Any point where the y-value satisfies the inequality is a house that Erica is interested in living.
[tex]\sf Point\: A: \quad x=-5 \implies 5 < 7(-5)-4 \implies -5 < -39 \implies no[/tex]
[tex]\sf Point\: B: \quad x=-4 \implies -2 < 7(-4)-4 \implies -2 < -32 \implies no[/tex]
[tex]\sf Point\: C: \quad x=2 \implies 1 < 7(2)-4 \implies 1 < 10 \implies yes[/tex]
[tex]\sf Point\: D: \quad x=-2 \implies 4 < 7(-2)-4 \implies 4 < -18 \implies no[/tex]
[tex]\sf Point\: E: \quad x=2 \implies 4 < 7(2)-4 \implies 4 < 10 \implies yes[/tex]
[tex]\sf Point\: F: \quad x=3 \implies -4 < 7(3)-4 \implies -4 < 17 \implies yes[/tex]
Tatiana has a special puzzle in which all of the pieces fit together in any way. There is no goal picture. Instead, the goal of the puzzle is to make different patterns and pictures using the pieces. If Tatiana has 50 unique puzzle pieces and she plans to use all of them, how many possible pictures can she create
It is an example of Permutation without repetition.
To find the number of pictures can create.
what is permutation and combination?An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.
Given that:
50 unique pieces of puzzle
Use them all to solve puzzle
No repetition is allowed therefore
Since no repetition is allowed because all puzzle pieces are required to be used.
Therefore each of the 50 pieces can be used max one time
Therefore if we start with piece like this " 1 2 3 .. up to ... 50 " it is one combination
Another could be "2 1 3 .. up to .. 50" or "3 1 2 .. up to 50" and so on
So we see that we can see that we can select the first piece in 50 ways 49 left which could be selected for second piece then 48, 47 respectively
Therefore 50X49X48X47X46X....X1 = 50!
Hence, It is an example of Permutation without repetition.
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Option is missing
A. Combination with repetition
B. Permutation with repetition
C. Combination without repetition
D. Permutation without repetition
A group of 18 patrons each owe $15 at a restaurant. What is the total amount owed by all 18 customers?
Answer:
$270
Step-by-step explanation:
18x15=$270
HOPE THAT HELPED:)
Please help me it would mean a lot!! due right now. Please show work thank youuuu
Answer:
area of A'B'C'D' = 18.4 units²
Step-by-step explanation:
given 2 similar figures with
ratio of corresponding sides = a : b , then
ratio of areas = a² : b²
here ratio of sides = 5 : 2
ratio of areas = 5² : 2² = 25 : 4
let x be the area of A'B'C'D' , then by proportion
[tex]\frac{25}{115}[/tex] = [tex]\frac{4}{x}[/tex] ( cross- multiply )
25x = 460 ( divide both sides by 25 )
x = 18.4
area of A'B'C'D' = 18.4 units²
Write [tex]sec^2x[/tex] in two equivalent forms
The two equivalent forms of [tex]sec^2x[/tex] are [tex]\frac{1}{cos^2x}[/tex] and [tex]1+tan^2x[/tex]
Equivalent forms forms of trigonometric expressionsThe given trigonometric expression is:
[tex]sec^2x[/tex]
Note that:
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
Substitute this equivalence to the given expression
[tex]sec^2(x)=\frac{1}{cos^2(x)}[/tex]
Also from [tex]cos^2(x)+sin^2(x)=1[/tex]
Divide through by [tex]cos^2x[/tex]
[tex]\frac{cos^2x}{cos^2x} +\frac{sin^2x}{cos^2x}=\frac{1}{sin^2x}[/tex]
Simplifying the resulting expression:
[tex]1+tan^2x=sec^2x\\\\sec^2x=1+tan^2x[/tex]
Therefore, the two equivalent forms of [tex]sec^2x[/tex] are [tex]\frac{1}{cos^2x}[/tex] and [tex]1+tan^2x[/tex]
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Light travels at a speed of approximately Light travels at a speed of approximately 1,000,000,000 kilometers per second (621,118,012 miles per second). 80,500 kilometers per hour (50,000 mph). 300,000 kilometers per hour (186,336 mph). 300,000 kilometers per second (186,333 miles per second).
The speed of light is 300,000 kilometers per hour. hence option c is correct.
According to the statement
we have to explain that the by how much speed the light travels.
So, Firstly
Light is the natural agent that stimulates sight and makes things visible.
and speed of light means that the distance covered by the light with respect to time.
So, it means those distance which is covered by the light with respect to time is called the speed of light.
The speed of light is measures in km, meters and in other units also.
And we can calculate the speed of light per hour or per minute or in other time measurements.
So, The speed of light is 300,000 kilometers per hour. hence option c is correct.
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Fatima wants to find the value of sine theta, given cotangent theta = four-sevenths. which identity would be best for fatima to use? cosine theta = startfraction 1 over secant theta endfraction sine squared theta cosine squared theta = 1 cosecant theta = startfraction r over y endfraction
Answer:
Step-by-step explanation:
From the right triangle with cot theta = 4/7 = (adjacent side / opposite side), Fatima can find the length of the hypotenuse using Pythagoras. This gives a value of 8.0823. So cos theta = 4 / 8.0823 = 0,49614,
Then she could find the values of sin theta using
sine squared theta + cos squared theta = 1.
Answer: its D or 1 + cotangent squared theta = cosecant squared theta
Step-by-step explanation:
Jordan is studying whether or not race affects high school graduation in utah. in this example, high school graduation is the?
The high school graduation is the dependent variable.
In this question,
Jordan is studying whether or not race affects high school graduation in utah.
A dependent variable is a variable in an expression that depends on the value of another variable. It is a variable that represents a quantity that changes based on other quantities being manipulated in an experiment. It is the variable being tested, and therefore, it is called the dependent variable.
In the above statement, the high school graduation gets affected by race. So, the the high school graduation is the dependent variable.
Hence we can conclude that the high school graduation is the dependent variable.
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Apply the distributive property to factor out the greatest common factor 15+21
The polynomial
f(x) =3x³+ 2x2 + 3x + 6
has *insert answer here*
possible rational roots.
options- 10, 14, 16, 11, 12
I keep getting 6 but that’s not an option lol
The Polynomial Roots are given as follows:
x₁=−1.2085
x₂=0.2709+1.2576i
x₃=0.2709−1.2576i
It is to be noted that the Polynomial 3x³+ 2x2 + 3x + 6 has no real rational roots that can be found using the rational root text. Hence, this was solved using the Qubic Formulas.
What are Polynomial Roots?
The roots (also known as zeroes or solutions) of a polynomial P (x) P(x) P(x) are the x values for which P (x) P(x) P(x) equals zero.
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Answer: 12
Step-by-step explanation:
I got it right
The number of pollinated flowers as a function of time in days can be represented by the function. f(x)
The average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
In the question, we are asked for the average increase in the number of flowers pollinated per day between days 4 and 10, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula {f(10) - f(4)}/{10 - 4}.
First, we find the value of the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex], for f(10) and f(4).
[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(10) = (3)^{\frac{10}{2} }\\\Rightarrow f(10) = 3^5 = 243[/tex]
[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(4) = (3)^{\frac{4}{2} }\\\Rightarrow f(10) = 3^2 = 9[/tex]
Thus, the average increase
= {f(10) - f(4)}/{10 - 4},
= (243 - 9)/(10 - 4),
= 234/6
= 39.
Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
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For complete question, refer to the attachment.
As part of your retirement planning, you purchase an annuity that pays 5.75% annual interest compounded quarterly If you make quarterly payments of $1600 how much will you have saved in 5 years? Instead, if you make quarterly payments of $800, how much will you have saved in 10 years?
Which of the following is the complete factorization of the polynomial below?
2x² +13x² +17x-12
a
jfjoydx9tdzrzfzixitxxytxixutx
what does a irrational number look like
A irrational number is a number that can't be expressed as a ratio of two whole numbers. That's it.
For examples (in increasing order of difficulty)
1 is a rational number because it is 1/1
0.75 is a rational number because it is equal to 3/4
2.333... (infinite number of digits, all equal to three) is rational because it is equal to 7/3.
sqrt(2) is not a rational number. This is not completely trivial to show but there are some relatively simple proofs of this fact. It's been known since the greek.
pi is irrational. This is much more complicated and is a result from 19th century.
As you see, there is absolutely no mention of the digits in the definition or in the proofs I presented.
Now the result that you probably hear about and wanted to remember (slightly incorrectly) is that a number is rational if and only if its decimal expansion is eventually periodic. What does it mean ?
Take, 5/700 and write it in decimal expansion. It is 0.0057142857142857.. As you can see the pattern "571428" is repeating in the the digits. That's what it means to have an eventually periodic decimal expansion. The length of the pattern can be anything, but as long as there is a repeating pattern, the number is rational and vice versa.
As a consequence, sqrt(2) does not have a periodic decimal expansion. So it has an infinite number of digits but moreover, the digits do not form any easy repeating pattern.
NEED HELP ASAP
Lucy pays $275 in advance on her account at the athletic club. Each time she uses the club, $5 is
deducted from the account. Write a linear function that gives the value remaining in her
account after x visits to the club. Find the value remaining in the account after 11 visits.
Answer:
Step-by-step explanation:
Please Help me with this problem!!! ASAP
The average rate of change is -5 per month
How to determine the average rate of change?The interval is given as:
July to December
From the graph, we have:
July = 110
December = 30
The average rate of a function over the interval (a, b) is calculated as:
Rate = [f(b) - f(a)]/[b - a]
So, we have:
Rate = (30 - 110)/(December- July)
This gives
Rate = (30 - 110)/(12 - 7)
Evaluate
Rate = -16
Hence, the average rate of change is -5 per month
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Which test represents the best choice if you wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr?
The test that represents the best choice if you wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr is one sample t-test
The purpose of the one sample t-test is to determine if a sample observations could follow a specific parameter like the mean.
This test is used to determine whether an unknown population mean is different from a specific value.
one sample t-test is used to compare the mean of a single group against that of a known mean.
We wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr
So this test (one sample t-test ) would be the best choice to compare mttr.
Therefore, the test that represents the best choice if you wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr is one sample t-test
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What is the range of function g if g (x) = f(x) + 3?
A. (3,00)
B. (-3, 3)
C. (-∞0, ∞0)
D. (-∞0, 3)
Proof : tan10 x tan20 x tan…70 x tan80=1
This follows from the identity
[tex]\cot(x) = \dfrac1{\tan(x)} = \tan(90^\circ - x)[/tex]
The overall product is 1 because
[tex]\tan(10^\circ) \tan(80^\circ) = \cot(80^\circ) \tan(80^\circ) = 1[/tex]
[tex]\tan(20^\circ) \tan(70^\circ) = \cot(70^\circ) \tan(70^\circ) = 1[/tex]
[tex]\tan(30^\circ) \tan(60^\circ) = \cot(60^\circ) \tan(60^\circ) = 1[/tex]
[tex]\tan(40^\circ) \tan(50^\circ) = \cot(50^\circ) \tan(50^\circ) = 1[/tex]
A potato was launched in the air using a potato gun. the function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each) a. what was the maximum height of the potato? b. what was the lowest height of the potato? c. what was the lowest time that applies to the actual situation? d. what is the greatest time that applied to the actual situation? e. using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? use set builder notation.
The answers to all the parts are given below.
To find the answers using a function:The height equation is:
h(t) = - 16t^2 + 100t + 10
A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.
v(t) = - 2 * 16 * t + 100 = 0
t = 100/(2*16) = 3.125s
Now we put this time in our height equation:
h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.
B) The lowest height of the potato will be h = 0ft when the potato hits the ground.
C) the lowest time that works for that function is t = 0s when the potato is fired by the gun.
D) the maximum time can be found when the potato hits the ground, after that point the equation does not work anymore, let's find it,
h(t) = 0 = -16t^2 +100t+10
we can solve it using Bhaskara's equation:
[tex]t=\frac{-100+-\sqrt{100^{2} +4*16*10} }{-2*16} =\frac{-100+-103.2}{-32}[/tex]
So the two solutions are:
t = 6.3s
t = -0.1s
We need to choose the positive time, as we already discussed that the minimum time that works for the equation is t = 0s.
so here the answer is t = 6.3s
E) the domain is 0s ≤ t ≤ 6.3s
The range is 0ft ≤ h ≤ 166.25 ft.
Therefore, the answers to all the parts are shown.
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WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
1st option
Step-by-step explanation:
let y = h(x) and rearrange making x the subject , that is
y = 6x - 6 ( add 6 to both sides )
y + 6 = 6x ( divide both sides by 6 )
[tex]\frac{y+6}{6}[/tex] = x
change y back into terms of x with x = [tex]h^{-1}[/tex] (x)
[tex]h^{-1}[/tex] (x) = [tex]\frac{x+6}{6}[/tex]
Can someone help me with these problems please!!
a.
i. In standard form y = 5x² - 20x + 27ii. The y intercept is (0, 27)iii. Find the graph in the attachmentb.
i. In standard form is y = 3x² + 6x + 15ii. The y-intercept is (0, 15)iii. Find the graph in the attachmentWhat is a quadratic function?A quadratic function is a function of the form y = ax² + bx + c
a. i. How to write the quadratic function y = 5(x - 2)² + 7 in standard form?To write y = 5(x - 2)² + 7, we expand the bracket and simplify.
So, y = 5(x - 2)² + 7
y = 5(x² - 4x + 4) + 7
y = 5x² - 20x + 20 + 7
y = 5x² - 20x + 27
So, the quadratic function y = 5(x - 2)² + 7 in standard form is y = 5x² - 20x + 27
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 5x² - 20x + 27
y(0) = 5(0)² - 20(0) + 27
y(0) = 0 - 0 + 27
y(0) = 27
The y intercept is (0, 27)
iii. The graph of y = 5(x - 2)² + 7Find the graph in the attachment
b. i. How to write the quadratic function y = 3(x + 1)² + 12 in standard form?To write y = 3(x + 1)² + 12, we expand the bracket and simplify.
So, y = 3(x + 1)² + 12
y = 3(x² + 2x + 1) + 12
y = 3x² + 6x + 3 + 12
y = 3x² + 6x + 15
So, the quadratic function y = 3(x + 1)² + 12 in standard form is y = 3x² + 6x + 15
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 3x² + 6x + 15
y(0) = 3(0)² - 6(0) + 15
y(0) = 0 - 0 + 15
y(0) = 15
The y-intercept is (0, 15)
iii. The graph of y = 3(x + 1)² + 12Find the graph in the attachment
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PLEASE HELP DUE TONIGHT
1. The time taken for the water to fall that much is 0.2 s
2. The initial speed of the water is 4 m/s
1. How to determine the time Height (h) = 20 cm = 20 / 100 = 0.2 mAcceleration due to gravity (g) = 9.8 m/s²Time (t) =?h = ½gt²
0.2 = ½ × 9.8 × t²
0.2 = 4.9 × t²
Divide both side by 4.9
t² = 0.2 / 4.9
Take the square root of both side
t = √(0.2 / 4.9)
t = 0.2 s
2. How to determine the initial speedHorizontal distance (s) = 80 cm = 80 / 100 = 0.8 mTime (t) = 0.2 sInitial speed (u) =?s = ut
Divide both sides by t
u = s / t
u = 0.8 / 0.2
u = 4 m/s
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Out of 500 people in a room, 200 of them are wearing red shirts. Of the people wearing red shirts, 15% are wearing red pants. What percentage of the people in the room are wearing both red shirts and red pants?
help me please im in a rush
Answer:
a.1
b. 17
Step-by-step explanation:
So the | | around an equation makes it an absolute value which can be defined as the "distance from zero" or in other words, if a value is positive, it stays positive, and if a value is negative, it becomes positive.
|-8 + 9| = |1| = 1
|-8| + 9 = 8 + 9 = 17
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Answer:
35449 people
Explanation:
Given equation: y = 1100.74x -1976.47
Here year '2005' represents x = 005 = 5
So, the year '2034' will represent x = 034 = 34
Insert this into equation:
y = 1100.74(34) -1976.47
y = 35448.69
y ≈ 35449 (rounded to nearest whole number)
Question 2: If you were to take a cross-section parallel to the base for one of your items, what shape would
you see? Can a cross-section be a sphere? Explain in two to three sentences.
The cross-section would be the same shape as the base. A cross-section cannot be a sphere because a cross-section must be two-dimensional, but a sphere is three-dimensional.
Porfa urgente para hoy
Si triplicamos la cantidad de cada artículo, el subtotal será de 2 940 soles, el impuesto al consumo será de 529,20 soles y el total será de 3 469,20 soles.
¿Cual es el coste total y los impuestos por cambiar la cantidad de artículos comprados?
En esta pregunta tenemos un recibo con una lista de productos, cantidades, precios unitarios y precios de compra, además de un impuesto que se aplica al consumo por concepto de los productos comprados y el total, el cual refleja tanto el subtotal como el concepto por impuestos.
En cuanto a la compra de una determinada cantidad para un artículo, el coste total respectivo es igual a producto del número de artículos por el precio unitario.
El subtotal se determina mediante la suma de los costes totales asociados a cada artículo y luego se le recarga con el impuesto al consumo. Por último, el total de compra es la suma del subtotal y los pagos tributarios.
Si triplicamos el número de cada artículo comprado, tenemos los siguientes costes para cada artículo:
Chompas de dralom
12 / 4 × 280 = 840
Chompas de Orlon
6 / 2 × 100
300
Chompas de lana de alpaca
15 / 5 × 600
1 800
El subtotal es 2 940 soles y el impuesto al consumo es 18 / 100 × 2 940 = 529,20 soles. Por tanto, el total es 3 469,20 soles.
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( will give brainlyest)
Write an expression equivalent to the following problems using the fewest number of terms. ( number 1)
Can someone help solve both of these? ASAP
Question 4
[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]
Question 5
[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]