a) Number of roots in the given polynomial is three.
b) Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}
c) The roots of the given polynomial are {2, 3i, -3i}.
Given polynomial is `P(x) = x³ - 2x² + 9x - 18`.a) Number of roots in the given polynomial is three. b) Possible rational roots of the given polynomial are expressed in the form of `p/q`, where p is a factor of the constant term `-18` and q is a factor of the leading coefficient `1`.Constant term of the given polynomial is `-18`. The factors of `-18` are 1, 2, 3, 6, 9, and 18. Leading coefficient of the given polynomial is `1`. The factors of `1` are ±1.∴ Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}.c) Let us check whether the possible rational roots satisfy the given polynomial. To check the roots, we can use synthetic division, which is an efficient method to check the roots of a polynomial. When `x = -1` is substituted in the given polynomial, we get P(-1) = (-1)³ - 2(-1)² + 9(-1) - 18= -1 + 2 - 9 - 18= -26, which is not equal to `0`.When `x = 1` is substituted in the given polynomial, we get P (1) = 1³ - 2(1)² + 9(1) - 18= 1 - 2 + 9 - 18=-10, which is not equal to `0`.
When `x = -2` is substituted in the given polynomial, we get P(-2) = (-2)³ - 2(-2)² + 9(-2) - 18= -8 + 8 - 18 - 18= -36, which is not equal to `0`.When `x = 2` is substituted in the given polynomial, we get P(2) = 2³ - 2(2)² + 9(2) - 18= 8 - 8 + 18 - 18= 0, which is equal to `0`.∴ `x = 2` is a root of the given polynomial. By using synthetic division method, we can find the remaining two roots. x - 2 | 1 - 2 9 - 18| | 2 0 18| | 1 0 9 0|Therefore, the factors of the given polynomial are `(x - 2)(x² + 9)`.The quadratic factor, `x² + 9`, does not have any real roots, as the discriminant is negative.∴ The roots of the given polynomial are {2, 3i, -3i}.
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Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?
the area of the Ferris wheel
the circumference of the Ferris wheel
the diameter of the Ferris wheel
the radius of the Ferris wheel
The amplitude οf the functiοn used tο mοdel the height οf a rider οn a Ferris wheel shοuld be equal tο the radius οf the Ferris wheel.
What is a Ferris wheel's typical height?212 feet is the average height. A 550-fοοt ferris wheel is the tallest οne. This may be fοund in Las Vegas, Nevada, and is knοwn as the high rοller.
The amplitude οf a periοdic functiοn, such as the height οf a rider οn a Ferris wheel as a functiοn οf time, is the maximum distance frοm the average οr equilibrium pοsitiοn. In this case, the average οr equilibrium pοsitiοn wοuld be the height οf the rider when the Ferris wheel is at its lοwest pοint. The distance frοm the lοwest pοint tο the highest pοint οf the Ferris wheel is equal tο the diameter, and half οf the diameter is equal tο the radius. Therefοre, the amplitude οf the functiοn shοuld be equal tο the radius οf the Ferris wheel.
The area and circumference οf the Ferris wheel are nοt directly related tο the height οf a rider as a functiοn οf time, sο they are nοt relevant tο the amplitude οf the functiοn.
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Answer: D. the radius of the Ferris wheel
Step-by-step explanation:
Which of these statements is true about the data in the scatter plot?
As x increases, y tends to increase.
As x increases, y tends to decrease.
As x increases, y tends to stay unchanged.
x and y are unrelated
The statement that correctly explains the association in the scatter plot is; A. Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.
When interpreting scatterplots, it is possible to claim that two variables have a negative connection when the values of one variable tend to fall as the values of the other variable rise.
Similarly to this, we can say that two variables have a positive connection when one variable's values tend to rise along with those of the other.
In the scatterplot shown, we can see that there is a negative correlation between the two variables because the y-value is falling while the x-axis is rising.
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I need help can y'all help me plssss
The first statement is correct, that the value of x is 55°.
The second statement is incorrect, the correct statement is the measure of the smaller angle is 35°.
What is the complementary angle?Complementary angles are those whose combined angle is exactly 90°
Part A :
The figure shows right-angled or complementary angle which means the sum of angles is 90°
Therefore we can say that,
x + x-20 = 90°
2x - 20 =90°
2x = 90° + 20
2x = 110°
x = 55°
Therefore the value of the x = 55°, the first statement correct.
The measure of the smaller angle is
= x - 20°
= 55° - 20°
= 35°
The second statement is incorrect.
The correct statement is a measure of the smaller angle is 35°.
Part B:
The figure shows the supplementary angle and the sum of the supplementary angle is 180°.
3x + 6x = 180°
9x = 180°
x = 20°
The first statement is incorrect, the correct statement is the value of x = 20.
The angle measure is 3x = 3 * 20 = 60° and 6x = 6 * 20 = 120°
This means that the second statement is correct.
Part C:
Given that the angle is complementary. the first angle is 2x and the second angle is (3x-5).
A complementary angle is the sum of the angles equal to 90°
2x + 3x-5 = 90
5x = 90 - 5
5x = 85
x = 17°
The first statement is incorrect. the correct statement is the value of x = 17.
The measure of the angle,
2x = 2 * 17 = 34
3x - 5 = 3 * 17 - 5 = 51 - 5 = 46
From the above result, second statement is also incorrect, the correct statement is the measure of the larger angle is 46°.
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Realiza la investigación de productos en una cadena de supermercados, observa cuales presentan valores con decimales, elabore una lista de 10 productos y realice diferentes operaciones de decimales con ellos, construya un problema de texto, demuestre lo que sabe de números decimales
Decimals are used to write a number that is not an integer. Decimals are numbers between integers.
The supermarket chain of Product are :
Bakery, Beverages, Non-food and pharmaceutical products (such as cigarettes, lottery tickets and over-the-counter medicines), rental of DVDs, books and magazines, including supermarket tabloids, greeting cards, toys, a small number of household items such as light bulbs, Personal care such as cosmetics, soaps, shampoos, Produce (fresh fruits and vegetables), etc.
Decimals are used together to represent whole numbers and fractions. Here we will separate whole numbers and fractions by inserting a “.”, called a decimal point. In decimal form, we write this as 1.5 pizzas.
Decimals are used to write a number that is not an integer. Decimals are numbers between integers. An example is 12.5, which is a decimal number between 12 and 13. Greater than 12, but less than 13.
Continuing with the previous example, 12.5 is the same number as the fractional 12½. This is true regardless of the complexity of the decimal point. For example, the number 0. 75 equals ¾. If you want, you can go further and say that 0.75 equals 75%.
Complete Question:
Investigate supermarket chain products, observe which products have decimals in their values, list 10 products and use them to perform different decimal operations, build a word problem and demonstrate your understanding of decimals.
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please help me, I don't know this! yes, my brain isn't braining
By secant line formula, the slopes corresponding to the lines are listed below:
m = 1 / 2 m = - 5 / 4 m = 7 / 5 m = - 2 m = 1 / 5 m = - 1 / 4 m = 3 m = - 1 / 2 m = 1 / 6How to determine the slope of a line by secant line formulaIn this problem we have nine representations of lines, whose slopes must be determined. A line is represented by equations of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slope.b - Intercept.According to analytic geometry, slope can be found by knowning the location of two points (initial, final) set on Cartesian plane and secant line formula:
m = (y₂ - y₁) / (x₂ - x₁)
Where:
m - Slope(x₁, y₁) - Coordinates of the initial point.(x₂, y₂) - Coordinates of the final point.Case 1: (x₁, y₁) = (0, - 3), (x₂, y₂) = (2, 1)
m = (2 - 0) / [1 - (- 3)]
m = 2 / 4
m = 1 / 2
Case 2: (x₁, y₁) = (- 3, 2), (x₂, y₂) = (1, - 3)
m = (- 3 - 2) / [1 - (- 3)]
m = - 5 / 4
Case 3: (x₁, y₁) = (- 3, - 4), (x₂, y₂) = (2, 3)
m = [3 - (- 4)] / [2 - (- 3)]
m = 7 / 5
Case 4: (x₁, y₁) = (0, 3), (x₂, y₂) = (3, - 3)
m = (- 3 - 3) / (3 - 0)
m = - 6 / 3
m = - 2
Case 5: (x₁, y₁) = (- 2, 1), (x₂, y₂) = (3, 2)
m = (2 - 1) / [3 - (- 2)]
m = 1 / 5
Case 6: (x₁, y₁) = (- 4, 3), (x₂, y₂) = (4, 1)
m = (1 - 3) / [4 - (- 4)]
m = - 2 / 8
m = - 1 / 4
Case 7: (x₁, y₁) = (2, - 4), (x₂, y₂) = (4, 2)
m = [2 - (- 4)] / (4 - 2)
m = 6 / 2
m = 3
Case 8: (x₁, y₁) = (- 4, - 1), (x₂, y₂) = (0, - 3)
m = [- 3 - (- 1)] / [0 - (- 4)]
m = - 2 / 4
m = - 1 / 2
Case 9: (x₁, y₁) = (- 2, 0), (x₂, y₂) = (4, 1)
m = (1 - 0) / [4 - (- 2)]
m = 1 / 6
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Dana and Emile allocate 2/3 of their partnership's profits and losses to Dana and 1/3 to Emile. The net income of the firm is $40,000. The journal entry to close the Income Summary will include a ________. (Do not round any intermediate calculations. ) A) credit to Income Summary for $26,667 B) debit to Dana, Capital for $13,333 C) credit to Emile, Capital for $26,667 D) debit to Income Summary for $40,000
The journal entry to close the Income Summary will include a C) credit to Emile, Capital for $26,667.
To close the Income Summary account, the net income of $40,000 needs to be allocated to the partners' capital accounts based on their profit and loss sharing ratio.
Dana is allocated 2/3 of the net income, which is $26,667 (2/3 x $40,000). Emile is allocated 1/3 of the net income, which is $13,333 (1/3 x $40,000).
Therefore, the journal entry to close the Income Summary account would be:
Credit Income Summary for $26,667 (to close the account)
Debit Dana, Capital for $26,667 (to allocate Dana's share of net income)
Debit Emile, Capital for $13,333 (to allocate Emile's share of net income)
This is calculated by multiplying the net income of $40,000 by the ratio of Emile's share (1/3), which equals $26,667.
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At which of the following values of x does f(x)= 2e^2x -32?
(1) ln5/2
(2) ln4
(3) ln8
(4) y= ln2/5
Therefοre , the sοlutiοn οf the given prοblem οf lοgarithm cοmes οut tο be ln(4) is the value οf x at which f(x) equals 0, and chοice is the right respοnse (2).
What exactly is a lοgarithm?The inverse οf an integer is represented mathematically by the lοgarithm. Therefοre, the expοnential that bc needs tο be multiplied by tο get a specific integer, x, is identical tο its base b expοnent. As an illustratiοn, 1000 = 103, sο lοg10 = 3 is 1000's base-10 lοgarithm, which is 3. As an example, the cube οf twenty is actually οne hundred while the base-10 derivative οf ten appears tο be twο. lοg 100 = 2.
Here,
The fοrmula is prοvided as f(x) = 2e(2x) - 32. and we must determine the x-value at which f(x) equals a particular number. Let's wοrk thrοugh each sοlutiοn:
(1) ln(5/2):
[tex]\Rightarrow f(ln(5/2)) = 2e^{(2*ln(5/2))} - 32[/tex]
[tex]\Rightarrow2e^{(ln(25/4))} - 32[/tex]
[tex]\Rightarrow 2(25/4) - 32[/tex]
[tex]\Rightarrow -19/2[/tex]
As a result, f(ln(5/2)) does not equal 0.
(2) ln(4):
[tex]\Rightarrow f(ln(4)) = 2e^{(2*ln(4))}- 32[/tex]
[tex]\Rightarrow 2e^{(ln(16))}- 32[/tex]
[tex]\Rightarrow 2(16) - 32[/tex]
[tex]\Rightarrow 0[/tex]
As a result, choice (2) is the appropriate response because f(ln(4)) equals 0.
(3) ln(8):
[tex]\Rightarrow f(ln(8)) = 2e^{(2*ln(8))} - 32[/tex]
[tex]\Rightarrow2e^{(ln(64))} - 32[/tex]
[tex]\Rightarrow 2(64) - 32[/tex]
[tex]\Rightarrow 96[/tex]
As a result, f(ln(8)) does not equal 0.
(4 y = ln(2/5):
This choice is illogical because we must determine the value of x, not y.
As a result, ln(4) is the value of x at which f(x) equals 0, and choice is the right response (2).
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You and your best friend want to take a vacation to Australia. You have done some research and discovered that it will cost $2500 for the plane tickets, all-inclusive hotel and resort, and souvenirs. You have already saved $2200. If you invest this money in a savings account with a 1. 55% interest rate compounded annually, how long will it take to earn enough money to go on the trip? Use the compound interest formula A = P (1 + i)n, where A is the accumulated amount, P is the principal, i is the interest rate per year, and n is the number of years. Round your final answer to the nearest tenth
It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.
First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:
Total cost of trip = 2500
Amount already saved = 2200
Amount to save = 2500 - 2200 = 300
Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:
A = P(1 + i)n
where:
A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)
P = principal = 2200
i = interest rate per year = 1.55%
n = number of years we need to save for
We can now solve for n:
2500 = 2200(1 + 0.0155)n
Divide both sides by 2200:
1.13636 = 1.0155n
Take the natural logarithm of both sides:
ln(1.13636) = n ln(1.0155)
Divide both sides by ln(1.0155):
n = ln(1.13636)/ln(1.0155) ≈ 4.4 years
Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.
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4.02 Lesson Check Arithmetic Sequences (4)
The given sequence is a recursive sequence. Hence -2, 9, -24, 75 is the first four terms of the sequence.
Arithmetic and recursive sequenceThe given sequence is a recursive sequence, where each term is defined in terms of the previous term. Here, each term is obtained by multiplying the previous term by -3 and adding 3. The first term, a1, is given. Using this, we can find the second term, a2, and then using a2, we can find a3, and so on.
Given: an = -3an-1 + 3 and a1 = -2
To find: the first four terms of the sequence
a1 = -2
a2 = -3a1 + 3 = -3(-2) + 3 = 9
a3 = -3a2 + 3 = -3(9) + 3 = -24
a4 = -3a3 + 3 = -3(-24) + 3 = 75
Therefore, the first four terms of the sequence are: -2, 9, -24, 75.
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Can someone answer this please?
The equation for the function g(x) is g(x) = (x + 4)² - 5.
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.
Where:
N represents an integer.
g(x) and f(x) represent a function.
Based on the graph of the parent function f(x) = x², an equation for g(x) in vertex form after a translation of 5 units downward and 4 units to the left is given by:
g(x) = (x + 4)² - 5.
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In a group of students, 30% like Computer only, 25% like both Computer and Optional Maths and 5% don't like any of the subjects. If 390 students like Optional Maths, find the total number of students by drawing a Venn-diagram. (Ans: 600)
Answer:
Let's use a Venn diagram to solve this problem.
First, let's label the three regions of the Venn diagram: Computer only (C), Optional Maths only (M), and both Computer and Optional Maths (C ∩ M). We can also label the region outside the circles as neither Computer nor Optional Maths (N).
We know that 30% of the students like Computer only, which means that the percentage of students in region C is 30%. Similarly, 25% of the students like both Computer and Optional Maths, so the percentage of students in region C ∩ M is 25%.
We are also given that 5% of the students don't like either subject, so the percentage of students in region N is 5%.
Finally, we are told that 390 students like Optional Maths, which includes the students in regions M and C ∩ M. We don't know the percentage of students in region M, but we do know that the percentage of students in region C ∩ M is 25%.
Using this information, we can set up an equation to solve for the total number of students:
C + M + C ∩ M + N = 100%
Substituting the percentages we know, we get:
30% + M + 25% + 5% = 100%
Simplifying the equation, we get:
M = 40%
This means that 40% of the students like Optional Maths only, which is the percentage of students in region M.
Now we can use the fact that 390 students like Optional Maths to solve for the total number of students:
M + C ∩ M = 390
0.4T + 0.25T = 390
0.65T = 390
T = 600
Therefore, the total number of students is 600.
Write your answer as a x,y pair. 2x+3y=7. Y=2x-11 Solve using the SUBSTITUTION METHOD
Answer:
(5, -1) or x = 5, y = -1
Step-by-step explanation:
[tex]\mathrm{Substitute\:}y=2x-11[/tex]
[tex]\begin{bmatrix}2x+3\left(2x-11\right)=7\end{bmatrix}[/tex]
[tex]8x-33=7[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:8x-33=7[/tex]
[tex]8x=40[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}8[/tex]
[tex]\frac{8x}{8}=\frac{40}{8}[/tex]
[tex]x=5[/tex]
[tex]y= 2x-11 \\ \mathrm{Substitute\:}x=5[/tex]
[tex]y=2\cdot \:5-11[/tex]
[tex]y=-1[/tex]
Answer:
(5, - 1 )
Step-by-step explanation:
2x + 3y = 7 → (1)
y = 2x - 11 → (2)
substitute y = 2x - 11 into (1)
2x + 3(2x - 11) = 7
2x + 6x - 33 = 7
8x - 33 = 7 ( add 33 to both sides )
8x = 40 ( divide both sides by 8 )
x = 5
substitute x = 5 into (2)
y = 2(5) - 11 = 10 - 11 = - 1
solution is (5, - 1 )
I don't need an explanation I would just like the answer.
a) The equation that represents the total amount that the twins earned is; j + r = 96000
b) An amount that represents what Ron earned in terms of what Jon earned is; r = 3j + 8000
How to Solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
We are told that;
j represents the amount that Jon earned
r represents the amount that Ron earned
Thus, if together they earned $96000, then we have;
j + r = 96000
Ron earned $8000 more than three times what Jon earned. Thus, we have;
r = 3j + 8000
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could someone help me on this too? im taking a dcp i need help asapppp
Twο pοints (8,8) and (-2,6) are the set οf the equatiοn [tex]y < \frac{3}{4} x+6\\[/tex] οf the graph [tex]y = \frac{3}{4} x+6[/tex].
What is Graph?Graph, a diagram that shοws hοw a variable varies in relatiοn tο οne οr mοre οther variables (such as a cοllectiοn οf pοints, lines, line segments, curves, οr regiοns).
Nοw we have tο find the value οf the equatiοn i.e. [tex]y < \frac{3}{4} x+6\\[/tex],
(x, y) = (8,8) , we get 8 < 12 , First pοint
(x, y) = (-4,3) , we get 3 = 3 , Nο match
(x, y) = (6,-2) , we get -2 < 10.5 , Secοnd Pοint
(x, y) = (0, 8) , we get 8 > 6 , Nο Match
(x, y) = (-9,2) , we get 2>-0.75 , Nο Match
Sο, we get οur pοints, which are pοints (8,8) and (-2,6) fοr the equatiοn [tex]y < \frac{3}{4} x+6\\[/tex].
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The following data points represent the number of songs each member of the band Python Sunboat has
written
5, 2, 9, 21, 12,3
Find the median number of songs.
Answer: 7
Step-by-step explanation:
To find the median, we need to first put the data points in order from least to greatest:
2, 3, 5, 9, 12, 21
There are six data points, so the median is the middle value. In this case, the middle two values are 5 and 9. To find the median, we take the average of these two numbers:
(5 + 9) / 2 = 7
Therefore, the median number of songs written by the members of Python Sunboat is 7.
A culture initially contains 400 bacteria. If the number of bacteria doubles every 3 hours, how many bacteria will there be at the end of 15 hours?
Answer:
Since the number of bacteria doubles every 3 hours, after 3 hours there will be 400 x 2 = 800 bacteria. After 6 hours, there will be 800 x 2 = 1600 bacteria. After 9 hours, there will be 1600 x 2 = 3200 bacteria. After 12 hours, there will be 3200 x 2 = 6400 bacteria. Finally, after 15 hours, there will be 6400 x 2 = 12800 bacteria. Therefore, there will be 12800 bacteria at the end of 15 hours.
Step-by-step explanation:
3 screenshots!!
giving brai. to whoever answers them all correct :)
Answer:
problem 1. 53/20 problem 2. 24/27. Problem 3. 22/48
Step-by-step explanation:
to solve the first two, the process is similar. For the first one, they can be simplifed back into fraction form and not mixed form, so 1 2/5 can be simplified by multiplying 5 by one then adding it to 2, which gives you 7/5, and the same process for 2 1/2, multiply 2 by two, get 4 add it to one to get 5/2. Now we have 7/5 + 5/2, when we have fractions that we need to add or subtract, but down have the same bottom number, the easiest way to get a answer is to multiply both bottom numbers together then multiply the top number by the opposite bottom number, so 5x4 = 20, 4x7=28, 5x5=25, and we get 28/20 + 25/20 = 53/20. The process for problem two is the same, but just with subtraction and different numbers.
for problem three, the process is almost the same, but the steps differ. The bag is made up of R G and P counters, 3/8 of them are red, 1/6 are green, and the rest are purple because nothing else is in the bag. So another way of saying this is 3/8 + 1/6 + purple = Full Amount in bag. But now we need purple, so we know 1/2 one half and so does 2/4, and since we have fractions we can find the amount in the bag by adding them, 3/8 + 1/6 = 26/48, and we know the full bag is 1/1 or 48/48, and fhe only one left is purple, so to get purple, we subtract 48/48 from 26/48 and get 22/48 which is the amount of purple.
PLEASE SHOW WORK!!!!!!!!!
Answer:
Step-by-step explanation:
If h is the height of the ball off the ground, if we want to find the time, t, when the ball hits the ground again, we set h equal to 0, because the height of something when it is on the ground is 0.
[tex]0=-t^2+4t[/tex] and solve for the values of t. Begin by factoring out a -t:
[tex]0=-t(t-4)[/tex]
By the Zero Product Property, either -t = 0 or t - 4 = 0. We already know that at time 0 the ball hit the ground for the first time because that was given in the problem. That means that the ball hit the ground for the second time 4 seconds later.
? : 4 = 5,4 : 3. Find ?
Answer:
? = 7.2
Step-by-step explanation:
The given equation is comprised of two ratios.
Using the given ratio 5.4 : 3, we can reduce it and see the ratio is 1.8 : 1
Now, using the same idea for the unknown value, we must multiply 1.8 by 4, giving 7.2.
There are 3 x as many blue counters as yellow. 45 blue counters are removed. There are now still 63 more blue counters than yellow. How many blue counters were there to start with
After 45 blue counters are removed, the remaining number of blue counters is 63 more than yellow counters. Setting up an equation, we find that there were 162 blue counters to start with.
Let's start by assigning variables to the unknowns:
Let x be the number of yellow counters.
Then, the number of blue counters is 3x.
After 45 blue counters are removed, the number of blue counters is 3x - 45.
Finally, there are 63 more blue counters than yellow, so we can set up the equation:
3x - 45 = x + 63
Solving for x, we get:
2x = 108
x = 54
Therefore, there were 3x = 3(54) = 162 blue counters to start with.
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3^2-(4/5/8)+1
please expert verfied asap i will give brainliest to who answer ffirst
Answer:
[tex]9.9[/tex]
Step-by-step explanation:
Interpreted:
[tex]3^2-(4\div5\div8)+1[/tex]
1) Simplify 4 ÷ 5 to 0.8.
[tex]3^2-0.8\div8+1[/tex]
2) Simplify 3² to 9.
[tex]9-0.8\div8+1[/tex]
3) Simplify 0.8 ÷ 8 to 0.1.
[tex]9-0.1+1[/tex]
4) Simplify 9 - 0.1 to 8.9.
[tex]8.9+1[/tex]
5) Simplify.
[tex]9.9[/tex]
How are geometric sequences and exponential functions alike?
How are they different?
Answer:
Geometric sequences and exponential functions are alike in that they both involve repeated multiplication by a constant factor. In a geometric sequence, each term is found by multiplying the previous term by the same constant factor. In an exponential function, the value of the function is found by raising a constant base to an exponent that increases by a constant amount.
However, they differ in the way they are expressed. In a geometric sequence, each term is written as a discrete value in the sequence, while in an exponential function, the value of the function is written as a continuous function of the input variable. Additionally, geometric sequences are often used to model discrete phenomena, while exponential functions are often used to model continuous phenomena.
Step-by-step explanation:
g how many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound?
6 pounds of chocolate worth $1.20 per pound must be mixed with 10 pounds of chocolate worth 90 cents per pound in order to create a mixture worth $1.00 per pound.
how many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound?To produce a mixture worth $1.00 a pound, 6 pounds of chocolate worth $1.20 per pound must be mixed with 10 pounds of chocolate worth 90 cents per pound.
Let us proceed as follows:
x is the amount of chocolate worth $1.20 per pound that must be mixed with 10 pounds of chocolate worth 90 cents per pound in order to create a mixture worth $1.00 per pound.
Using the formula:
Price of chocolate (x) + Price of chocolate ($0.90) = Price of mixture ($1.00)
The following equation can be created:
1.20x + 0.9(10) = 1(10 + x)
Simplify: 1.20x + 9 = 10 + x1.20x - x = 10 - 91.20x - x = 1
Divide both sides by 0.2 to simplify the equation:
6x = 5x = 6
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let us make a tabe of values folliwong the rula that she save twice as much as she saved the day before
Answer:
We can use the expression 2x = y , where 'x' is the amount she saves yesterday and y being the amount she saves this day.
Table = if x = 0 , y = 0
if x = 1 , y = 2
if x = 2 , y =4
if x = 4 , y= 8
Find the area of a circle with circumference is 60 CM
Answer:
900/π square centimeters or 286.62 square centimeters
Step-by-step explanation:
The circumference of a circle is given by the formula:
C = 2πr
where C is the circumference and r is the radius of the circle.
We are given that the circumference is 60 cm, so we can set up the equation:
60 = 2πr
Solving for r, we get:
r = 60/(2π) = 30/π
The area of a circle is given by the formula:
A = πr^2
Substituting the value of r, we get:
A = π(30/π)^2 = 900/π square centimeters
Therefore, the area of the circle is approximately 286.62 square centimeters, rounded to two decimal places.
A card is randomly drawn from a standard deck of 52 cards. What is the probability that the card is a king of diamonds, given that the card drawn is a king?
Answer:
There are four kings in a standard deck of 52 cards, so the probability of drawing a king is 4/52 or 1/13.
Since we know that the card drawn is a king, there are now only four possible cards that could have been drawn: the king of spades, the king of hearts, the king of clubs, and the king of diamonds.
Out of these four possibilities, only one of them is the king of diamonds. Therefore, the probability that the card is a king of diamonds, given that the card drawn is a king, is 1/4.
In other words, the conditional probability of drawing the king of diamonds given that a king has been drawn is:
P(king of diamonds | king) = P(king of diamonds and king) / P(king) = 1/52 / 4/52 = 1/4
Hope this helps! If not, I'm sorry. Feel free to ask for help from me! :]
A rectangular prism has a base with an area of 200cm2. The. Volume of the prism is 3,000cm3 what is the height of the prism
Answer:
height = 15 cm
Step-by-step explanation:
Base area of a prism B = hw where h = height, w = width
So B = lw = 200 cm²
Volume V = lwh = 3000 cm³
V/B = lwh/lw = h
h = 3000cm³/200cm = 15 cm
Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 53−x=251 The solution set is White an equation for line L in point-slope form and slope-intercept form. Lis perpendicular lo y=4x. White an equation for line t in point-slope farm. y=−41x+c (Sumplyy your onswer. Use integors or tractons for arty rumbers in the equation) Wile an equation for ine L in slopesindoreept form y−y1=−41(x−x1) (5mplfy vour answer. Use integprs or fractions for any nurbers ti the equation)
The equation for line L in slope-intercept form is y = -1/4x + x₁/4 + y₁
The exponential equation is 53−x=251. Therefore, we need to express each side as a power of the same base and then equate exponents. Let's express both sides with the same base 5. We know that 251 is the same as 5². Thus, the equation can be rewritten as:
53−x=251=5².
We need to express 53−x as a power of 5. To do that, we can write it as:
53−x = 5³/x.
Now, we can substitute this expression into our equation to get:
5³/x=5²
Let's multiply both sides of the equation by x to eliminate the fraction:
5³=5²x.
Divide both sides by 5² to get:x = 5. We can check our solution by plugging it back into the original equation:
53−5=25, which is true.
Thus, the solution set is {5}.The equation for line L in the point-slope form: We know that L is perpendicular to y=4x. Thus, the slope of L is -1/4. We also know that L passes through a point (x₁, y₁). Let's write the point-slope form of the equation:
y - y₁ = -1/4(x - x₁).
The equation for line L in slope-intercept form: Let's solve this equation for y to get it in slope-intercept form:
y - y₁ = -1/4(x - x₁).
Multiply both sides by 4 to eliminate the fraction:
4y - 4y₁ = -x + x₁.
Simplify by moving -x + x₁ to the right side:
4y = x₁ - x + 4y₁.
Add x to both sides:
4y + x = x₁ + 4y₁
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A consumer is trying to decide between two long-distance callingplans. The first one charges a flat rate of $0. 10 per minute,whereas the second charges a flat rate of $0. 99 for calls up to 20minutes in duration and then $0. 10 for each additional minuteexceeding 20 (assume that calls lasting a noninteger number ofminutes are charged proportionately to a whole-minute'scharge). Suppose the consumer's distribution of call durationis exponential with parameter λ. Which plan is better if expected call duration is 10 minutes? 15minutes? [Hint: Let h1(x) denote the cost for the firstplan when call duration is x minutes and let h2(x) bethe cost function for the second plan. Give expressions forthese two cost functions, and then determine the expected cost foreach plan. ]
The calling plan was a logical decision that was made. For calls with a shorter estimated time (10 minutes), the first plan is selected; for calls with an extended expected duration, the second plan is favoured (15 minutes).
Let the costs for the first and second plans, respectively, be denoted by h₁(x) and h₂(x), while the call lasts for x minutes.
The expressions for these two cost functions are as follows, according to the information available:
h₁(x) = 10x
h₂(x) = 99; if x ≤ 20 and 99 + 10(x - 20); if x > 20
Let X represent how long the call was. The exponential distribution of X has a parameter value of λ = 1/10 if the anticipated call time is 10 minutes.
That is, X ~ exp(λ = 1/10)
The exponential distribution's density function with parameter λ = 1/10 is,
f(x) = 1/10[tex]e^{-x/10}[/tex]; if x > 0 and 0; if otherwise
Calculate the anticipated cost of the initial plan E[h₁(x)].
E[h₁(x)] = [tex]\int^{\infty}_{-\infty}h_{1}(x)\cdot f(x)dx[/tex]
E[h₁(x)] = [tex]\int_{-\infty}^{0}10x\cdot 0dx+\int^{\infty}_{0}10x\cdot \frac{1}{10}e^{-x/10}dx[/tex]
E[h₁(x)] = 0 + [tex]\int^{\infty}_{0}x\cdot e^{-x/10}dx[/tex]
E[h₁(x)] = [tex][-10xe^{-x/10}-100e^{-x/10}]^{\infty}_{0}[/tex]
E[h₁(x)] = 100
Calculate the anticipated cost of the initial plan E[h₂(x)].
E[h₂(x)] = [tex]\int^{\infty}_{-\infty}h_{2}(x)\cdot f(x)dx[/tex]
E[h₂(x)] = [tex]\int_{-\infty}^{0}99dx+\int^{20}_{0}99\cdot \frac{1}{10}e^{-x/10}dx + \int^{\infty}_{20}(99+10(x-20))\cdot \frac{1}{10}e^{-x/10}dx[/tex]
E[h₂(x)] = 0 + [tex]\frac{99}{10}\int^{20}_{0}e^{-x/10}dx - \frac{101}{10}\int^{\infty}_{20}e^{-x/10}dx+\int^{\infty}_{20}xe^{-x/10}dx[/tex]
E[h₂(x)] = [tex]\frac{99}{10}[-10e^{-x/10}]^{20}_{0} - \frac{101}{10}[-10e^{-x/10}]^{\infty}_{20} + [-10xe^{-x/10}-100e^{-x/10}]^{\infty}_{20}[/tex]
E[h₂(x)] = -99e⁻² + 99 - 101e⁻² + 200e⁻² + 100e⁻²
E[h₂(x)] = 99 + 100e⁻²
E[h₂(x)] = 112.5335
E[h₂(x)] > E[h₁(x)] (112.53 > 100) is what has been seen. Hence, the first strategy is chosen when a 10-minute call is anticipated.
The exponential distribution's density function with parameter λ = 1/15 is,
f(x) = 1/15[tex]e^{-x/15}[/tex]; if x > 0 and 0; if otherwise
Calculate the anticipated cost of the initial plan E[h₁(x)].
E[h₁(x)] = [tex]\int^{\infty}_{-\infty}h_{1}(x)\cdot f(x)dx[/tex]
E[h₁(x)] = [tex]\int_{-\infty}^{0}10x\cdot 0dx+\int^{\infty}_{0}10x\cdot \frac{1}{15}e^{-x/15}dx[/tex]
E[h₁(x)] = 0 + [tex]\frac{2}{3}\int^{\infty}_{0}x\cdot e^{-x/15}dx[/tex]
E[h₁(x)] = [tex]\frac{2}{3}[-15xe^{-x/15}-225e^{-x/15}]^{\infty}_{0}[/tex]
E[h₁(x)] = 150
Calculate the anticipated cost of the initial plan E[h₂(x)].
E[h₂(x)] = [tex]\int^{\infty}_{-\infty}h_{2}(x)\cdot f(x)dx[/tex]
E[h₂(x)] = [tex]\int^{20}_{0}99\cdot \frac{1}{15}e^{-x/15}dx + \int^{\infty}_{20}(99+10(x-20))\cdot \frac{1}{15}e^{-x/15}dx[/tex]
E[h₂(x)] = [tex]\frac{99}{15}\int^{20}_{0}e^{-x/15}dx - \frac{101}{15}\int^{\infty}_{20}e^{-x/15}dx+\frac{2}{3}\int^{\infty}_{20}xe^{-x/15}dx[/tex]
E[h₂(x)] = [tex]\frac{99}{15}[-15e^{-x/15}]^{20}_{0} - \frac{101}{15}[-15e^{-x/15}]^{\infty}_{20} + [-15xe^{-x/15}-225e^{-x/15}]^{\infty}_{20}[/tex]
E[h₂(x)] = -99[tex]e^{-4/3}[/tex] + 99 - 101[tex]e^{-4/3}[/tex] + 200[tex]e^{-4/3}[/tex] + 150[tex]e^{-4/3}[/tex]
E[h₂(x)] = 99 + 150[tex]e^{-4/3}[/tex]
E[h₂(x)] = 138.54
E[h₂(x)] < E[h₁(x)] (138.54 < 150) is what has been seen. Hence, the first strategy is chosen when a 15-minute call is anticipated.
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Calculate x in the following ratio: x:12 =6:3
Answer: [tex]x=24[/tex]
Step-by-step explanation: Since the ratio of 6:3 is a 2:1 ratio simplified, you know that x will need to double the value on the other side. Therefore, you can just multiply 12 by 2 to get the x-value which is 24. Another method is to see that the 3 on the other side of the ratio is 1/4 the value of 12. This means that the 6 is 1/4 the value of x. if you multiply 4 on both sides x=24. Those are the two methods I recommend you use to solve these ratio problems.
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{Equation:}\\\\\large\boxed{\mathsf{6:3}}\\\\\large\textsf{Simplifying for:}\\\\\large\boxed{\rightarrow \mathsf{x:12}}\\\\\large\textsf{Simplifying:}\\\\\large\boxed{\mathsf{\rightarrow 6\times 4: 3\times4}}\\\\\large\boxed{\mathsf{\rightarrow{24:12}}}\\\\\\\huge\text{Therefore your answer should be: }\\\huge\boxed{\mathsf{\bold{24}:12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]