Answer:
cost of television: $924
Cost of DVD player: $308
Step-by-step explanation:
we make a system of equations
T- television
D- dvd played
t+d=1232
3d=t
3d+d=1232
4d=1232
/4. /4
d=308
Dvd player costs $308
Now to find television
3(308)=t
924=t
Television costs $924
Hopes this helps please mark brainliest
what is an interaction term in the context of regression analysis
When one independent variable affects the result differently based on the values of another independent variable, this is known as an interaction.
What does the statistical term "interaction" mean?
When two or more variables interact to impact a third variable in a non-additive way, this is known as an interaction in statistics.
To put it another way, the two variables interact to produce a result that is greater than the sum of their parts.
Give a definition of interaction and an example?
a time when two or more items or people interact or communicate with one another - There isn't enough interaction between the management and the employees.
Language games typically aim to promote student interaction.
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An empty cubical carton i of ide 9cm. Can you fit in 1000 1cm cube in it? Jutify
Answer: Side of an empty cubicle carton = 9 cm.
Now as we know that volume of the cube is the cube of its side.
So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.
Now we have to find out can 1000 cubes of side 1cm fit in it.
So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3
So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.
Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.
So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,
⇒VV′=7291000=0.729 < 1
So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.
Step-by-step explanation:
I really hope this works!
Hope you Have a Great Day!! :)
consider a new dam where the height is doubled and the width is only one third of the original value. the ratio of the total force exerted on the new dam to that on the original dam fnew f is given by
the total force exerted on the new dam to that on the original dam f new is given by F = 624010000 lb.
What is Pascal's Principle.?
Consider a flat surface that is immersed vertically in a fluid whose weight density is p, according to Pascal's Principle.
A flat surface experiences fluid force (F) which is
F = ∫ph(x)w(x) dx
where h(x) is the height of the point x in the x-axis' vertical direction and w(x) is the surface's width.
to determine fluid force applied
Assume that x is equal to the height of the water. At height x on the dam, width of the dam is w(x) = 200 ft (given), and height is h(x) = x ft.
F = ∫ph(x)w(x) dx
F =0→100 ∫62.4 x 200 dx
F = 12480* 0 →100∫ x dx
F = 12480* 0 →100(x²/2)
F =
F = 6240((100)²- (0)²)
F= 6240(10000)
F = 624010000 lb
Hence the total force exerted on the new dam to that on the original dam f newf is given by F = 624010000 lb.
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Under his cell phone plan, liam pays a flat cost of $69. 50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine xx, the number of gigabytes liam can use while staying within his budget.
The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Let the number of gigabytes consumed be x,
The total cost per month will be 69.50 + 5x
accoding to the question the bill would not exceed $90.
So the inequality,
69.50 + 5x ≤ 90
Simplification for the maximum gigabyte he can buy,
5x ≤ 90 - 59.90
5x ≤ 20.5
x ≤ 4.1
Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
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The table shows the weights of apples at a grocery store.
Answer:
Is that all
_______
_______
Line N passes through (1/2, -6) and is parallel Line Q which has an undefined slope. Write the equation of Line N.
The equation of the line which passing through the point and parallel to the line which has undefined slope is y=0(x)-6
Given that,
The point is (1/2,-6)
We have to find the equation of the line which passing through the point and parallel to the line which has undefined slope.
We know that,
The equation of the line has a formula that is y=mx+b
m is the slope of the line
b is the intercept
m is slope that is undefined means
m is 0.
Now, b is
y=0(x)+b
y=b
Here y is from the point -6
b is -6
So, we get equation has
y=0(x)-6
Therefore, The equation of the line which passing through the point and parallel to the line which has undefined slope is y=0(x)-6
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
answer Asap!!!!!!!!!!!!
The three statements about his solution that are true include the following:
1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
2. He did not multiply the numerator and denominator by the correct number to equal 1,500.
5. He should have multiplied the numerator and denominator by 75, not 30, because 20 × 75 = 1,500.
How to determine the true solutions?Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:
10/20 = x/1500
Multiplying the mathematical expression by 75, we have the following:
75 × (10/20) = x/1,500
750/1500 = x/1500
1,500x = (750 × 1,500)
x = (750 × 1,500)/1,500
x = 750.
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In an Arithmetic Progression (AP), the first
term is 3, and the sum of the first and the sixth
terms is 20. What is the 8th term
Answer:
The 8th term of the AP= 113/5 or 22.6
Answer:
22.6
Step-by-step explanation:
Given:
a = 3a + a₆ = 20Find the value of a₆:
[tex]\implies a+a_6=20[/tex]
[tex]\implies a_6=20-a[/tex]
[tex]\implies a_6=20-3[/tex]
[tex]\implies a_6=17[/tex]
Therefore:
a = 3a₆ = 17General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
Where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.n is the position of the term.Substitute a = 3 and a₆ = 17 into the formula and solve for d:
[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\implies a_n=3+(n-1)2.8[/tex]
[tex]\implies a_n=3+2.8n-2.8[/tex]
[tex]\implies a_n=2.8n+0.2[/tex]
To find the 8th term, substitute n = 8 into the equation for the nth term:
[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]
Factorise fully the following:
4x³ + 24x²
Answer:
4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)
4 x^2 (x + 6) seems to be the lowest factor
Factorise this equation + workings out!! Please help!!!!
Answer:(2x+1)(3x-4)
Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)
Answer:
(3x - 4)(2x - 1)
Step-by-step explanation:
6x^2 - 5x - 4
When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)
x^2 - 5x - 24
Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)
24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.
As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.
One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.
Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.
(6x - 8)(6x - 3)
We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.
(6x - 8)/2 and (6x - 3)/3. 3*2 = 6
(3x - 4)(2x - 1)
Gianna is going to use a computer at an internet cafe. The cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use. Make a table of values and then write an equation for C , C, in terms of t , t, representing the total cost of using a computer for t t minutes at the internet cafe.
A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:
C t
$10.60 1
$11.20 2
$11.80 3
C = 0.60t + 10.
How to write an equation for the total cost?In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:
Let the variable C represent the total cost in dollars.Let the variable t represent the amount of time in minutes.Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:
C = 0.60t + 10
When t = 1, we have:
Total cost, C = 0.60(1) + 10
Total cost, C = $10.60.
When t = 2, we have:
Total cost, C = 0.60(2) + 10
Total cost, C = $11.20.
When t = 3, we have:
Total cost, C = 0.60(3) + 10
Total cost, C = $11.80.
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e.) if the car's speed 65 kilometers per hour it is possible that bus speed 75 kilometers per hour
explain or justify ur answer
If the car's speed is 65 kilometres per hour, then the bus' speed may be 75 kilometres per hour.
How to find the distance travelled by an object?
The distance travelled by an object in a specified direction is velocity×time.
if the car's speed is 65 kilometres per hour then in 2 hours it will travel a distance of 65×2 kilometres.
65×2=130 kilometres
if the bus' speed is 75 kilometres per hour then in 2 hours it will travel a distance of 75×2 kilometres.
75×2=150 kilometres
So, after 2 hours the distance between the two vehicles will be 130+150= 280 kilometres
which is less than 350 kilometres.
Hence, it is possible that if the car's speed is 65 kilometres per hour then the bus' speed is 75 kilometres per hour.
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The marginal revenue (in thouand of dollar) from the ale of x handheld gaming device i given by the following function. R′(x)=4x(x^225,000)^(− 2/3)
The total revenue function if the revenue from 115 devices $2116 is 200 when R'(x)=4x(x²+25000[tex])^{2/3}[/tex].
Given that,
The following function calculates the marginal revenue (in thousands of dollars) from the sale of a portable gaming system.
R'(x)=4x(x²+25000[tex])^{2/3}[/tex]
We have to find the total revenue function if the revenue from 115 devices $2116.
We know that,
R'(x)=4x(x²+25000[tex])^{2/3}[/tex]
Integrating on both sides
R(x)= [tex]\int {4x(x^{2} +25000)^{2/3} } \, dx[/tex]
Let x²+25000=t
=> 2xdx=dt
=> 4xdx=2dt
We get,
R(x)= [tex]\int {2t^{-2/3} } \, dt[/tex]
R(x)= [tex]6t^{1/3}[/tex]+C
By Substitution then
R(x)= 6(x²+25000[tex])^{1/3}[/tex]+C
We get
Given R(115)=$2,116 or 2.116 (in thousands of dollars) and x=115 units
Then total revenue function(in thousands of dollars)
2.116= 6(115²+25000[tex])^{1/3}[/tex]+C
C=200
Therefore, The total revenue function if the revenue from 115 devices $2116 is 200.
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Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x
A)
(0, 0)
B)
(–4, 0) and (4, 0)
C)
(–4, 0) and (0, 0)
D)
(0, 0) and (4, 0)
What is the measure of m? 28 n 7 m = 7√ [?] Give your answer in simplest form. I would really appreciate your help.
Answer:
[tex]7\sqrt{5}[/tex]
Step-by-step explanation:
Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].
Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]
find the perimeter of the triangle. a triangle is drawn. all the angles of the triangle are marked with a single arc. three sides of a triangle are labeled (x plus 5 )inches, (2 x minus 3 )inches and (21 minus x )inches.
If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x
The perimeter of the triangle is the summation of all three sides of the triangle
Perimeter = a + b + c
= (x + 5) + (2x - 3) + (21 - x)
= 2x + 23
= 23 + 2x
Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle 23 + 2x.
Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.
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read questions A and B... Must give 2 answers
For a student with a shoe size of 9, the student's height is equal to 65 inches.
For a student with a height of 60 inches, the student's shoe size is equal to 6.5.
How to determine the approximate of a student?From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:
y = 0.50x - 23.5
Where:
x represents the height of a student.y represents the shoe size of a student.For a student with a shoe size of 9, the student's height is given by:
y = 0.50x - 23.5
0.50x = y + 23.5
Student's height, x = (y + 23.5)/0.50
Student's height, x = (9 + 23.5)/0.50
Student's height, x = 32.5/0.5
Student's height, x = 65 inches.
For a student with a height of 60 inches, the student's shoe size is given by:
y = 0.50x - 23.5
y = 0.50(60) - 23.5
y = 30 - 23.5
y = 6.5
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is the statement a valid null hypothesis?
A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.
What is meant by null hypothesis?A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.
The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.
Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.
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Please see the attachment below.
Need explanation
Answer:
16.(a) 24
16.(b) See attachment.
Step-by-step explanation:
Cumulative frequency means ‘running total’. A cumulative frequency diagram plots this running total so you can estimate the median and the quartiles easily.
Part (a)According to the given cumulative frequency graph, the number of necklaces that have a mass 21 g or less is 16.
Therefore, an estimate of the number of necklaces with a mass of 21 g or greater is:
[tex]\implies 40-16=24[/tex]
Part (b)To draw a box plot to represent the data, estimate the median and quartiles from the graph.
Calculate the position of the median and quartiles, then go to the position on the vertical scale of the graph and read off the value from the horizontal axis. (See attached annotated graph).
[tex]\sf Median \; position=\dfrac{40}{2}=20[/tex]
So the median = 22
[tex]\sf Q_1 \; position = \dfrac{1}{4} \times 40=10[/tex]
So Q₁ = 18
[tex]\sf Q_3 \; position = \dfrac{3}{4} \times 40=30[/tex]
So Q₃ = 24
Draw the box plot with the calculated median and quartiles, and the given lowest and highest values. (See second attachment).
Draw a box from Q₁ to Q₃ (18 to 24).Add the median as a the vertical line through the box at 22.Draw whiskers from each quartile to the minimum value 3 and maximum value 28.At 103°F, a certain insect chirps at a rate of 101 times per minute, and at 105°F, they chirp 107 times per minute. Write an equation in slope-intercept form that represents the situation.
An equation in slope-intercept form that represents the situation is y = 3x - 208.
How to calculate the slope of a line?Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided, we have the following points:
Points on x-axis = (103, 105).
Points on y-axis = (101, 107).
Substituting the given points into the formula, we have;
Slope, m = (107 - 101)/(105 - 103)
Slope, m = 6/2
Slope, m = 3
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (103, 101), an equation in slope-intercept form is given by:
y - y₁ = m(x - x₁)
y - 101 = 3(x - 103)
y - 101 = 3x - 309
y = 3x - 309 + 101
y = 3x - 208.
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Scott bought a desktop computer and a laptop computer. Before finance charges and the laptop cost $350 more than the desktop. He paid for the computers using two different financial plans. For the desktop the interest rate was 6.5% per year and for the laptop it was 9% per year. The total finance charges for one year for $388. How much did each computer cost before finance charges
The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
What are mathematics operations?A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.
From the question , we are given that the laptop costs $350 more than the desktop, therefore,
let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .
The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;
388 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that the cost of desktop = x -350
therefore:
1,798- 350 = 1448
The cost of laptop = $1798
The cost of desktop = $1448
Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
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The line graph below displays the average value of a 2000 Toyota Camry since the year 2000. A trendline has been added to the data. V represents value in dollars of the car and t represents the time in years since 2000.
a. Consider the variables “Value” and “time”. Which variable is the independent variable and which variable is the dependent variable?
b. Find an equation for the value as a function of the number of years since 2000.
c. Write a sentence that identifies and interprets the y intercept of the trendline. Use
appropriate units.
d. Write a sentence that identifies and interprets the slope of the trendline. Use
appropriate units.
e. Use the equation of the trendline to predict the value of the car in 2017. Use your
appropriate units. Show your work.
The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;
a. Independent variable; Time
Dependent variable; Value
b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t
c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500
d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]
e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]
What is a trendline in a graph or chart?A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.
a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.
Therefor;
The independent variable is the ''time''The dependent variable is the value under study, therefore;
The dependent variable is the ''Value''b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;
m = (5,000 - 22,500)/(15 - 0) = -3,500/3
The equation is therefore;
V - 22,500 = -3,500/3·t
V = -3,500/3·t + 22,500
The equation for the value is; V = (22,500 -(3,500/3)·tc. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500
d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.
e. In the year 2017, t = 17, therefore;
V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]
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The following histogram shows part of the probability distribution of the size (in megatons of released energy) of large meteors that hit the Earth's atmosphere. (A large meteor is one that releases at least one megaton of energy, equivalent to the energy released by a small nuclear bomb.)
That a large meteor will release at least 6 megatons of energy.The following histogram shows part of the probability distribution of the size (in megatons of released energy) of large meteors that hit the Earth's atmosphere. A large meteor is one that releases at least one megaton of ene equivalent to the ene released nuclear bomb a Sma A Probability 026 023 020 018 17 015 013 012 3 4 6 8 90 10 13 14 15 16 17 Energy (megatons) Calculate or estimate the following probabilities. (Round your answers to three decimal places.) (a) That a large meteor hitting the Earth's atmosphere wi release between 1 and 4 megatons of energy. 0.304 (b) That a large meteor hitting the Earth's atmosphere will release between 9 and 10.5 m of energy. 0.029 (c) That a large meteor will release at least 6 megatons of energy. 0,387
a) Probability that Meteor will release between 1 and 4 megatons of energy: 0.304
b) Probability that Meteor will release between 9 and 10.5 megatons of energy: 0.029
c) Probability that Meteor will release at least 6 megatons of energy: 0.613
What is histogram?
The spread and size of the data are measured using histograms. We can virtually analyse the data based on the histogram.
From the Histogram we get:
a) Probability that Meteor will release between 1 and 4 megatons of energy= P [X=1 to X=4]
= [0.156+0.088+0.060]
=0.304
b) Probability that Meteor will release between 9 and 10.5 megatons of energy= P [X=9 to X=10.5]
= [0.020+0.009]
=0.029
c) Probability that Meteor will release at least 6 megatons of energy = 1- P[X≤5]
= 1-P [X=1 to X=5]
= 1- [0.156+0.088+0.060+ 0.046+0.037]
= 0.613
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JE
Write an equation for a line perpendicular to y = 3a + 3 and passing through the point (-6,6)
Answer:
Step-by-step explanation:
A line that is perpendicular to another will have the opposite slope.
y = [tex]-\frac{1}{3}[/tex]a + b
To find b, substitute y and a with the given values
6 = [tex]-\frac{1}{3}[/tex](-6) + b
6 = 2 + b
-2 -2
4 = b
thus
y = [tex]-\frac{1}{3}[/tex]a + 4
Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x + 4y = 16
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
6x + 4y = 16 ( subtract 6x from both sides )
4y = - 6x + 16 ( divide through by 4 )
y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is
y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form
Write the given expression as a single trigonometric function. 2 sine (startfraction 3 pi over 8 endfraction) cosine (startfraction 3 pi over 8 endfraction)
The single trigonometric function form of the expression is 2sin(3π/8) cos(3π/8).
Trigonometric function:
In math, trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle.
Given,
Here we need to write the given expression as a single trigonometric function. 2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)
Here we have the expression,
2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)
Now, we have to convert this into the form of trigonometric function,
For that we have to rewrite the given expression based on the arithmetic operators, then we get the resulting function as,
=> 2sin(3π/8) cos(3π/8).
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Answer:C
Step-by-step explanation:
did it on edge
How do you write 760 percent as a fraction or as a mixed number?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
760% can be written in fraction form as 38/5.
760% can be written in mixed form as 7(3/5).
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
760%
This can be written as a fraction.
760/100
= 76/10
= 38/5
or
= 7(3/5)
Thus,
760% can be written in fraction form as 38/5.
760% can be written in mixed form as 7(3/5).
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For the complex number z = startfraction 5 startroot 3 endroot over 4 endfraction minus startfraction 5 over 4 endfraction i ,what is the polar form?.
2.5(cos 5π/6 + i sin 5π/6) is the polar form of the complex number
How to find the polar form of a complex number?Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)
Given: the complex number (5√3)/4 - 5/4 i
In polar form:
(5√3)/4 - 5/4 i = r(cosθ + isinθ)
θ = tan⁻¹( (-5/4) / (5√3 /4) )
θ = -30°
θ = -30+180 = 150°
θ = 5π/6
r = √( (5√3)/4)² +(- 5/4)²) = 2.5
Thus,
(5√3)/4 - 5/4 i = r(cosθ + isinθ)
r(cosθ + isinθ) = 2.5(cos 5π/6 + i sin 5π/6 )
Therefore, the polar form of the complex number is 2.5(cos 5π/6 + i sin 5π/6)
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a publisher reports that 54t% of their readers own a personal computer. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 200200 found that 44d% of the readers owned a personal computer. is there sufficient evidence at the 0.100.10 level to support the executive's claim? step 1 of 7 : state the null and alternative hypotheses.
hybrids research When she does, the camden depositor is actually higher than the reported percentage. Here, we have the report 126 percent, the winners on the portion computer. It indicates that the proportion of the underling hypothesis at noon will be equal to 26.
The abon 26 point notte will be greater than the b of the means 10. In this question, which is the right-hand exam, we will provide the sembiante 340, which will be equal to 31 percent, and we must contend with the statistical test. The test is therefore equal to the z moving forward. It will be calculated using the following formula: hat: minus b over square root, times: 1 minus p over the hot equal to 131 p equal to 261 square 261 minus 26. If we compare it to my 340 point, we get 126 times 74 divided by 340, then we take the square root of that number. The 131 minus 7.26 is then divided by the industry standard.I respond with a number equal to 2.10, rounding up to two decimal places before moving on to the step's following inquiry. 3. This is the 110 test since the test pair is on 1 here and then the next 1 in his right hand. The choice must be made hypotheses, though. Rule and we need to identify the critical value, and since that will be the right hand, we must make sure that the critical value is both equal to and far beyond that. 05. It will check the z table to see if the value equals 1.645, and if it does, we'll use the decision rule to reject the null hypothesis. If so, the test result will exceed the cutoff of 1.645 points, and we will observe Because the test we determined to be equivalent to 2.10 is higher than the 1.645 point, we can observe that. We will thus rule out the known hypothesis and come to the conclusion that there is sufficient evidence to back up the prediction that the proportion will be higher than 26%.
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does a gasoline additive improve mileage? drivers logged their mileage on a tank of gas with and without the additive. the sample of 10 drivers had an average difference (with additive - without) in mileage of 4.1 mpg with a standard deviation of 5 mpg. what is the test statistic for this test?
The test statistic for the given test is t = 2.59.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
Given data:
[tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0
Now the test statistic can be computed as
[tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]
[tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]
Hence, the test statistic for the given test would be t = 2.59.
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