Answers
Solution:
Give the following below
[tex]\begin{gathered} amplitude=3 \\ period=\frac{\pi}{2} \\ midline,\text{ }y=-1 \\ Passing\text{ through the point }(0,2) \end{gathered}[/tex]To find the cosine function, we will apply the general formula for cosine function below
[tex]\begin{gathered} f(x)=a\cos(bx-c)+d \\ Where \\ a\text{ is the amplitude} \\ b\text{ represents the speed of the cycle} \\ d\text{ is the vertical shift} \\ \frac{c}{b}\text{ is the phase shift \lparen horizontal shift\rparen} \\ Period=\frac{2\pi}{b} \end{gathered}[/tex]To find the value of b
[tex]\begin{gathered} Period=\frac{\pi}{2} \\ \frac{2\pi}{b}=\frac{\pi}{2} \\ Crossmultiply \\ b\times\pi=2\times2\pi \\ b=\frac{4\pi}{\pi} \\ b=4 \end{gathered}[/tex][tex]\begin{gathered} a=3 \\ b=4 \\ d=-1 \\ c=0 \end{gathered}[/tex]Substitute the values of the variables into the general formula for cosine function
[tex]\begin{gathered} f(x)=a\cos(bx-c)+d \\ f(x)=3\cos(4x-0)-1 \\ f(x)=3\cos4x-1 \end{gathered}[/tex]Applying a graphing tool,
The graph of one cycle of the function is shown below
Related Questions
please help!
The Equation P= 2.5m + 35 represents the price P (in dollars) of a bracelet, where m is the cost of the materials (in dollars). The price of a bracelet is $115. What is the cost of the materials?
Answers
Polynomials are algebraic expressions with variables and coefficients.
cost of the materials = (115 - 35) / 2.5 = $77.5
How do you find the number of solutions a polynomial has?Remember from the chapter on Quadratic Functions that every quadratic equation has two solutions. A quadratic equation has a degree of two, which leads us to believe that it has two solutions. The degree will always tell us how many solutions a polynomial has.Polynomials are algebraic expressions with variables and coefficients. Variables are also known as indeterminates. For polynomial expressions, we can perform arithmetic operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable.Equation P= 2.5m + 35
The price of a bracelet is $115.
P = 115.
cost of the materials = (115 - 35) / 2.5 = $77.5
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what is the possibility of having three boys and one girl and a family with four children assuming there is an equal probability of having a boy or a girl gone to two decimal places
Answers
Since girls and boys have equal probability, iin a family with four children, they have probability equal to
[tex]P(\text{girl)}=P(\text{boy)}=\frac{1}{4}[/tex]so, the probability of having 3 boys and 1 girls is
[tex]P(3\text{boys }\cap1girl)=P(3boys)\cdot P(1girl)=\frac{3}{4}\cdot\frac{1}{4}=\frac{3}{16}[/tex]that is, the answer is 3/16 which is equal to 0.19.
What is the total number of zeros in the number (100,000,000)^2
A 18
B 12
C 16
D 10
Answers
Complete the sentence.
35 is *blank*
times as much as 5.
Answers
(PLEASE HELP) A function has the function rule y = -2x+1. If the output is 9, what is the input?
Answers
9 = -2x + 1
to solve : subtract 1 from each side so you have 8 = -2x
then : divide each side by -2
you will have the answer :
x or input, = -4
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4. If there were 2348 no votes, what was the total
number of votes?
Answers
A city's residents voted on whether to raise property taxes. The yes votes outnumbered the no votes 5 to 4. The total number of votes = 1043 if there were 2348 no votes.
What is Ratio and proportion?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.
For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls). In the ratio, the product of means equals the product of extremes.
If the cross products of two ratios are equal, they are said to be equal. The Proportion Formula is as follows: a: b:: c: d a b = c d
Therefore,
The total number of votes = 1043
yes votes / no votes = 5/4
Means there were a total of 9 votes;
So we could say:
No votes/Total votes = 4/9
So using total of 2348 votes, we can set up a proportion:
No votes/Total votes = 4/9 = x/2348
Cross multiplying ,
9392 = 9x
∴ x = 9392/9
= 1043
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the probability that a radish seed will germinate is 0.7. a gardener plants seeds in batches of . find the standard deviation for the binomial random variable x, the number of seeds germinating in each batch. round to three decimals.
Answers
The standard deviation for the number of seeds germinating in each batch is 1.3.
Given, the probability that a radish seed will germinate is 0.7.
In binomial distribution, standard deviation is given as:
σ = √np(1-p)
Where "n" is the number of observations
"p" is probability of getting success
We are given that:
Total batches of seed = 8
Probability that a radish seed will germinate is 0.7
Here success is getting radish seed germinated
Then, the standard deviation for the number of seeds germinating in each batch.
Plugging in values in formula, we get:
σ = √(8)(0.7)(1-0.7)
= √(8)(0.7)(0.3)
= √1.68
= 1.29614 ≈ 1.3
Therefore the standard deviation for the number of seeds germinating in each batch is 1.3
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5x-19y= 14
How do you put this is slope intercept form
Answers
1. Subtract 5x on both sides
5x - 19y = 14
→ -19y = 14 - 5x
2. Divide both sides by -19
-19y = 14 - 5x
→ y = 5/19x - 14/19
The slope-intercept form is:
y = 5/19 - 14/19
In triangle GHJ, Angle G=25°, Angle H=46°, and h=37mm. Determine the length of side g to the nearest millimeter.
Answers
The length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.
Given that, in triangle GHJ, ∠G=25°, ∠H=46°, and h = 37 mm.
What is sine rule in triangle?The sine rule of a triangle is sin A/a = sin B/b = sin C/c.
From triangle GHJ
∠G+∠H+∠J = 180°
⇒ 25°+46°+∠J = 180°
⇒ ∠J = 109°
Using sine rule
sin 109°/g = sin 25°/37
⇒ 0.945/g = 0.4226/37
⇒ 34.965 = 0.4226g
⇒ g = 82.73 mm
⇒ g ≈ 83 mm
Therefore, the length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.
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The graph of g(x) is obtained by reflecting the graph of f(x)=−3|x| over the x-axis.
Which equation describes g(x)?
A:g(x)=3|x|
B:g(x)=−|x+3|
C:g(x)=|x+3|
D:g(x)=−3|x|
Answers
The equation of the graph after it is reflected is g(x) = 3|x|
How to determine the image of the reflected graph equation?The equation of the graph is given as
f(x) = -3|x|
The transformation rule is given as
Reflection over the x-axis
The mathematical representation of this transformation rule is
(x, y) = (x, -y)
The above transformation rule means that
g(x) = -f(x)
So, we have
f(x) = -3|x|
Substitute f(x) = -3|x| in g(x) = -f(x)
g(x) = -1 * -3|x|
Evaluate
g(x) = 3|x|
Hence, the equation of the reflected graph is g(x) = 3|x|
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Please help! Angle BA and BD are given. measure of CBD is 4x+52. Measure of angle ABC 8x-10. What measure of CBD.
Answers
Based on the definition of complementary angles, the measure of angle CBD is: 68°.
How to Find the Measures of Complementary Angles?If two lines are perpendicular to each other, they form a right angle. In the diagram given, we know that line BA is perpendicular to line BD, therefore the measure of angle ABD would be a right angle = 90°.
Thus, angle CBD and angle ABC are complementary angles because they form a right angle.
Therefore:
The measure of angle CBD + the measure of angle ABC = 90°.
Given:
Measure of angle CBD = 4x + 52
Measure of angle ABC = 8x - 10
Substitute
(4x + 52) + (8x - 10) = 90
Solve for x
4x + 52 + 8x - 10 = 90
Combine like terms
12x + 42 = 90
12x + 42 - 42 = 90 - 42
12x = 48
12x/12 = 48/12
x = 4
Find the measure of angle CBD by plugging in the value of x:
Measure of angle CBD = 4x + 52 = 4(4) + 52
Measure of angle CBD = 68°
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Isiah’s credit card statement shows a debt of $385. What value would represent this situation, and why?
Answers
Answer:
-385
a negative is nice
Step-by-step explanation:
Question 3 of 25
Imagine that you are given two linear equations in slope-intercept form. You
notice that the slopes are different, but the y-intercepts are the same. How
many solutions would you expect for this system of?
Answers
For this system of equations, there will be infinitely many solutions.
Two equations are said to represent a line when they have the same slope and y-intercept. In this instance, one equation is created by adding a constant to the other equation.
Such equations will lay on each other on a graph if we plot them since they represent the same line. We can claim that these equations have an endless number of solutions because every point on that line will satisfy both of the aforementioned equations.
Here's an illustration:
Eq. 1: 2x + y = 4.
4x + 2y Equals 8 in equation 2
The second equation is created by multiplying the previous equation by two, as can be seen if you look at the two equations. The same outcome will be obtained for both if we write them in slope intercept form, as illustrated below:
Equation 1's slope intercept form is y = -2x + 4
Equation 2's slope intercept form is 2y = -4x + 8 and y = -2x + 4
The y-intercept and slope of both equations are identical. Equation 2 applies to any place that satisfies Equation 1. We can therefore draw the conclusion that there are an endless number of solutions to two linear equations with the same slope and y-intercept.
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Answer:
1
Step-by-step explanation:
Alejandra wants to buy 12 ounces of gluten-free edible cookie dough that costs $1.25 per ounce. Select all equations that correctly represent how much Alejandra will pay for her cookie
dough, Y.
A) y = 12 x 1.25
B) y = 12/1.25
C) 12 + 1.25 = Y
D) 12 • 1.25 = Y
Answers
Answer:
A and D
Step-by-step explanation:
its A and D, trust
3 connecting lines are shown. Line A B is horizontal. Line A C is about half the length of A B. Line B C is about one-third of the length of A B. Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
Answers
We cannot form a triangle with the given three segments.
Because BC + AC < AB
∴ the three segments do not form a triangle,
What exactly is a Triangle?A triangle is a polygon that has three sides, three angles, and three vertices.A triangle's basic property is that the sum of the lengths of its two sides should be greater than the length of its third side.Here given ,
A, B, and C are the three points.
These three points must be used to form a triangle.
AC is equal to (1/2) of AB in length.
BC equals (1/3) of AB in length.
The third side's length is AB.
According to the property, the sum of the lengths of the two sides should be greater than the length of the third side.
Because the side AB is the largest, the sum of AC and BC should be greater than AB.
AB > BC + AC
(1/2) AB + (1/3) AC equals AB.
As a result, BC + AC AB cannot form a triangle.
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PLEASE HELP!!!!!!
1. Spencer went to the county fair and spent his money only on ride tickets and fair admission. He bought 17 tickets for the rides and spent a total of $30.75 at a county fair. The county fair charges $1.25 per ticket for the rides and the price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets. (a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (b) Explain your answer to Part 1a.
Answers
The linear equation that represents how much he spent is given as y = 1.25x + 9.55
Linear EquationA linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear function is given y = mx + c
m = slopec = interceptTo solve this problem, we can simply use the values given to write a linear equation.
Can be written as
[tex]30.75 = 1.25x + c\\x = 17\\30.75 = 1.25(17) + c\\c = 30.75 - 21.25\\c = 9.55\\[/tex]
The equation to represent this problem is y = 1.25x + 9.55
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Solve for x.
A) 6
B) 7
C) 4
D) 5
Answers
your answer is D) 5!
Julian has 51 books in a bookcase with
2 shelves. The bottom shelf has 3 more than
twice as many books as the top shelf. How
many books are on each shelf?
Answers
There are 16 books on the shelf
How to calculate the number of books on the shelf ?Let y represent the number of books on the top shelf
The number of books on the bottom shelf = 2y + 3
The total number of books in the bookcase is 51
The number of books on each shelf can be calculated as follows
y + (2y+3)= 51
y +2y +3= 51
collect the like terms
3y + 3= 51
3y= 51-3
3y= 48
divide by the coefficient of y which is 3
y= 48/3
y= 16
Hence there are 16 books on each shelf
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identify the irrational numbersselect all that apply1. 0.7292. 0.01953473. -124. [tex] \sqrt[]{18} [/tex]
Answers
The options are analyzed as follows:
1: The overline 0.729 means:
[tex]0.729729729\ldots[/tex]This is a non- terminating recurring decimal hence it is rational.
2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.
3. The number -12 is rational since it is an integer.
4.The number 4.565656... is a non terminating recurring decimal hence it is rational.
5. The number given by:
[tex]\sqrt[]{18}=3\sqrt[]{2}=4.242640687\ldots[/tex]Since square root of 2 is irrational and 3 is rational the product is irrational.
Also the decimal is non terminating non recurring hence it is irratonal.
So the options 2 and 5 are irrational.
help for points please and thanks
Answers
the tallest living man at one time had a height of cm. the shortest living man at that time had a height of cm. heights of men at that time had a mean of cm and a standard deviation of cm. which of these two men had the height that was more extreme?
Answers
Thus here, the height of the tallest person is more extreme as per the z-score.
What is the z-score?
Z-scores let statisticians and traders know whether a score falls within the norm for a given data set or deviates from it.Analysts can also modify scores from multiple data sets using Z-scores to create scores that are more accurately compared to one another.You may determine how many standard deviations you are from the mean by looking at the absolute value. A z-score of zero indicates that a value is on the mean. A Z-Score of +1 indicates that the value is one standard deviation above the mean.Formula for z-score: [tex]\frac{X-\mu }{\sigma }[/tex]
Z-score for the tallest person = {258-176.07}/{7.32}
= 11.1926.
Similarly, Z-score for the shortest person = -7.0587.
The more the absolute value, the more extreme the value.
Thus here, the height of the tallest person is more extreme as per the z-score.
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EXPRESS THE TRIG RATIOS AS FRACTIONS IN SIMPLEST TERMS (50 POINTS)
Answers
The value of cos F and sin E are equal to one another or they are equal angles since they have the same ratios
Trigonometric RatioTo solve this problem, we have to use the respective trigonometric ratio required.
Using SOHCAHTOA, we can use this to solve for all the unknown.
cos F
To solve for cos F, we can use the cosine value of F
[tex]cos F = \frac{adjacent}{hypothenuse} \\cos F = \frac{\sqrt{39} }{20}[/tex]
Sin E
To solve for sin E, we can use the Sine value of E
[tex]sin E = \frac{opposite}{hypothenuse} \\sin E = \frac{\sqrt{39} }{20}[/tex]
The value of cos F and sin E are the same.
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. Estimate: 186,231 + 88,941
Answers
To estimate the sum, we need to round the decimals as:
186,231 ≈ 186
88,941 ≈ 89
So, we sum 186 and 89 as:
186 + 89 = 275
Therefore, the estimated sum of 186,231 + 88,941 is 275
Answer: 275
275,000
What is the slope of the line represented by the table of value
Answers
Answer:
The slope of the line represented by the table value is -8/5
Step by step
See attachment
You can find the change in y over change in x
By subtracting the x values, one from the other, the rate is consistent 5.
By subtracting the y values, one from the other, the rate is consistent -8
Slope is y/x so -8/5.
You can also chose two pairs of coordinates and find change in y over change in x.
(-7, 9)
(-2,1)
1 - 9 over -2 - -7
-8/5 slope
how many ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box?
Answers
By the concept of permutation and combinations there are 7,484,400 ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box.
What are permutation and combination?Putting things or numbers in order is known as a permutation. Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.
The number of ways to sort identifiable things into indistinguishable bins is 11 or "double-factorial," which is defined as 11 (as shown). Given that the bins are distinct, that is multiplied by 6! Following are several explanations for the 11!!11!! There are 11 potential companions for the chosen "first" object. Following that decision, there will be 10 items left, which indicates that the next arbitrary object will have 9 companions. then do it again. A more traditional strategy would be this. The objects that fit in the first container have 122 possibilities, the second bin has 102 possibilities, and so on.
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if a number is chosen at random from the following list, then what is the probability that it is prime? (A prime number can only be divided by 1 and itself) 2, 3, 5, 7, 11, 13, 17, 19?
Answers
The probability that the chosen number from the list of the given number is prime number is 1.
The probability of an event E is defined as,
P(E) = Total favorable outcomes/Total possible outcomes
In this case,
The sample space is 2, 3, 5, 7, 11, 13, 17, 19.
Total possible outcomes are 8.
One number is chosen at random, the chosen number has to be a prime number,
Total prime number in the sample space are 2, 3, 5, 7, 11, 13, 17, 19.
So. total favorable outcomes are 8.
So, the probability that the chosen number is prime number,
P(E) = 8/8
P(E) = 1.
So, the probability of the chosen number to be a prime number is 1.
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50% of the insects are ants and 50% orbitals if there are 19 ants how many insects are there
Answers
There are a total of 38 insects.
It is given that 50% of the insects are ants.It is said that 50% of the insects are beetles.There are 19 ants out of the total insects.Let the total number of the insects be "x".The percentage of both the insects is given.Also, the exact number of one of the insects is given.From the above data, we can easily form an equation in terms of percent and the exact number of insects.We know that 50% of all the insects are ants.50% of "x" is 19.0.5*x = 19x = 38Hence, the total number of insects is 38.To learn more about percentage, visit :
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Marcy is 5 ft 5 in. tall. To find the height of a building, she measured her shadow and the building's shadow. What is the height h of the building?
Answers
Marcy is a 5-ft-5 in. She took measurements of both her own shadow. h=520 is the building's height.
Given that,
Marcy is a 5-ft-5 in. She took measurements of both her own shadow and that of the structure in order to determine its height.
We have to find what is the building's height, h.
Use the fact that 1 feet is equivalent to 12 inches to convert all measures to a single unit, inches.
We convert
MN=26×12=312 inches.
QR=3×12+3=36+3=39 inches.
PQ=5×12+5=60+5=65inches.
Since the Sun's rays that generate LN and PR are parallel, they are also parallel. the angles they make with the earth as a result are consistent:
∠N≅∠R
The Right Angle Congruence Theorem illustrates ∠M≅∠Q.
As a result, according to the Angle-Angle Similarity △LMN~△PQR
Calculate a ratio using the known lengths of the sides and the unknown length (height of the building).
PQ/QR=LM/MN
65/39=h/312
h=65×312/39
h=20280/39
h=520
Therefore, h=520 is the building's height.
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Emma rotated trapezoid LMNO 90° clockwise on the coordinate plane. If angle M is 110°
and angle O is 70°, what is the degree measurement of angle M'?
Answers
110
Step-by-step explanation:
the answer is 110 cause i don't know I just searched the answer for you you welcome
DUE TODAY ASAP!! Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will Megan and Connor have saved the same amount?
Answers
In 14 weeks they both will have saved the same amount if Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the number of weeks on which Megan and Connor have saved the same amount.
Total amount(Megan) = 50 + 5.50x
Total amount(Connor) = 18.50 + 7.75x
Equate both equations:
50 + 5.50x = 18.50 + 7.75x
2.25x = 31.5
x = 14
Thus, in 14 weeks they both will have saved the same amount if Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week.
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