The frequency is 1 /period = 1 / [ 2 pi ]
Final answer:
The frequency of the function f(x) = 2cos(x) - 4 is 1/(2π), meaning the function completes one full cycle every 2π units along the x-axis.
Explanation:
The frequency of a function in mathematics describes how often the function repeats its pattern over a certain interval. In the case of the function f(x) = 2cos(x) - 4, the frequency is determined by the coefficient of x inside the cosine function. The standard form of the cosine function is cos(bx), where the frequency is |b|/(2π), because a sine or cosine function oscillates between +1 and -1 every 2π radians, as denoted in Figure 16.10.
In this instance, b = 1 since there is no coefficient multiplying x inside the cosine. Therefore, the frequency of the function f(x) is |1|/(2π), which simplifies to 1/(2π). This frequency means that the function completes one full cycle every 2π units along the x-axis.
If John invests $600 in a savings account earning interest at a rate of 6% compounded semiannually how much will be in account after 8 years
Answer:
$962.82 will be in John's account after 8 years if compounded semiannually.
Step-by-step explanation:
The formula used to find the amount after 8 years is:
A = P(1+ r/n)^nt
Where A = future value
P= principal value
r = interest rate ( in decimals)
n = no of times interest is compounded
t = time
Putting the values:
P = $600
r = 6% = 0.06
n = 2
t = 8
A= 600 *(1+0.06/2) ^2(8)
A= 600 *(1.03) ^16
A =600*1.605
A = 962.82
So, $962.82 will be in John's account after 8 years if compounded semiannually.
Describe the shape of the data distribution.
Answer: Positively Skewed
Step-by-step explanation: I believe it looks to me like it's positively skewed. If you Google how negatively skewed and positively skewed distributions look like, I think it would help you. But hope this helped! :)
Answer: Symmetric
Step-by-step explanation:
For a box plot , a symmetric data set displays the median in the middle of the box.
Also, We know that a distribution is said to be skewed if it has longer whisker at one side than the other.
But in the given box plot , the median looks at the middle of the box.
Therefore, the given box-plot describes a symmetric distribution.
everyone at camp takes turns being on lunch duty. You and your friend are in charge of making sandwiches. you both can make 1 sandwich in two minutes. Your friend arrives 10 minutes earlier than you and starts making sandwiches.
a. write equations that model the number of sandwiches made as a function of the number of minutes it takes you and your friend to each make sandwiches.
b. how many sandwiches will each of you make in 20 minutes?
c. how are the graphs of the equations from part (a) related? justify your answer.
help
Answer:
Step-by-step explanation:
A. you: Number of sandwiches = .5 * time
friend: # of sandwiched = .5 * t + 5
B. Your friend makes 10 and you make 5
The equations y1=x/2 and y2=(x+10)/2 model the sandwich-making process, where y1 and y2 are the number of sandwiches you and your friend make respectively. In 20 minutes, you can make 10 sandwiches and your friend can make 15 sandwiches. The graphs of these equations are lines with the same slope, indicating the same rate of sandwich-making but different start times.
Explanation:Let's define the variables first. Let's say x stands for time in minutes, and y1 and y2 stand for the number of sandwiches you and your friend make, respectively.
a) The equations modeling the number of sandwiches made as a function of time would be y1 = x/2 for you (since you make one sandwich in 2 minutes) and y2 = (x+10)/2 for your friend (since your friend starts 10 minutes earlier than you).
b) If x is 20 minutes: for you, replacing x in the equation y1 = x/2, we get the number of sandwiches you make (y1) is 20/2 = 10 sandwiches. For your friend, replacing x in the equation y2 = (x+10)/2, we get the number of sandwiches your friend makes (y2) is (20+10)/2 = 15 sandwiches.
c) In comparison, the graphs of the two equations are lines with the same slope (0.5), indicating the same sandwich-making rate. However, they have different y-intercepts, signifying that your friend started earlier and therefore made more sandwiches.
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Which expression is equivalent to 5(2x-7)?
Answer:
E
Step-by-step explanation:
The given expression is
5(2x-7)
In order to check the options we will have to simplify the expression so that we can match with the answers.
To simplify the expression , first we have to multiply the 5 written outside the bracket with the terms inside the bracket i.e. 2x -7
So,
=> 5(2x-7)
Multiplying 5 inside
=> (5)(2)x - (5)(7)
=> 10x - 35
So, comparing with the given options, we observe that option E is the correct answer..
The scatterplot below was created from a table of values and represents the relationship between the number of seconds spent doing sit ups and the number of steps completed from some of the members of a physical education class
Answer:
The answer is 8
Step-by-step explanation:
count them
There are 8 data points plotted in the given scatterplot. The given scatterplot gives the relationship between the given variables.
What the scatterplot represents?The scatterplot represents the relationship between the two sets of data values from a table. It takes the data values as the coordinate points to plot the graphThese data points on the graph show either an increase or a decrease or sometimes no change.Counting the data points in the given scatterplot:The given graph is a scatterplot between two variables
The given plot shows the graph is increasing as the time increases. And in the graph, there are 8 data points.
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In a circle of radius 30 inches, a central angle of 35° will intersect the circle
forming an arc of length
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ °rees\\ \cline{1-2} r=&30\\ \theta =&35 \end{cases}\implies s=\cfrac{\pi (35)(30)}{180} \\\\\\ s=\cfrac{35\pi }{6}\implies s\approx 18.32596[/tex]
Answer: 18.33 inches
Step-by-step explanation:
A P E X
which type of graph would display the volunteer totals for each of the 20 clinics
Answer:A dot plot.
Step-by-step explanation: it shows the 5 number summary.
The correct answer is dot plot!
Given L (-4,3) and M (-7,-2) what is the length of LM?
A. 34 square rooted
B. 8 squared rooted
C. 74 squared rooted
D. 122 squared rooted
A. 34 square rooted
[tex]lm = \sqrt{34} [/tex]
Using interval notation , identify the domain for the function!!! Math 3 - 10 points. Help needed
Answer:
The domain by the interval notation is (-∞ , 3)∪(3 , 4)∪(4 , ∞) ⇒ 3rd answer
Step-by-step explanation:
* Lets revise how to find the domain of the function
- The domain is all values of x that make the expression defined
- To find where the expression is undefined put the denominator
equal 0, to get the values of x which make denominator equal to 0
- The domain will be all the real number except those values
* Now lets solve the problem
∵ f(x) = (x² - 9)/(x² - 7x + 12)
- Let the denominator x² − 7x + 12 equal to 0
∵ x² − 7x + 12 = 0 ⇒ factorize it
- Consider the form x² + bx + c
- Find a pair of integers whose product is c and whose sum is b
- In this case, whose product is 12 and whose sum is −7
- They are -3 and -4
- Write the factored form using these integers.
∴ (x -3)(x - 4) = 0 ⇒ put each bracket = 0
∴ x - 3 = 0 or x - 4 = 0
∵ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∵ x - 4 = 0 ⇒ add 4 to both sides
∴ x = 4
∴ The domain of f(x) is all real number except 3 and 4
* The domain by the interval notation is
(-∞ , 3)∪(3 , 4)∪(4 , ∞)
If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ?
2 square root of 2 over 3
negative 2 square root of 2 over 3
2 square root of 2
negative 2 square root of 2
Answer:
2√2 / 3 (first answer choice)
Step-by-step explanation:
If tan Ф < 0, then Ф must be in either Quadrant II or Quadrant IV.
If sin Ф = +1/3, then Ф (for this problem) is in Quadrant II.
Remembering that sin Ф = opp / hyp = 1 / 3, we use the Pythagorean Theorem to find the adj side:
adj² + 1² = 3², or
adj² + 1 = 9, or adj² = 8. Since Ф is in Quadrant II, adj is negative.
The value of cos Ф = adj / hyp = √8 / 3 = 2√2 / 3
Which of the following data could be graphed using a dot plot?Select all that apply.
Data suitable for dot plots are quantitative and involve individual values. Options A), D), E), and F) can be graphed using dot plots because they involve numerical data where each dot represents an individual value. Options B) and C) involve categorical data, which are not typically displayed using dot plots.
A dot plot is a type of graphical display that uses dots to represent the frequency or distribution of data points along a number line. It is suitable for displaying quantitative data that consists of individual values. Let's analyze each option:
A) Time taken to complete a test:
Yes, this data could be graphed using a dot plot. Each dot would represent a student's time taken to complete the test, and the position of the dot along the number line would correspond to the time taken.
D) Number of cars in a household:
Yes, this data could also be graphed using a dot plot. Each dot would represent a household, and the position of the dot along the number line would correspond to the number of cars in that household.
E) Number of siblings:
Yes, the number of siblings could be graphed using a dot plot. Each dot would represent an individual, and the position of the dot along the number line would correspond to the number of siblings that individual has.
F) Distance driven to school:
Yes, this data could also be graphed using a dot plot. Each dot would represent a student, and the position of the dot along the number line would correspond to the distance driven to school by that student.
Options B) Favorite pet and C) Zip Code do not lend themselves well to dot plots. Favorite pet is a categorical variable, and dot plots are typically used for displaying quantitative data. Similarly, zip codes are categorical and do not have a natural numerical order suitable for a dot plot.
So, the data that could be graphed using a dot plot are A), D), E), and F). Each dot plot would display the distribution of values for the respective variables, providing a visual representation of the data's spread and concentration.
Complete question :- Which of the following data could be graphed using a dot plot? Select all that apply.
A) Time taken to complete a test
B) Favorite pet
C) Zip Code
D) Number of cars in a household
E) Number of siblings
F) Distance driven to school
The amount of an 18% tip can be found by multiplying the bill by 0.18. Which of the following equations could be used to find the amount of a bill that has a tip of $9.72?
Answer: $54
Step-by-step explanation:
18% of $54 is $9.72
Answer:
Bill amount is $54
Step-by-step explanation:
Tip is a gratuity and amount of money which a customer gives for some specific services workers on the the work they performed. It is the additional amount to the original value of the service
As per given data
Percentage of Tip = 18% = 0.18
Formula for Tip
Tip = Bill amount x Tip rate
$9.72 = Bill amount x 0.18
Bill amount = $9.72 / 0.18
Bill amount = $54
If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
40 cm2
80 cm2
200 cm2
400 cm2
Area is defined as a product of sides when we talk about squares.
[tex]A=a\cdot a=20\cdot20=\boxed{400}[/tex]
The area of the front cover of notebook is 400 centimetres squared.
Hope this helps.
r3t40
Answer:
400 cm
Step-by-step explanation:
if you stand at the beach and a wave crest hits you every seven seconds, what is the period of this wave?
The period of the wave is this explanation: A group will 'modulate' the wave amplitude; it's like another long wave on top. So the first wave in a group is tiny, the next one is bigger and so on until you get the biggest one in the middle of the group. Then they get smaller again. The last one is tiny, so the biggest wave in the group is in the middle, and if there are 14 waves in a group, the seventh wave is the biggest.
6. A baker wants to reduce the amount of sugar in his cake recipes. He decides to reduce the amount
used in 1 cake by 1/2 cup. He then uses 4 cups of sugar to bake 6 cakes.
How much sugar was originally in each cake recipe?
To find the original amount of sugar in each cake recipe, we can set up a proportion and solve for x. The original amount of sugar in each cake recipe was 7/6 cups.
Explanation:To solve this problem, we can use a proportion to find the original amount of sugar in each cake recipe. Let x represent the original amount of sugar in each cake recipe. We know that reducing the amount of sugar by 1/2 cup from 1 cake results in 4 cups of sugar for 6 cakes. So we can set up the proportion:
(x - 1/2) / 1 = 4 / 6
Cross-multiplying, we get (x - 1/2) * 6 = 4 * 1. Simplifying further, we have 6x - 3 = 4. Adding 3 to both sides, we get 6x = 7. Finally, dividing both sides by 6, we find that x = 7/6 cups of sugar.
Therefore, the original amount of sugar in each cake recipe was 7/6 cups.
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Which of these triangle pairs can be mapped to each other using a single reflection?
Answer:
the first option is correct
Step-by-step explanation:
State whether the given measurements determine zero, one, or two triangles. C = 37°, a = 16, c = 14
Two triangles: b ≈ 2.62 or 22.94
Answer:
sides are a = 16 c = 14 b =22.96
angles are A = 43.39° B = 99.61° C = 37°
Step-by-step explanation:
using sine law of triangle,
[tex]\frac{sin A}{a} = \frac{Sin B}{b}= \frac{sinC}{c}[/tex]
using,
[tex]\frac{sin A}{a} = \frac{sinC}{c}[/tex]
given that,
C= 37° a = 16 c = 14
now,
[tex]\frac{sin A}{16} = \frac{sin37^o}{14}[/tex]
sin A = 0.687
A = 43.39°
hence B = 180° - (43.39° + 37°)
B = 99.61°
[tex]\frac{sin 43.39^o}{16} = \frac{sin99.61^o}{b}[/tex]
b = 22.96
Hence, there will be only one triangle which will form and there
sides are a = 16 c = 14 b =22.96
angles are A = 43.39° B = 99.61° C = 37°
Please help I will mark BRAINLIEST
Answer:
x ≤ -4
Step-by-step explanation:
Less than or equal to ≤
x ≤ -4
Factor x10 - y2
I need the answer
Answer:
(x^5 - y)(x^5 + y)
Step-by-step explanation:
What is the average rate of change of the function over the interval x = 0 to x = 4? f(x) = 2x - 1
Enter your answer in the box.
Answer:
2
Step-by-step explanation:
The average rate of change of a function over the interval a to b is:
(f(b) − f(a)) / (b − a)
In this case:
(f(4) − f(0)) / (4 − 0)
(7 − -1) / 4
2
The weight, in pounds, of each wrestler on the high school wrestling team at the beginning of the season is listed below.
178 142 112 150 206 130
A. What is the median weight of the wrestlers?
15 points!!!!
Step 1: Order the numbers from least to greatest
112, 130, 142, 150, 178, 206
The two middle numbers are 142 and 150.
The number between 142 and 150 is 146.
The median weight is 146 pounds.
The median weight of the wrestlers is 146 pounds.
To find the median weight, we need to arrange the weights in ascending order and identify the middle value(s).
Arrange the weights in ascending order:
112, 130, 142, 150, 178, 206
Since there is an even number of weights (6), the median is the average of the 3rd and 4th weights.
The 3rd weight is 142, and the 4th weight is 150.
Calculate the median:
(142 + 150) / 2 = 292 / 2 = 146
Please help me. I'm so desperate not even my group chat is helping
Answer:
5 between Martin's place and the school
Step-by-step explanation:
I don't know if you can draw a diagram from by directions, but you can try. It will help you to see the problem.
Draw
Draw a line that looks like this on your paper.
<===============:
school X Martin's place
Now draw a line going upwards from the arrow head.
∧ Haley's place.
|
|
|
|
|
|
<=============:
school x Martin's place
Label the distance from the school to Haley's place as 12
I can't draw a line between martin's place and Haley's but you can. Label it as 13
So the givens are
c = distance between Haley's place and Martin's = 13
b= distance from the school to Haley's is 12
a = ? Distance from Martin't and the school = x
Formula
c^2 = a^2 + b^2
Solution
13^2 = 12^2 + a^2
169 = 144 + a^2 Subtract 144 from both sides.
169 - 144 = 144 - 144 + a^2
25 = a^2
sqrt(25) = sqrt(a^2)
a = 5
The distance from Martin's place to the school (a) is 5 units, determined using the Pythagorean theorem with given values of 12 units from the school to Haley's place (b) and 13 units between Haley's and Martin's places (c).
Distance from the school to Haley's place (b): 12
Distance between Haley's place and Martin's place (c): 13
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substitute the given values:
13^2 = a^2 + 12^2
Simplify the equation:
169 = a^2 + 144
Subtract 144 from both sides:
25 = a^2
Take the square root of both sides:
a = √25
Simplify:
a = 5
Therefore, the distance from Martin's place to the school (a) is 5 units.
Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.
Answer:
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
Step-by-step explanation:
Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230.
Step 1: P = 200, r = 5, t = 3
Step 2: I = 200*0.05* 3
Step 3: I = 30
Step 4: 30 + 200 = 230
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
Above it is given, that annual compound interest rate of 5%
So, she should have calculated using the compound interest formula.
[tex]A=p(1+r/n)^{nt}[/tex]
So, amount becomes :
[tex]A=200(1+0.05)^{3}[/tex]
[tex]A=200(1.05)^{3}[/tex] = $231.53.
Answer:
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
Step-by-step explanation:
Just did it
The surface area of a sphere having a diameter of 8 inches is:
64 is the correct answer
Answer: [tex]A = 201.06\ in^2[/tex] or [tex]A = 64\pi\ in^2[/tex]
Step-by-step explanation:
The surface area of a sphere is calculated by the following formula
[tex]A = 4\pi r^2[/tex]
Where r is the radius of the sphere
In this case we know that the diameter d of the sphere is
[tex]d=8\ inches[/tex]
So the radius r is:
[tex]r=\frac{d}{2}\\\\r=\frac{8}{2}\\\\r=4\ inches[/tex]
So the surface area of the sphere is:
[tex]A = 4\pi (4)^2[/tex]
[tex]A = 64\pi[/tex]
[tex]A = 201.06\ in^2[/tex]
m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
Answer:
Final answer is x=23.
Step-by-step explanation:
Given that m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
We know that sum of all three angles of a triangle equals 180 degree.
So we can write equation:
m∠A + m∠B + m∠C = 180°
60° +(3x − 2)° + (2x + 7)° = 180°
60 +3x − 2 + 2x + 7 = 180
67 +5x − 2 = 180
65 +5x = 180
5x = 180 - 65
5x = 115
[tex]x=\frac{115}{5}[/tex]
x=23
Hence final answer is x=23.
How does multiplying a vector by a scalar value of -pi / 4 change the vector?
Answer:
The vector will change in direction and decrease in magnitude
Step-by-step explanation:
Given:
vector multiplication by -π/4
-π/4= -0.785
Due to the negative sign "-", the, vector will change/reverse its direction.
And as of the magnitude, 0.785<1 hence the magnitude of vector will be decreased by this factor !
Help please? I can’t figure out how to find the value of each trig ratio.
Answer:
51.34
Step-by-step explanation:
First, things first, identify the opposite, adjacent, and hypotenuse.
Since you are trying to find the value of x, the length measuring 4 is the adjacent because it is one of the lengths that creates that angle measure you are trying to find. 5 is the opposite because the angle is on the opposite side of the length. The [tex]\sqrt{41}[/tex] is the hypotenuse.
Now, which trig equation do you want to use?
sin(x) = opposite / hypotenuse
cos(x) = adjacent / hypotenuse
tan(x) = opposite / adjacent
Let's first try solving with sine.
sin(x) = 5/[tex]\sqrt{41}[/tex]
Since you want to find the angle, you have to use the [tex]sin^{-1} (\frac{5}{\sqrt{41}} )=x[/tex]
Plug it into your calculator, then you should get something like this: 51.34019175.
That is the angle measurement of x.
Let's use cosine.
cos(x) = 4/[tex]\sqrt{41}[/tex]
Again, since you want to find the angle, you have to use the [tex]cos^{-1} (\frac{4}{\sqrt{41}} )=x[/tex]
Plug it into your calculator, then you should get something like this: 51.34019175.
You realize that it gave the same answer, right? Yep, let's also do tangent.
tan(x) = 5/4
Again, since you want to find the angle, you have to use the [tex]tan^{-1}(\frac{5}{4}} )=x[/tex]
Type it into the calculator and you should get 51.34019175 again!
A travel website sells tickets to a city for two airlines. Among those buying tickets, 20% fly airline A, and 80% fly airline B. If the price of a ticket is $600 for airline A and $360 for airline B, what is the expected revenue of an airline ticket sold by this travel website? (Note: Airline A has much more desirable departure times than Airline B, so it charges more.)
Answer:
The expected revenue of an airline ticket sold by this travel website is $408
Step-by-step explanation:
For the revenues per ticket we have;
airline A; 600
airline B; 360
For the probability of choosing the airlines we have;
airline A; 20% = 0.2
airline B; 80% = 0.8
Therefore, the expected revenue of an airline ticket sold by this travel website is;
600(0.2) + 360(0.8) = 408
Therefore, the expected revenue of an airline ticket sold by this travel website is $408
Solve the word problems using systems.
The sum of two numbers is 842. The difference is 314. Find the numbers.
Answer:
The numbers are 578 and 264
Step-by-step explanation:
Let
x-----> the greater number
y----> the smaller number
we know that
x+y=842 -----> equation A
x-y=314 -----> equation B
Adds equation A and equation B
x+y=842
x-y=314
------------
x+x=842+314
2x=1,156
x=578
Find the value of y
578+y=842
y=842-578=264
Find the surface area of a square pyramid with a length of 5 cm and a slant height of 8 cm
Answer:
105 square cm.
Step-by-step explanation:
The surface area of a square pyramid is
[tex]SA=A_{base}+4A_{lateral \ side}.[/tex]
1. The base is the square with side length of 5 cm, thus
[tex]A_{base}=5\cdot 5=25\ cm^2.[/tex]
2. The lateral side is the triangle with the base of 5 cm and the height of 8 cm. Thus,
[tex]A_{lateral \ side}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}=\dfrac{1}{2}\cdot 5\cdot 8=20\ cm^2.[/tex]
Now, the surface area of the pyramid is
[tex]SA=25+4\cdot 20=105\ cm^2.[/tex]
Answer:
The surface area of a square pyramid is: 105 cm^2
Step-by-step explanation:
The surface area of a pyramid is given by the following formula
[tex]A = l ^ 2 + 4 * (0.5) lh[/tex]
Where
l is the length of one of the sides of the square base
h is the height of the pyramid
We know that h = 8 cm and l = 5 cm
[tex]A = 5 ^ 2 + 4 * (0.5) * 5 * 8\\\\A = 25 + 2 * (40)\\\\A = 105\ cm ^ 2[/tex]