Explanation:
A function is even if f(x) = f(-x), so in this case, f(x) and f(-x) are equal to:
[tex]f(x)=2x+x^3[/tex][tex]\begin{gathered} f(-x)=2(-x)+(-x)^3 \\ f(-x)=-2x-x^3 \end{gathered}[/tex]Type the correct answer in the box. The area is ___ (BLANK) square units.
The figure is a trapezoid, and the area of a trapezoid can be calculated with the formula below:
[tex]A=\frac{(B+b)h}{2}[/tex]Where B is the greater base, b is the smaller base and h is the height.
To find the measure of the smaller base, we need to find the missing piece to the right of the value "3 units" (let's call it x).
To calculate it, we can use the total length of the greater base:
[tex]\begin{gathered} 9+x+3=21\\ \\ 12+x=21\\ \\ x=21-12\\ \\ x=9 \end{gathered}[/tex]Therefore the smaller base is 3 + 9 = 12 units.
Now, calculating the trapezoid area, we have:
[tex]A=\frac{(21+12)5}{2}=\frac{33\cdot5}{2}=82.5\text{ u^^b2}[/tex]A tela telephone company offers two different types of billing the First Choice was to pay $10 per month plus $0.09 per MB of data the second choice is to pay $16 per month plus $0.07 per MB of data part a writing system of equations to model the situation the total cost for 1 month with each company Part B how many MB of data would you have to use in one month in order for both plans to cost the same amount explain how you determine your answer
Hi, can you help me answer this question please, thank you
We have the following information from the question:
[tex]\begin{gathered} sample\text{ size, n=18} \\ \text{standard deviation=0.4} \\ \text{sample mean, }\bar{\text{x}}=\frac{sum\text{ of data values}}{\text{number of data values}} \\ \bar{x}=\frac{3149.94}{18} \\ \bar{x}\cong175 \end{gathered}[/tex]a) To get the critical value, we would find the significance level first.
Thus, we have:
[tex]\begin{gathered} \text{Significance level, }\alpha=1-confidence\text{ interval} \\ C.I=80\text{\%=0.8} \\ \alpha=1-0.8 \\ \alpha=0.2 \end{gathered}[/tex][tex]\begin{gathered} \text{Critical value=Z}_{\frac{\alpha}{2}}=Z_{\frac{0.2}{2}}=Z_{0.1}=1.28\text{ ( from the z-table)} \\ \text{Therefore, critical value=}\pm\text{1.28}0 \end{gathered}[/tex][tex]\begin{gathered} S\tan dard\text{ deviation of the sample mean, }\sigma_{\bar{x}}=\frac{\sigma}{\sqrt[]{n}} \\ \sigma_{\bar{x}}=\frac{0.4}{\sqrt[]{18}}=0.0943 \end{gathered}[/tex]b) To find the confidence interval, we have to obtain the Margin of Error first.
[tex]\text{Margin of Error,E}=\text{critical value}\times\text{standard deviation of the sample mean(standard error)}[/tex][tex]\begin{gathered} E=1.28\times0.0943 \\ E=0.1207 \end{gathered}[/tex]Therefore, the Confidence Interval is:
[tex]\bar{x}-E<\mu<\bar{x}+E[/tex][tex]\begin{gathered} 175-0.1207<\mu<175+0.1207 \\ 174.88<\mu<175.12 \end{gathered}[/tex]Pre calculus 28.An object is traveling around a circle with a radius of 3 feet. It is completing 1 full revolutionevery 5 seconds. What is the linear speed (in ft/sec) and the angular speed (in rad/sec)?
We need to find the linear and the angular speeds of an object traveling around a circle.
The radius r of the circle is 3 feet. Thus, the perimeter p of the circle is:
[tex]\begin{gathered} p=2\pi r \\ \\ p=2\pi(3\text{ ft}) \\ \\ p=6\pi\text{ ft} \end{gathered}[/tex]Also, we know that the object completes one full revolution every 5 seconds.
Thus, to find the linear speed V, we need to divide the number of feet it travels by the number of seconds it takes:
[tex]\begin{gathered} V=\frac{p}{5\text{ sec}} \\ \\ V=\frac{6\pi\text{ ft}}{5\text{ sec}} \\ \\ V=1.2\pi\text{ ft/sec} \end{gathered}[/tex]ow, tnotice that the complete revolution has 2π radians.
Then, to find the angular speed ω, we need to divide the number of radians it travels by the number of seconds it takes:
[tex]\begin{gathered} \omega=\frac{2\pi\text{ rad}}{5\text{ sec}} \\ \\ \omega=0.4\pi\text{ rad/sec} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \text{ linear speed: }1.2\pi\text{ ft/sec} \\ \\ \text{ angulat speed: }0.4\pi\text{ rad/sec} \end{gathered}[/tex]7.Use the model to predict the number of people infected in 15 days.Answer:
Step 1:
The model of the table is shown below:
Step 2:
The equation of the model is
y = 140.6t + 371.6
Step 3:
To predict the number of people infected in 15 days, substitute t = 15
[tex]\begin{gathered} y\text{ = 140.6 }\times\text{ 15 + 371.6} \\ \text{y = 2109 + 371.6} \\ \text{y = 2480}.9 \\ y\text{ = 2481} \end{gathered}[/tex]Final answer
2481
what is the value of x in this triangle?A. 70B. 63C. 93D. None of the above
The sum of the angles in a triangle is 180 degrees. It means that
110 + 5x + 2x = 180
110 + 7x = 180
7x = 180 - 110
7x = 70
x = 70/7
x = 10
The value of x in the triangle is 10
Therefore, the correct option is
D. None of the above
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 41 and a standard deviation of 7. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 27 and 55?
The distribution of the number of phone calls with a mean of 41 and a standard deviation of 7. 95.44% is the percentage of the daily phone calls between 27 and 55.
Given that,
The distribution of the number of phone calls handled by each of the 12 receptionists in a mid-sized company is bell-shaped, with a mean of 41 and a standard deviation of 7. When applying the empirical rule.
We have to find what percentage of daily phone calls, on average, fall between the range of 27 and 55.
Mean=41
Standard deviation=7
x=27 and 55
Let, x₁=27 and x₂=55
First calculate z-score for the daily sample of 27 calls.
Formula z-score=(x-mean)/standard deviation.
z-score=(27-41)/7
z-score=-14/7
z-score=-2
So, z-score for the daily sample of 27 calls is -2.
Now, calculate z-score for the daily sample of 55 calls.
z-score=(55-41)/7
z-score=14/7
z-score=2
So, z-score for the daily sample of 55 calls is 2.
We can see that there is a change in z-score of 27 and 55 that is -2 and 2.
By using normal distribution table
The percentage of the daily phone calls between 27 and 55 =
0.9772-0.0228=0.9544
Therefore, 95.44% is the percentage of the daily phone calls between 27 and 55.
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Linus what to buy ribbon to make three bookmarks. One bookmark will be 14,5 inches long and the other two will be 9,25 inches long. How much ribbon should he buy in centimeters ( assume 1 inche=0,0254 meters)
Given:
ribbon's long as 14.5 inches one and 9.25 inches two ribbons.
Total ribbon needed = 14.5+2(9.25)
[tex]\text{Total ribbon needed}=14.5+18.5[/tex][tex]\text{Total ribbon needed}=33\text{ inches}[/tex][tex]\text{Total ribbon needed}=33\times0.0254\times100\text{ cm}[/tex][tex]\text{Total ribbon needed}=83.82\text{ cm}[/tex]Therefore, He should but 83.82 cm long ribbon.
if 32 is added to the data set which statement is true
We have a dataset: 13, 6, 13, 8, 2, 19, 11, 16, 17, with size n = 9.
We will add 32 to it.
In this case, the mean will be affected, as it depends on each individual value of the dataset. As the number is greater than all the numbers in the dataset, it will be greater than the actual mean. Then, the mean will increase.
The median may or may not change, depending on the values of the set.
Then, we can find the median before and after the addition.
First, we have to sort the data: 2, 6, 8, 11, 13, 13, 16, 17, 19.
The median, for a size n =9, will be located in the fifth place, so the median is 13.
Then, the dataset has 4 values below and 4 values above the median.
When we add 32, it will be the greatest value, so we will have a dataset of size n =10 and sorted as: 2, 6, 8, 11, 13, 13, 16, 17, 19, 32.
The median will be the average between the fifth and sixth place. Both values are 13, so the average, and therefore, the median will be also 13.
Then, in this case, the mean increases but the median does not.
Answer: The mean will increase and the median will remain the same.
What is the equation for the following graph?option 1: y=1/2x+2option 2: y= -1/2x+2option 3: y=2x+2option 4: y= -2x+2
The Solution.
The equation of the given graph is an equation of a line, which is given as the formula below:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m = slope} \end{gathered}[/tex]First, we shall pick any 2 coordinates in the given line graph:
(-4,0) and (0,2)
[tex]\begin{gathered} (-4,0)\rightarrow(x_1=-4,y_1=0) \\ (0,2)\rightarrow(x_2=0,\text{ }y_2=2) \end{gathered}[/tex]The slope ( m) is given as below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the appropriate values given above, we get
[tex]m=\frac{2-0}{0--4}=\frac{2}{4}=\frac{1}{2}[/tex]So, the equation of the graph is :
[tex]\begin{gathered} y-0=\frac{1}{2}(x--4) \\ \\ y=\frac{1}{2}(x+4) \\ or \\ 2y=x+4 \end{gathered}[/tex]Ngoc needs to mix a 10% alcohol solution with a 60% alcohol solution to create 200 milliliters of a 22.5% solution. How many milliliters of each solution must Ngoc use?
Ngoc needs to mix a 10% alcohol solution with a 60% alcohol solution to create 200 milliliters of a 22.5% solution. How many milliliters of each solution must Ngoc use?
Let
x -----> milliliters of solution at 10%
y -----> milliliters of solution at 60%
we have
x+y=200 ------> equation A
Remember that
10%=0.10
60%=0.60
22.5%=0.225
so
0.10x+0.60y=0.225(200) -----> equation B
solve the system of equation s A and B
Solve by graphing
using a graphing tool
see the attached figure
please wait a minute to draw the system
the solution is the point (150,50)
therefore
milliliters of solution at 10% is 150milliliters of solution at 60% is 50Four less than the amount of cents in a number of dimes
Question is attached, im confused on the steps to follow.
A year has 52 weeks.
Since Officer Milton has 3 weeks of vacation, then he works for 49 weeks a year.
Since he visits 3 groups per week, the total number of groups that he visists in a year is:
[tex]49\times3=147[/tex]Therefore, the correct choice is option C) 147.
What is A-B.If A is 32 and B is 30
To solve the exercise, we subtract the given numbers:
[tex]\begin{gathered} A=32 \\ B=30 \end{gathered}[/tex][tex]A-B=32-30=2[/tex]Solve the system of equations using a table and graph. X-2y=3. Y+3x=-5
[tex]x = 3 + 2y.....(3)equation[/tex]
[tex]y + 3(3 + 2y) = - 5 \\ y + 9 + 6y = - 5 \\ y + 6y = - 5 - 9 \\ 7y = - 14 \\ \frac{7y}{7} = \frac{ - 14}{7} \\ y = - 2[/tex]
[tex]x = 3 + 2y \\ x = 3 + 2( - 2) \\ x = 3 - 4 \\ x = - 1[/tex]
ATTACHED IS THE SOLUTION.
Write a coordinate proof: Given: Coordinates of triangle DEF, H is the midpoint of DA, G is the midpoint of EA . Prove: Side DG is congruent to side EH Here is the image down below. I have to fill in the blanks with each of the correct choices that are provided down below.
SOLUTION
Consider the image in the below
From the diagram above,
[tex]\begin{gathered} H\text{ is the mid point of AD} \\ \text{And } \\ G\text{ is the midpoint of AE} \end{gathered}[/tex]Then we obtain the coordinate of H and G
Using the coordinate of midpoint formula,
[tex]\begin{gathered} \text{Coordinate of H is } \\ (-\frac{2h+0}{2},\frac{2k+0}{2})=(\frac{-2h}{2},\frac{2k}{2})=(-h,k) \end{gathered}[/tex]Then
[tex]\begin{gathered} \text{Coordinate of G } \\ (\frac{2h+0}{2},\frac{2k+0}{2})=(\frac{2h}{2},\frac{2k}{2})=(h,k) \end{gathered}[/tex]Then use the distance formula to fined the lenght of |EH| and |DG|
The Distance formula is given by
[tex]\text{Distance}=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Hence
[tex]\begin{gathered} U\sin g\text{ the coordinatesH= (-h,k) and E= (2h,0) } \\ \text{Then} \\ |EH|=\sqrt[]{(2h-(-h)^2+(0-k)^2} \\ |EH|=\sqrt[]{(3h)^2+(-k)^2} \\ \text{Then } \\ |EH|=\sqrt[]{9h^2+k^2} \end{gathered}[/tex]Then
[tex]\begin{gathered} \text{ Using the coordinatesG= (h,k) and D=(-2h,0) for |DG|} \\ |DG|\text{ =}\sqrt[]{(-2h-h)^2+(0-k)^2} \\ |DG|=\sqrt[]{(-3h)^2^{}+(-k)^2} \\ \text{hence } \\ |DG|-=\sqrt[]{9h^2+k^2} \end{gathered}[/tex]
Hence
Since we obtain the same expression above
Then
[tex]\begin{gathered} |EH|=|DG| \\ or \\ |DG|=|EH| \end{gathered}[/tex]therefore
[tex]|DG|\cong|EH|[/tex]Therefore
Answer: DG is congruent to side EH
given the sequence write an explict formula and find the 78th term-23 -27 -31 -35
We see that there is a difference of 4 between each number:
[tex]\begin{gathered} -23-4=-27 \\ -27-4=-31 \\ -31-4=-35 \end{gathered}[/tex]and so on. Then, we can propose the following formula:
[tex]a_n=-23-4\cdot n[/tex]For instance, when n=0 we have
[tex]\begin{gathered} a_0=-23+0 \\ a_0=-23 \end{gathered}[/tex]when n=1, we have
[tex]\begin{gathered} a_1=-23-4\cdot1 \\ a_1=-23-4 \\ a_1=-27 \end{gathered}[/tex]when n=2, we have
[tex]\begin{gathered} a_2=-23-4\cdot2 \\ a_2=-23-8 \\ a_2=-31 \end{gathered}[/tex]and so on. Then, in order to compute the 78th term, we must substitute n=78 in our formula. It yields,
[tex]\begin{gathered} a_{78}=-23-4\cdot78 \\ a_{78}=-23-312 \\ a_{78}=-335 \end{gathered}[/tex]and the answer is -335
16. Find the measure of 2 ABC in circle D.a. 100A100b. 50C. 140d. 25
we have that
m by inscribed angle
so
mm
x-5/2=yI need the answers on a table
Given the equation:
[tex]y=x-\frac{5}{2}[/tex]Since the required table is not given, we will solve for values of x from -3 to 3.
[tex]\begin{gathered} \text{When }x=-3,y=-3-\frac{5}{2}=-5.5 \\ \text{When }x=-2,y=-2-\frac{5}{2}=-4.5 \\ \text{When }x=-1,y=-1-\frac{5}{2}=-3.5 \\ \text{When }x=0,y=0-\frac{5}{2}=-2.5 \\ \text{When }x=1,y=1-\frac{5}{2}=-1.5 \\ \text{When }x=2,y=2-\frac{5}{2}=-0.5 \\ \text{When }x=3,y=3-\frac{5}{2}=0.5 \end{gathered}[/tex]You can then place this in a table of x and y values.
You can use the same process to complete any table.
A line passes though two points A(-2, 2). B(-1, 2). What is the slope:
Answer:
The slope is 0
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Where the values of x and y are from the known points
Here the points are (-2,2) and (-1,2)
So we have (x1,y1) = (-2,2) and (x2,y2) = (-1,2)
This means, x1 = -2 , x2 = -1 , y1 = 2 and y2 = 2
We now plug these values into the slope formula
Recall slope = (y2 - y1) / (x2 - x1)
==> plug in x1 = -2 , x2 = -2 , y1 = 2, y2 = 2
Slope = (2 - 2) / (-1 - (-2)
==> remove parenthesis
Slope = (2-2) / (-1 + 2)
==> simplify addition and subtraction
Slope = 0 / 1 = 0
If point M is located at (-8, 3), which ordered pair below represents a 180-degree rotation about the originof point M?
A 180-degree rotation about the origin transforms point (x, y) into (-x,-y). then:
M(-8, 3) → M'(8, -3)
Simplify the absolute value 8|cos | if = sin−1 8/x for some real number x. (Give your answer in terms of .)
The absolute value of 8|Cosθ| is 8√(x² - 8²)/|x|.
The value of the angle θ is Sin−1 (8/x). We need to find the absolute value of 8|Cosθ|.
θ = Sin−1 (8/x)
Sinθ = 8/x
We know the trigonometric identity that Sin²θ + Cos²θ = 1.
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
(8/x)² + Cos²θ = 1.
Cos²θ = 1 - (8/x)²
Cos²θ = (x² - 8²)/x²
Cosθ = √[(x² - 8²)/x²]
Cosθ = √(x² - 8²)/x
Multiply both the sides with 8.
8Cosθ = 8√(x² - 8²)/x
Apply modulus on both the sides.
A modulus function is one that returns the absolute value of a number or variable.
8|Cosθ| = 8√(x² - 8²)/|x|
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 9 km/h slower than the other. If the two buses are 514 kilometers apart after 2 hours, what is the rate of each bus?
[tex]8 \sqrt{5} + 2 \sqrt{45} [/tex]combine these radicals
Answer
Option C is correct.
8√5 + 2√45 = 14√5
Explanation
We need to simplify
8√5 + 2√45
Note that 45 = 9 × 5
8√5 + 2√45
= 8√5 + 2√(9 × 5)
= 8√5 + 2[√9 × √5]
√9 = 3
8√5 + 2[3 × √5]
= 8√5 + 2(3√5)
= 8√5 + 6√5
= 14√5
Hope this Helps!!!
Answer to this question
Step-by-step explanation:
6. What is the range of the relation y = 2x+ + 3x if the domain is the set (-2,-1,0}? 1) {2,1,0} 2) {2,-1,0) 3) {-1,-5,0 4) {10,1,0}
For the given relation
[tex]y=2x^2+3x[/tex]With domain {-2, -1, 0}.
The domain represents all possible values of x, also called input, of the relationship and the range represents all the values of y, also called output, obtained when you replece the formula with the given values of x.
To determine the range of the valiable you have to do as follows:
For x=-2
[tex]y=2(-2)^2+3(-2)=2[/tex]For x=-1
[tex]y=2(-1)^2+3(-1)=-1[/tex]For x=0
[tex]y=2(0)^2+3\cdot0=0[/tex]For the relation with domain {-2,-1,0} the range is {2, -1, 0}
The correct option is number 2)
Each of the 6 students reported the number of movies the saw in the past year.11, 17, 11,8, 15, 9find the Median & Mean number of movies that each student saw round to the nearest tenth
Solution
The median is the middle number in a sorted, ascending or descending, list of numbers
We need to arrange them in ascending order
8, 9, 11, 11, 15, 17
The middle numbers are 11 and 11
Median = (11 + 11)/2 = 11.
Mean is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list.
[tex]\text{ Mean}=\frac{8+9+11+11+15+17}{6}\approx11.8[/tex]Median is 11
The mean is 11.8
A mine shaft which slopes at an angle of 19° to the horizontal is driven into a hillside for
400 m. How much lower, to the nearest metre, is the end of the shaft than the beginning?
The end of shaft is 137.731m lower at the beginning.
What is angle?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex.
Angles' Components:
Vertex: The intersection of two lines or sides at an angle is called a vertex.
Arms: The angle's two sides linked at a single end.
Initial Side: A line that is straight from which an angle is made.
from the given figure:
tan(19) = BC/AB
BC = 400 × tan(19)
BC = 137.731m
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Suppose that $21,800 is invested in a certificate of deposit for 3 years at 9.6% annual interest to be compounded semi-annually. How much interest will this investment earn? Round your answer to the nearest cent, if necessary.
The total compound interest is $7,081.8 , which interest will this investment earn.
What is compound interest?
Compound interest is interest that builds up over a set length of time on both principal and interest. The principal is also used to account for the interest that has accrued on a principal over time.Interest on the principal plus compounded interest is known as compound interest.Initial balance= 21,800$
Interest rate =9.6%
Term=3yrs0mos
Compounding frequency=semi-annually (2/Yr)
CI= P(1+(r/n)^nt-P
The final balance is $28,881.8.
The total compound interest is $7,081.8.
The total compound interest is $7,081.8 , which interest will this investment earn.
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The profit, in dollars, made by selling x bottles of 100% All-Natural Certified Free-Trade Organic Sasquatch Tonic is given by P ( x ) = − x 2 + 85 x − 620 for 0 ≤ x ≤ 95 . How many bottles of tonic must be sold to make at least $ 130 in profit? Write answer in interval notation.
The number of bottles of tonic that must be sold to make at least $130 in profit is [10, 75]
How to determine the number of bottles?The profit function is given as
P(x) = -x^2 + 85x - 620
The earnings are given as
Earnings = at least $130
This means that
P(x) ≥ 130
So, we have
-x^2 + 85x - 620 ≥ 130
Subtract 130 from both sides of the inequality
So, we have
-x^2 + 85x - 750 ≥ 0
Divide through by -1
So, we have
x^2 - 85x + 750 ≤ 0
Expand the expression
x^2 - 75x - 10x + 750 ≤ 0
Factorize
x(x - 75) - 10(x - 75) ≤ 0
Factor out x - 75
(x - 75)(x - 10) ≤ 0
Split
x - 10 ≤ 0 and x - 75 ≤ 0
Solve for x
x ≤ 10 and x ≤ 75
Combine the inequality
10 ≤ x ≤ 75
Express as interval
10 ≤ x ≤ 75 = [10, 75]
Hence, the number of bottles is [10, 75]
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