Answer:
[tex] \boxed{(f + g)(x) = {x}^{2} - x + 6} [/tex]
Given:
[tex]f(x) = {x}^{2} + 1 \\ \\ g(x) = 5 - x[/tex]
To Find:
[tex](f + g)(x) = f(x) + g(x)[/tex]
Step-by-step explanation:
[tex] = > f(x) + g(x) = ({x}^{2} + 1) + (5 - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 1 + 5 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 6 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - x + 6[/tex]
Two points A and B are on opposite sides of a building. A surveyor selects a third point to place a transit. Point C is 49 feet from point A and 71 feet from point B. The angle ACB is 45°. How far apart are points A and
B? Round your answer to the nearest tenth as needed.
O A 111.2 ft
O B. 99.5 ft
O c. 70.61
OD. 50.2 ft
Answer:
According to the Law of Cosines, the correct answer would be D) 50.2 feet
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his average income for the remaining 8 months so that his average income for the year is $1,780.75?
Solve for x.
(2x+2)(3x+5)
Answer:
x = -1 x = -5/3
Step-by-step explanation:
Assuming we want the zeros
(2x+2) (3x+5) =0
Using the zero product property
2x+2 = 0 3x+5 =0
2x = -2 3x = -5
x = -2/2 x = -5/3
x = -1 x = -5/3
Answer:
x=-1, or -5/3
Step-by-step explanation:
When you add (2x+2)(3x+5)=0, it becomes a equation that you can solve for. I would advise you to separate both the parts of the equation so it becomes (2x+3)=0 and (3x+5)= 0 and that's how you can subract and divide easier in order to get the solutions. Hope this helps!!
An oblique cone has a height equal to the diameter of the base. The volume of the cone is equal to 18π cubic units. An oblique cone has a diameter of 2 x and a height of 2 x. The volume of the cone is 18 pi cubic units. What is the radius of the cone? 2 units 3 units 6 units 9 units
Answer:
3 units
Step-by-step explanation:
The formula for the volume of the cone is given by
[tex]V=\frac{1}{3} \pi r^{2}h[/tex]
[tex]V=18\pi\ unit^{3} \\\\ r=\frac{2x}{2} =x\ units \\ \\ h=2x\ units[/tex]
Substituting in above formula
[tex]18\pi=\frac{1}{3} \pi*x^{2}*2x\\ \\ 54=2x^{3} \\ \\ x^{3} =27\\ \\ x=\sqrt[3]{27} \\ \\ x=3\ units[/tex]
Thus, the radius of the cone is 3 units.
What’s the correct answer for this? Select all the ones that apply
Answer:
B and D
Step-by-step explanation:
<JKB = <FGC (SINCE BITH THEIR BISECTORS BISECT THEM MAKING A 90° ANGLE)
AND
<BKL = 90° (BECAUSE OF THE BISECTOR)
Answer:
B and D
Step-by-step explanation:
B and D
Read the sentences below. Choose the correct option to show which sentence uses a colon correctly.
a) We’ve chosen two cities to visit London: and Paris.
b) We’ve chosen: two cities to visit London and Paris.
c) We’ve chosen two cities: to visit London and Paris.
d) We’ve chosen two cities to visit: London and Paris.
Answer:
d
Step-by-step explanation:
colons are used to list
4. Find the volume of the given solid bounded by the elliptic paraboloid z = 4 - x^2 - 4y^2, the cylinder x^2 + y^2 = 1 and the plane z = 0.
5. Sketch the region of integration and change the order of integration.
Answer:
2.5π units^3
Step-by-step explanation:
Solution:-
- We will evaluate the solid formed by a function defined as an elliptical paraboloid as follows:-
[tex]z = 4 - x^2 -4y^2[/tex]
- To sketch the elliptical paraboloid we need to know the two things first is the intersection point on the z-axis and the orientation of the paraboloid ( upward / downward cup ).
- To determine the intersection point on the z-axis. We will substitute the following x = y = 0 into the given function. We get:
[tex]z = 4 - 0 -4*0 = 4[/tex]
- The intersection point of surface is z = 4. To determine the orientation of the paraboloid we see the linear term in the equation. The independent coordinates ( x^2 and y^2 ) are non-linear while ( z ) is linear. Hence, the paraboloid is directed along the z-axis.
- To determine the cup upward or downwards we will look at the signs of both non-linear terms ( x^2 and y^2 ). Both non-linear terms are accompanied by the negative sign ( - ). Hence, the surface is cup downwards. The sketch is shown in the attachment.
- The boundary conditions are expressed in the form of a cylinder and a plane expressed as:
[tex]x^2 + y^2 = 1\\\\z = 4[/tex]
- To cylinder is basically an extension of the circle that lies in the ( x - y ) plane out to the missing coordinate direction. Hence, the circle ( x^2 + y^2 = 1 ) of radius = 1 unit is extended along the z - axis ( coordinate missing in the equation ).
- The cylinder bounds the paraboloid in the x-y plane and the plane z = 0 and the intersection coordinate z = 4 of the paraboloid bounds the required solid in the z-direction. ( See the complete sketch in the attachment )
- To determine the volume of solid defined by the elliptical paraboloid bounded by a cylinder and plane we will employ the use of tripple integrals.
- We will first integrate the solid in 3-dimension along the z-direction. With limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ). Then we will integrate the projection of the solid on the x-y plane bounded by a circle ( cylinder ) along the y-direction. With limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] ). Finally evaluate along the x-direction represented by a 1-dimensional line with end points ( -1 , 1 ).
- We set up our integral as follows:
[tex]V_s = \int\int\int {} \, dz.dy.dx[/tex]
- Integrate with respect to ( dz ) with limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ):
[tex]V_s = \int\int [ {4 - x^2 - 4y^2} ] \, dy.dx[/tex]
- Integrate with respect to ( dy ) with limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] )
[tex]V_s = \int [ {4y - x^2.y - \frac{4}{3} y^3} ] \, | .dx\\\\V_s = \int [ {8\sqrt{( 1 - x^2 )} - 2x^2*\sqrt{( 1 - x^2 )} - \frac{8}{3} ( 1 - x^2 )^\frac{3}{2} } ] . dx[/tex]
- Integrate with respect to ( dx ) with limits: ( -1 , 1 )
[tex]V_s = [ 4. ( arcsin ( x ) + x\sqrt{1 - x^2} ) - \frac{arcsin ( x ) - 2x ( 1 -x^2 )^\frac{3}{2} + x\sqrt{1 - x^2} }{2} - \frac{ 3*arcsin ( x ) + 2x ( 1 -x^2 )^\frac{3}{2} + 3x\sqrt{1 - x^2} }{3} ] | \limits^1_-_1\\\\V_s = [ \frac{5}{2} *arcsin ( x ) + \frac{5}{3}*x ( 1 -x^2 )^\frac{3}{2} + \frac{5}{2} *x\sqrt{1 - x^2} ) ] | \limits^1_-_1\\\\V_s = [ \frac{5\pi }{2} + 0 + 0 ] \\\\V_s = \frac{5\pi }{2}[/tex]
Answer: The volume of the solid bounded by the curves is ( 5π/2 ) units^3.
I need help ASAP thank you!!!!
Answer:
V = 175 yd^3
Step-by-step explanation:
V = B*h
The base is the area of the triangle
B = 1/2 (5*7) = 35/2
so
V = 35/2 * 10
V = 175 yd^3
Answer:
175 yd
Step-by-step explanation:
The volume of a triangular prism can be calculated by the area of the base times its height. The bases are always the odd shapes out, so here it is the triangles with the "height" being the distance between the two bases.
The area of the base here is [tex]\frac{5*7}{2}[/tex]=17.5.
Multiplying that by the "height" gives 17.5×10= 175 yards.
what is one and two thirds divided by four fifths
Answer:
2 and 1/12
Step-by-step explanation:
pls mrk brainliest
Answer: 25/12
Step-by-step explanation: One and two thirds is equal to 5/3, so now all you have to do is divide 5/3 by 4/5. To divide fractions you multiply the first fraction to the reciprocal of the second fraction. The reciprocal simply means to switch the numerator with the denominator. Multiply 5/3 by 5/4. To multiply fractions you need to multiply straight across. 5 times 5 is 25 and 3 times 4 is 12, so the answer is 25/12.
How are you suppose to simplify a^-n ?
Answer:
1/a^n
Step-by-step explanation:
To simplify, you remove the negative by "flipping" what side it is on.
a^-n/1 -> 1/a^n
Answer:
[tex]\frac{1}{a^n}[/tex]
Step-by-step explanation:
[tex]a^{-n}[/tex]
You would apply exponent rule which is [tex]a^{-b}=\frac{1}{a^b}[/tex]:
[tex]=\frac{1}{a^n}[/tex]
Can someone tell me what 58-(1/4)^2 is
Answer:
57.9375
Step-by-step explanation:
Answer:
The answer above this is correct
Gary drew a rectangle with a perimeter of 12 inches. Then he tried to draw a square with a pe
of 12 inches
Select the dimensions of the rectangle drawing.
1 inch by 5 inches
12 inches by 5 inches
5 inches by 3 inches
12 inches by 1 inch
Select the dimensions of the square drawing.
5 inches by 5 inches
1 inch by 1 inch
3 inches by 3 inches
12 inches by 12 inches
Answer:
A. 1 inch by 5 inches
B. 3 inches by 3 inches
Step-by-step explanation:
The perimeter of a rectangle is the sum of the sides of the rectangle. The perimeter of a rectangle can be represented mathematically as
perimeter of a rectangle = 2l + 2w
where
l = length
w = width
perimeter = 12 inches
perimeter of a rectangle = 2l + 2w
12 = 2(l + w)
divide both sides by 2
l + w = 12/2
l + w = 6
Base on the option the dimension can only be 1 inches by 5 inches because the sum can give 6.
Square
The perimeter of the square is 12 inches.
perimeter of a square = 4l
where
l = length
12 = 4l
divide both sides by 4
l = 12/4
l = 3 inches
The length should be 3 inches by 3 inches.
Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children:
(a) What is the probability of getting one child of each sex? [5]
(b) What is the probability that at least one girl is born? [5]
(c) What is the probability that at least one boy is born? [5] and
(d) What is the probability that both children are the same sex? [5]
Answer: .250
Step-by-step explanation:
The population of Wyoming is about ? Times the population of Colorado
How do you do this question
Answer:
the answer for the question is 26√13/12
The depth of water at the end of a pier varies with the tides. The low tides occur on a particular day at 2:00 a.m. and 2:00 p.m. with a depth of 1.1 m. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 5.3 m. A large boat needs at least 3 m of water to be safely secured at the end of the pier. What is the first time in the morning that is it safe for the boat to be tied to the pier
Answer:
4:42 a.m.
Step-by-step explanation:
The earliest low tide occurs by 2:00 a.m. and the earliest high tide occurs by 8:00 a.m.
Between these hours, 6 hours elapsed.
The lowest point is 1.1 m and increases steadily to 5.3 m.
Let us take 2:00 a.m. as the zeroth hour, and 8:00 a.m. as the 6th hour, we can safely interpolate as below,
0 = 1.1 m
x = 3 m
6 = 5.3 m
we solve as [tex]\frac{x - 0}{6 - 0}[/tex] = [tex]\frac{3 - 1.1}{5.3 - 1.1}[/tex]
[tex]\frac{x}{6}[/tex] = [tex]\frac{1.9}{4.2}[/tex]
4.2x = 11.4
x = 2.71 hours from 2:00 a.m.
= 2 hrs + (0.71 x 60)min = 2 hrs 42.6 min
the time will approximately be by 4:42 a.m.
What is the lowest value of the range of the function shown on the graph? 0 3
Answer:
-2
Step-by-step explanation:
Edge 2020
Answer: B. -2
Step-by-step explanation: On Edge!!!!!
Suppose tortilla chips cost 22.5 cents per ounce. If a bag costs $3.07, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
Answer:
13.64 ounces
Step-by-step explanation:
Cost per ounce = $0.225
Cost per bag = $3.07
The number of ounces in a bag of chips is given by the cost per bag divided by the cost per ounce:
[tex]n=\frac{3.07}{0.225}\\ n=13.64\ ounces[/tex]
There are 13.64 ounces in a bag of chips.
Find the value of the function sin 460
Answer:
Sin(460 radians)= .97054
sin(460 degrees)= 0.98480775301
Step-by-step explanation:
I'm not sure where you are from, but usually you are allowed to use a calculator. (At least I was when I took Algebra 2/Trig in 6th grade.)
You never specified radians or degrees so I will answer both.
sin(460 radians)= .97054
sin(460 degrees)= 0.98480775301
If you are not allowed to use a calc, then I suggest looking at unit circle videos on Khan Academy.
A company is planning to manufacture snowboards. The fixed costs are $ 100$100 per day and total costs are $55005500 per day at a daily output of 20 boards. A. Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
Answer:
The equation for total cost function is
C(x)=100+270x
Step-by-step explanation:
Variable cost per per board =total cost per day-fixed cost per day/daily output
total cost per day is $5,500
fixed cost per day is $100
20 boards are produced per day
variable cost per board=($5,500-$100)/20=$270 per day
Total cost C(x)=fixed cost per day+ variable per board*number of daily output
Since daily output is represented also by x ,total cost function is given thus:
C(x)=100+270x
The equation for total cost function is C(x)=100+270x
The calculation is as follows:Variable cost per board =total cost per day-fixed cost per day ÷ daily output
Here
total cost per day is $5,500
fixed cost per day is $100
20 boards are produced per day
So,
variable cost per board=($5,500-$100) ÷20
=$270 per day
Now the equation is
C(x)=100+270x
Learn more: https://brainly.com/question/13981855?referrer=searchResults
Simplify.
Rewrite the expression in the form y^n
y^-4•y^3
Answer:
[tex]y^{-1}[/tex]
Step-by-step explanation:
This question is asking us to rewrite the original expression it in the form [tex]y^n[/tex]
First we have
[tex](y^{-4} )y^3[/tex]
By the law of exponents we know that when we are multiplying expressions that have the same base, we need to add up the exponents.
Thus, this would mean that, in order to multiply this expression, we need to sum up the exponents so we have:
[tex]-4+3=-1[/tex]
Thus, this expression can be rewritten as:
[tex](y^{-4} )y^3=y^{-4+3} =y^{-1}[/tex]
The following list shows how many brothers and sisters some students have: 3, 2, 3, 2, 1, 2, 1, 3, 4, 5, 4, 3, 1, 2 State the mode(s). I need anser?
Answer:
2 and 3
Step-by-step explanation:
Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.
Answer:
4.5 inches
Step-by-step explanation:
Put the given values in the volume formula and solve for width:
V = LHW
138.24 = (3.2)(9.6)W
138.24/30.72 = W = 4.5
The width of the prism is 4.5 inches.
You are interested in conducting a survey at your school to determine if gender or ethnicity is related to perceptions about educational opportunity. The school has 1,800 students but you only have resources to interview 100. The student body is approximately equally divided between males and females. Twelve percent of the school's population is Asian American, 8% is African American, 10% is Native American, and 70% is Caucasian. You are interested in being able to generalize the results of your survey to the entire student body. Describe a technique for obtaining a sample of size 100 that would have a reasonable chance of producing results that could be generalized to the entire school. Suppose you sent the surveys out to classes and asked the students to complete them and return them to the main office. Would the returns be likely to be biased in any direction? If so, why? In what direction? Suppose you decide to conduct the survey by personal interview. Members of the student council, all of whom happen to be Caucasian, will conduct personal interviews with the selected students. One of the survey questions reads, "Do you agree or disagree with the following statement: All students, regardless of ethnicity, have equal opportunity to become part of student government." What potential bias is present in this question?
Answers
We can use cluster sampling here. In this case, the population is divided into sampling units or clusters, for example, zone within educational or geographical areas. Having divided the population into clusters, we can use simple random sampling to select the clusters to be examined. Consider Asian American as one cluster, African american as another cluster and so on. According to the size of the cluster randomly select individuals from each cluster for a total of 100 individuals.
Generally there would be bias in accordance to the differnce in ethnicity. Also if the selected students are in a younger, then the teachers opnion would play a very big role there.
The question itself is a source of bias and it seems to give an idea to the students to think in these lines. The question can be better worded to get a correct answer. Even if there is equal opportunity, some students may read the question and give a negative answer.
Which is the best solution that represents the equation x2=196
Answer:
-14, 14
Step-by-step explanation:
[tex] {x}^{2} = 196 \\ x = \pm \sqrt{196} \\ x = \pm \: 14 \\ x = 14 \: \: or \: \: x = - 14 \\ x = \{ - 14, \: \: 14 \}[/tex]
Answer:
[tex]x = 14[/tex]
x= -14
Step-by-step explanation:
[tex] {x}^{2} = 196 \\ x = \sqrt{196} \\ x = 14[/tex]
x= -14
To check whether the answer is correct,
[tex] {x}^{2} = 196 \\ [/tex]
[tex]x = 14[/tex]
[tex] {14}^{2} = 196 \\ 14 \times 14 = 196 \\ 196 = 196[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Twelve bears eat five pounds of honey in one day. At the same rate, how many pounds of honey will 20 bears eat in three days?
Answer:
25
Step-by-step explanation:
Find the center and radius of the circle x2+y2=16
Answer:
The standard form of the equation of a circle is
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
where (a,b) are the coords of the centre and r , the radius.
x
2
+
y
2
=
16
is in this form
with a = b = 0 and r = 4
hence this circle has centre at the origin (0,0) and radius 4
The intercepts will therefore be (± 4,0) and (0, ± 4 )
the number of terms in AP-11,-8,-5......is
Step-by-step explanation:
If you look care fully from that number -11 he plused 3 to every number .
-11+3=-8
-8+3=-5
-5+3=-2
From the topic of sequence and series
Tyler attempts 240 free throws in 60 minutes. How many free throws did he attempt per minute?
4
40
180
300
Answer:
its A aka 4
Step-by-step explanation:
The data below are the frequency of cremation burials found in 17 archaeological sites. a. Obtain the mean, median, and mode of these data. b. Which measure of center do you think works best here? 85 67 45 47 524 32 31 272 2141 45 390 28 86 424 59 256 143 a. The mean is 275. (Round to one decimal place as needed.) The median is nothing. (Round to one decimal place as needed.) Select the correct choice below and fill in any answer boxes within your choice. A. The mode is nothing. (Round to one decimal place as needed.) B. There is no mode. b. Which measure of center works best here?
Answer:
(a) The mean of the data is 275.
(b) The median of the data is 85.
(c) The mode of the data is 45.
(d) The measure of center that works best here will be median.
Step-by-step explanation:
We are given below the frequency of cremation burials found in 17 archaeological sites. Arranging those in ascending order we get;
28, 31, 32, 45, 45, 47, 59, 67, 85, 86, 143, 256, 272, 390, 424, 524, 2141.
(a) The formula for calculating mean for the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{28+ 31+ 32+ 45+ 45+ 47+ 59+ 67+ 85+ 86+ 143+ 256+ 272+ 390+ 424+ 524+ 2141}{17}[/tex]
= [tex]\frac{4675}{17}[/tex] = 275
So, the mean of the data is 275.
(b) Since, the number of observations (n) in our data is odd (i.e. n = 17) , so the formula for calculating median is given by;
Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{17+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{18}{2} )^{th} \text{ obs.}[/tex]
= [tex]9^{th} \text{ obs.}[/tex] = 85
So, the median of the data is 85.
(c) Mode is that value in our data which appears maximum number of times in our data.
So, after observing our data we can see that only number 45 is appearing maximum number of times (2 times) and all other numbers are appearing only once.
So, the mode of the data is 45.
(d) The measure of center that works best here will be median because there are outliers in our data (means extreme values) and mean gets affected by the outliers.
So, the best measure would be median as it represents the middle most value of our data.
