A trapezoid is a quadrilateral with exactly one pair of parallel sides.
Formula for area: [tex]A = \frac{1}{2}(^{b}1 + ^{b}2)(h)[/tex]
In this formula, the bases are the parallel sides.
Now plug the information into the formula.
[tex]A = \frac{1}{2} (3 + 5)(9)[/tex].
Follow your order of operations, simplify inside the parentheses first.
[tex]A = \frac{1}{2}(8)(9)[/tex].
(1/2)(8) is 4 so we have (4)(9) which is 36.
So the area of the trapezoid is 36.
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 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
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:
How do you do this question
Answer:
the answer for the question is 26√13/12
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y, z) = x2 + y2 + z2; x4 + y4 + z4 = 7
Answer:
The maximum value is +√21 and the minimum value is -√21
Step-by-step explanation:
f(x,y,z) = x² + y² + z². Let g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0
Using Lagrange multipliers,
df/dx = λg/dx, df/dy = λg/dy. and df/dz = λg/dz
df/dx = 2x, df/dy = 2y, df/dz = 2z
dg/dx = 4x³, dg/dy = 4y³, dg/dz = 4z³
So, df/dx = λg/dx ⇒ 2x = 4λx³ (1)
df/dy = λg/dy ⇒ 2y = 4λy³ (2)
df/dz = λg/dz ⇒ 2z = 4λz³ (3)
From (1) 4λx³ - 2x = 0
2λx³ - x = 0
x(2λx² - 1) = 0
solving, x = 0 or (2λx² - 1) = 0 ⇒ 2λx² = 1 ⇒ x = ±1/√(2λ) since x ≠ 0
From (2) 4λy³ - 2y = 0
2λy³ - y = 0
y(2λy² - 1) = 0
solving, y = 0 or (2λy² - 1) = 0 ⇒ 2λy² = 1 ⇒ y = ±1/√(2λ) since y ≠ 0
From (3) 4λz³ - 2z = 0
2λz³ - z = 0
z(2λz² - 1) = 0
solving, z = 0 or (2λz² - 1) = 0 ⇒ 2λz² = 1 ⇒ z = ±1/√(2λ) since z ≠ 0
g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0
(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0
3 (1/√(2λ))⁴ = 7
(1/√(2λ))⁴ = 7/3
1/√(2λ) = ⁴√7/3
√(2λ) = ⁴√3/7
2λ = √3/7
λ = 1/2(√3/7)
Since x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3
Also y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3
and z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3
Substituting x,y and z into f(x,y,z) we have
f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21
The maximum value is +√21 and the minimum value is -√21
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
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
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?
A mixture of gases consists of N2, O2, H2 and F2. The total pressure of the mixture is 511.56 kPa. The pressure of the N2 is 584 mm Hg, the pressure of the O2 is 196 kPa and the pressure of the H2 is standard pressure. What is the pressure of the F2 (in mm Hg)?
Answer:
Step-by-step explanation:
The total pressure of a gas is the sum of the partial pressures of the gases that it consists of. It means that
N2 + O2 + H2 + F2 = pressure of mixture
1 kpa = 7.50061683 mmhg
The total pressure of the mixture is 511.56 kPa. Converting to mmHg, it becomes
511.56 × 7.50061683 = 3837.02 mmhg
The pressure of the O2 is 196 kPa. Converting to mmhg, it becomes
196 × 7.50061683 = 1470.12 mmhg
Since the the pressure of the H2 is standard pressure, it means that the pressure is 760 mmhg
Also, pressure of the N2 is 584 mm Hg
Therefore,
1470.12 + 760 + 584 + F2 = 3837.02
2814.12 + F2 = 3837.02
F2 = 3837.02 - 2814.12
F2 = 1022.9 mm Hg
Dilate the point B(-4,5) by a scale factor of 3 with the center at the origin.
Identify the coordinates of the pre-image.
B(-4,5)
Identify the scale factor.
Scale factor: n = 3
Multiply the scale factor by each coordinate
the pre-image to find the coordinates of the image.
B'(3(-4), 3(5))
The image point B' has coordinates B ( , )
Answer:(-12,15)
Step-by-step explanation:
My Instagram: kxng_V2
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:
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]
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!!
Find the distance between the two points rounding to the nearest tenth (if necessary).
(2, -8) and (5, -6)
Answer:
Submit Answer
attempt 1 out of 2
Approximately 3.6
:) Hope this helps
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!
Line k has an equation of y = -2x - 6. Perpendicular to line k is line I, which passes through
the point (3, 6). What is the equation of line l?
Write the equation in slope-intercept form. Write the numbers in the equation as proper
fractions, improper fractions, or integers.
Answer:
y = x/2 +9/2
Step-by-step explanation:
y = -2x - 6.
The equation of the line perpendicular to the above equation has a slope 1/2
The equation of a slope is
y2-y1/x2-x1 = 1/2
To form an equation of the line we chose a point that lies on the graph which is perpendicular to y = -2x - 6 and an arbitrary point (x,y)
A point is given us already and that point is (3, 6).
Tie all together to compute the slope we have;
y-6/x-3 = 1/2
2(y-6) = x-3
2y-12= x-3
2y = x-3+12
2y= x+9
Dividing through by 2 we have
y = x/2 +9/2
y = x/2 + 4.5
The required equation is 2x-y =0, interception point is (0,0) and the equation is in integers.
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
The equation of a line which passes through point (x₁, y₁) with slope m can be given by,
y - y₁ = m(x - x₁)
The given equation of line k is y= -2x-6 (1).
The slope of line k = -2.
Since, line l is perpendicular to line k,
Slope of line l = 2
Line l passes through the point (3,6), therefore, the equation of line l,
y-6= 2(x-3)
⇒2x-y =0 (2)
To find interception point of slope of line l,
Substitute y=0, in equation (2) ,
x intercept = 0
Substitute x=0, in equation (2),
y intercept = 0
The equation is 2x-y =0, and it is in integer form.
To know more about Slope on :
https://brainly.com/question/16180119
#SPJ2
Please answer this correctly
Answer:
24 cm
Step-by-step explanation:
Assuming that the triangles are similar,
then the ratio of their sides must be the same.
in this case you are dealing with 2 longest sides and the 2 shortest sides.
We are asked to find the y (the length of the shortest side of the blue triangle)
because they are similar, we can form a ratio with their sides:
Purple Long Side / Blue Long Side = Purple Short Side / Purple Long side
100 / 80 = 30 / y
100y = (30)(80)
y = (30)(80) / 100
y = 24 cm
Answer:
y = 24
Step-by-step explanation:
Since these triangles are similar, you can set up a proportion like this:
[tex]\frac{100}{80} =\frac{30}{y}[/tex]
→Cross multiply:
[tex]\frac{100y}{2400}[/tex]
→Divide 2400 by 100:
y = 24
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]
I need help I think I have the but I might be wrong
Answer:
D
Step-by-step explanation:
3 to 7 is about 4.
There are 18 students attending band camp, 4 girls and 14 boys. What is the
ratio of girls to boys at band camp?
Answer:
4:14 or 2:7
Step-by-step explanation:
there are 4 girls and 14 boys
the ratio is 4:14
correct me if this is wrong
Answer:
2/7
Step-by-step explanation:
two find the answer you need to reduce 4 and 14 into the lowest common denominator.
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
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.
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.
HELP ILL GIVE YOU BRAINLIEST IF YOUR RIGHT ‼️‼️‼️‼️
Answer:
first question: 36
second question: 5
Step-by-step explanation:
for the first question, the parentheses just mean you are multiplying. so it would be 2 x 3 x 6 which equals 36.
For the second question, you would add d and g together and e and f, then subtract the sum of e and f from the sum of d and g.
(2 + 12) - (3 + 6)
14 - 9 = 5
Step-by-step explanation:
d=2
e=3
f=6
g=12
therefore , (2)×(3)×(6)
=36
2. d=2
e=3
f=6
g=12
(d+g) - (e+f)
(2+12) - (3+6)
(14) -(9)
=5.
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.
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.
nevermind...
what is the domain?
(-infinity,infinity) -answer
(-infinity, 4)
(-4, 4)
(0, 4)
What is the range?
(-infinity, infinity)
(-infinity, 4) -answer
(-4, 4)
(0, 4)
Answer:
its A for the domain and B for the range
domain: (-infinity,infinity) Range: (-infinity,4]
Step-by-step explanation:
Answer:
its 3
Step-by-step explanation:
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.
Does anyone know the answer to this?
Answer:
1.88
Step-by-step explanation:
From Trigonometry Identity;
Cos 20° = AC/ CB
AC = Cos 20° × CB
= Cos 20° × 2
= 1.879
= 1.88 ( to the nearest hundredth)