Answer:
.
Step-by-step explanation:
.
The mean age of 5 people in a room is 27 years.
A person enters the room.
The mean age is now 35.
What is the age of the person who entered the room?
Answer:
main age = total age/total people
if Main age is = 27
[tex]27 = \frac{ \times }{5} [/tex]
and x = 135
Total age is = 135
then main age is 35
[tex][35 = \frac{y}{6} [/tex]
and y = 210
first main age - second main age = age of the person participating
210 - 135 = 75
the age is = 75HAVE A NİCE DAY
Step-by-step explanation:
GREETINGS FROM TURKEY
The function f is defined by f(x)=2x+5/x+4 find f (3x)
Answer:
[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]
Step 2: Find
Substitute in x [Function f(x)]: [tex]\displaystyle f(3x) = \frac{2(3x) + 5}{3x + 4}[/tex]Simplify: [tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]Plz help. I’m finding surface area. I need the answer in units. Thank you.
Answer:
C. 17 units
Step-by-step explanation:
Surface area of rectangular prism is given as:
A = 2lw + 2lh + 2wh
A = 930 square units
l = 12 units
h = 9 units
w = ? (We're to find the width)
Plug in the value into the formula
930 = 2*12*w + 2*12*9 + 2*w*9
930 = 24w + 216 + 18w
Add like terms
930 - 216 = 42w
714 = 42w
Divide both sides by 42
714/42 = 42w/42
17 = w
w = 17 units
Which graph represents the solution of x2 + y2 < 25 and y2 <6x?
Answer:
The center of the circle is found at h,k
These values represent the important values for graphing and analyzing a circle.
Center: 0,0
And also,
Algebra Graph x^2+y^2=25 x2 + y2 = 25 x 2 + y 2 = 25 This is the form of a circle.
And also,
Simple and best practice solution for X2+y2=25 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework. If it's not what You are looking for type in the equation solver your own equation and let us solve it.
And also,
Match the values in this circle to those of the standard form. The variable r r represents the radius of the circle, h h represents the x-offset from the origin, and k k represents the y-offset from origin. The center of the circle is found at (h,k) ( h, k).
And also,
Ox (0) 6°x= 1) 6x ** + y = 25 SOLUTION (a) Since f(x) = 25 - x2 0, we can interpret this integral as the area under the curve y = 25 - x2 from 0 to 5 . But since y2 = 25 - x2 , we get x2 + y2 = 25, which shows that the graph of fis a quarter-circle with radius 5 in the top figuer
And also,
(3x2y2)3 Final result : 32x2y2 Reformatting the input : Changes made to your input should not affect the solution: (1): "y2" was replaced by "y^2".
And thats all!
Solution graph is image 2.
We first graph [tex]x^2+y^2=25[/tex]. This is a circle with center = (0,0) and radius = [tex]\sqrt{25} =5[/tex].
For [tex]x^2+y^2<25[/tex], we'll shade inside the circle.
[tex]y^2=6x[/tex] is a parabola.
we make a table for it.
x -1 0 1
y -6 0 6
For [tex]y^2<6x[/tex] we'll shade inside the parabola.
So the graph will be image 1.
So the solution region is image 2.
Learn more: https://brainly.com/question/15816805
What is the product (4.42 x 103)(5 x 10^) written in
scientific notation?
Answer:
2.2763 x 10 to the power of 4
for some reason it doesn't let me put in the explanation
what is the slope of a line parallel to the line whose equation is 2x+5y=10
Answer:
1. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -1
Find the area of the surface generated when the given curve is revolved about the y-axis. The part of the curve y=4x-1 between the points (1, 3) and (4, 15)
Answer:
Step-by-step explanation:
Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.
Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1
4x = y + 1
[tex]x = \dfrac{y+1}{4}[/tex]
[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
By integration, the required surface area in the revolve is:
[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]
where;
g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
∴
[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]
[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]
[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]
[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]
For any real number √a²
a
- |al
lal.
-a
Answer:
|a|
Step-by-step explanation:
For any positive or negative a, when you square it, the answer is positive.
The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.
Answer: |a|
A decorative wall in a garden is to be built using bricks that are 5 1/2 inches thick and mortar joints are 1/4 inch thick. What is the height of the wall?
Step-by-step explanation:
how many layers of bricks are used ?
also, I assume, the thickness of bricks means actually their height when laid.
but still, I cannot answer that, as nothing indicates if there is only one layer of bricks or 2 or 3 or 4 or ...
Please help:
Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary
Statements and Reasons
Answer:
See Below.
Step-by-step explanation:
We can write a two-column proof.
Statements: Reasons:
[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex] Given
[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex] Vertical Angles are Congruent
[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex] Linear Pair
[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex] Substitution
[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex] Substitution
[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex] Definition of Supplementary Angles
Analyze the figure below and complete the instructions that follow.
Answer:
C. 468 mm²
Step-by-step explanation:
Surface area of the composite solid = 2(LW + LH + WH)
Length (L) = 12 mm
Width (W) = 6 mm
Height (H) = 2 + 7 = 9 mm
Plug in the values into the formula
Surface area = 2(12*6 + 12*9 + 6*9)
Surface area = 2(72 + 108 + 54)
Surface area = 2(234)
= 468 mm²
What is the value of M
Answer:....... no clue ut pls mark me brainiest
Step-by-step explanation:
I NEED HELP ILL MARK!!!
Answer:
c) tan
Step-by-step explanation:
For the 63-deg angle, YZ is the opposite leg. The unknown side, AY, is the adjacent leg. The trigonometric ratio that relates the opposite and adjacent legs is the tangent.
Answer: c) tan
what is the correct equation ?
Answer:
B
Step-by-step explanation:
B is the correct equation
PLS HELP please give an explanation if you don’t have one pls still give answer
What is the mode of the data?
Weight of Dogs In the Pet Store
Stem Leaves
0 3, 8
1 0, 1, 4, 7,
2 2, 4, 5
3 5 0 | 3 = 3 pounds
4 0
A. 17
B. 3
C. no mode
D. 40
Answer:
No mode
Step-by-step explanation:
Mode = number that appears the most
No number appears more than 1 time
Hence there is no mode
Answer:Should be no mode tell me if i'I'm wrong
Step-by-step explanation:
Convert.
{} {}
minutes ==equals 888 hours 373737 minutes
9514 1404 393
Answer:
517 minutes
Step-by-step explanation:
There are 60 minutes in an hour, so 8×60 = 480 minutes in 8 hours.
In 8 hours 37 minutes, there are ...
480 min + 37 min = 517 minutes
Allen is looking through his weekly local grocery store newspaper ads he notices that Costco is advertising a pack of 60 eggs for $9.35 Safeway is advertising a dozen eggs for $4.79 and Trader Joe's is advertising a pack of 18 eggs for $6.18 which store is offering the better deal?
Answer:
Costco
Step-by-step explanation:
We find the cost per egg for each of the three stores.
Costco:
$9.35/(60 eggs) = $0.15583/egg
Safeway:
$4.79/(12 eggs) = $0.39917/egg
Trader Joe's:
$6.18/(18 eggs) = $0.34333/egg
The best deal is Costco.
Answer:
Costco
Step-by-step explanation:
[tex]\frac{60}{9.35}: \frac{1}{y}[/tex]
60 × y = 1 × 9.35
60y = 9.35
60y ÷ 60 = 9.35 ÷ 60
[tex]y=\frac{187}{1200}[/tex]
[tex]\frac{12}{4.79}: \frac{1}{y}[/tex]
12 × y = 1 × 4.79
12y = 4.79
12y ÷ 12 = 4.79 ÷ 12
[tex]y=\frac{479}{1200}[/tex]
[tex]\frac{18}{6.18}: \frac{1}{y}[/tex]
18 × y = 1 × 6.18
18y = 6.18
18y ÷ 18 = 6.18 ÷ 18
[tex]y=\frac{103}{300}=\frac{412}{1200}[/tex]
The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the lower class limits.
Answer:
79.5, 110.5, 141.5, 172.5, 203.5, 234.5
Step-by-step explanation:
Given
The attached distribution
Required
The lower class limits
To do this, we simply subtract 0.5 from the lower interval
From the attached distribution, the lower intervals are:
80.0, 111.0, 142.0, 173,0 .......
So, the lower class limits are:
[tex]80.0-0.5 = 79.5[/tex]
[tex]111.0-0.5 = 110.5[/tex]
[tex]142.0-0.5 = 141.5[/tex]
[tex]173.0-0.5 = 172.5[/tex]
[tex]204.0-0.5 = 203.5[/tex]
[tex]235.0-0.5 = 234.5[/tex]
Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)
(Q.1)
[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]
Then substituting into the DE gives
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]
and both sides match, so y is indeed a valid solution.
(Q.2)
[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have
[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]
Integrate both sides (on the left, the numerator suggests a substitution):
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]
Given y (2) = e ³, we find
[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]
[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]
so that the particular solution is
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]
[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]
[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]
(Q.3) I believe I've already covered in another question you posted.
The edge of a cube was found to be 30 cm with a possible error in measurement of 0.5 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.) My Notes Ask Your Teacher
(a) the volume of the cube maximum possible error relative error percentage error cm
(b) the surface area of the cube maximum possible error relative error percentage error cm Need Help? ReadTalk to Tuter
Answer with Step-by-step explanation:
We are given that
Side of cube, x=30 cm
Error in measurement of edge,[tex]\delta x=0.5[/tex] cm
(a)
Volume of cube, [tex]V=x^3[/tex]
Using differential
[tex]dV=3x^2dx[/tex]
Substitute the values
[tex]dV=3(30)^2(0.5)[/tex]
[tex]dV=1350 cm^3[/tex]
Hence, the maximum possible error in computing the volume of the cube
=[tex]1350 cm^3[/tex]
Volume of cube, [tex]V=(30)^3=27000 cm^3[/tex]
Relative error=[tex]\frac{dV}{V}=\frac{1350}{2700}[/tex]
Relative error=0.05
Percentage error=[tex]0.05\times 100=5[/tex]%
Hence, relative error in computing the volume of the cube=0.05 and
percentage error in computing the volume of the cube=5%
(b)
Surface area of cube,[tex]A=6x^2[/tex]
[tex]dA=12xdx[/tex]
[tex]dA=12(30)(0.5)[/tex]
[tex]dA=180cm^2[/tex]
The maximum possible error in computing the volume of the cube=[tex]180cm^2[/tex]
[tex]A=6(30)^2=5400cm^2[/tex]
Relative error=[tex]\frac{dA}{A}=\frac{180}{5400}[/tex]
Relative error in computing the volume of the cube=0.033
The percentage error in computing the volume of the cube=[tex]0.033\times 100=3.3[/tex]%
Find the area of the following figure with the indicated dimensions.use pi.
Answer:
The answer is "47.5354".
Step-by-step explanation:
In the given graph it is a half-circle and a triangle.
So, the diameter of the circle is 6.2 so the radius is 3.1
[tex]\text{Area of a circle}= \pi r^2\\\\\text{Area of a triangle}= \frac{1}{2} b h\\\\[/tex]
Calculating the total area of the shape:
[tex]= \pi r^2+\frac{1}{2} \times b\times h\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\= 30.1754+17.36\\\\=47.5354\\\\[/tex]
You are designing an experiment using human subjects. The study will include 30 participants. Of these, 16 will be placed in the experimental group and the remaining 14 will be placed in the control group. In how many ways can you assign participants to the two groups?
Answer:
The participants can be assigned in 224 different ways.
Step-by-step explanation:
Given that you are designing an experiment using human subjects, and the study will include 30 participants, of which 16 will be placed in the experimental group and the remaining 14 will be placed in the control group, to determine in how many ways can you assign participants to the two groups the following calculation must be performed:
16 x 14 = X
224 = X
Therefore, the participants can be assigned in 224 different ways.
Each student at some college has a mathematics requirement M (to take at least one mathematics course) and a science requirement S (to take at least one science course). A poll of 150 sophomore students shows that: 60 completed M, 45 completed S, and 25 completed both M and S
Find the number of students who have completed
(a) At least one of the two requirements
(b) Exactly one of the two requirements
(c) Neither requirement.
all students = 150
M = 60
S = 45
M and S = 25
(a) At least one of the two requirements:
M or S = M + S - (M and S) = 60 + 45 - 25 = 80
(b) Exactly one of the two requirements:
(M or S) - (M and S) = 80 - 25 = 55
(c) Neither requirement:
(all students) - (M or S) = 150 - 80 = 70
The total mass of 8 identical dictionaries is 9.92 kilograms. What is the mass, in kilograms, of one dictionary? Enter your answer in the space provided
when 5 is added to 2 times a number , the results is 45. find the number
Answer:i think its 20
Step-by-step explanation: 20 x 2 is 40 plus 5 is 45
Answer:
✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20
Step-by-step explanation: Algebra.com
Which rectangle has an area of 18 square units? On a coordinate plane, a rectangle is 2 units high and 7 units wide. On a coordinate plane, a rectangle is 2 units high and 6 units wide. On a coordinate plane, a rectangle is 3 units high and 5 units wide. On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
option "B"
You Welcome
Step-by-step explanation:
Which table represents a linear function?
Х
1
2
3
4
y
3
6
12
24
х
1
2
3
4
у
2.
5
9
14
х
1
2
3
4
у
-3
-5
-7
-9
х
1
2
3
4
у
-2
-4
-2
0
Answer:
3
Step-by-step explanation:
x 1,2,3,4
y-3,-5,-7,-9
[tex]y = - 3 - (x - 1) \times 2[/tex]
The linear function is given by y = 7x - 4
A linear function is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept
From the table, using the points (1, 3) and (4, 24):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{24-3}{4-1}(x-1)\\\\ y=7x-4[/tex]
The linear function is given by y = 7x - 4.
Find out more on linear function at: https://brainly.com/question/4025726
5/6 ÷ 1/3 - 2/3 (2/5)
Answer:
[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]
Step-by-step explanation:
5/6 ÷ 1/3 - 2/3 (2/5)
= 5/6 ÷ 1/3 - 2/3 × 2/5= 5/2 - 2/3 × 2/5= 5/2 - 4/15= 67/30 or 2 7/30Hope it helps you! \(^ᴥ^)/
One urn contains 6 blue balls and 14 white balls, and a second urn contains 12 blue balls and 7 white balls. An urn is selected at random, and a ball is chosen from the urn. a. What is the probability that the chosen ball is blue? b. If the chosen ball is blue, what is the probability that it came from the first urn?
Answer:
a) 0.4658 = 46.58% probability that the chosen ball is blue
b) 0.322 = 32.2% probability that it came from the first urn
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. What is the probability that the chosen ball is blue?
6/20 = 0.3 of 0.5(first urn)
12/19 = 0.6316 out of 0.5(second urn).
So
[tex]P(A) = 0.3*0.5 + 0.6316*0.5 = 0.4658[/tex]
0.4658 = 46.58% probability that the chosen ball is blue.
b. If the chosen ball is blue, what is the probability that it came from the first urn?
Event A: Blue Ball
Event B: From first urn
From item a., [tex]P(A) = 0.4658[/tex]
Probability of blue ball from first urn:
0.3 of 0.5. So
[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.4658} = 0.322[/tex]
0.322 = 32.2% probability that it came from the first urn