Answer:
i) 0.63
ii) 0.37
iii) 0.37
iv) 0.77
v) 0.51
Step-by-step explanation:
Total resistance value = 108
A = high shock resistance
B = high scratch resistance
when a disk is selected at random
i) P(A) = P ( high shock resistance )
= ( 55 + 13 ) / 108
= 68/108 = 17/27 = 0.63
ii) P( B ) = P ( high scratch resistance )
= ( 10 + 30 ) / 108
= 40 / 108 = 10/27 = 0.37
iii) P(A') = 1 - P(A)
= 1 - 17/27 = 10/27 = 0.37
iv) P( A U B ) = P(A) + P(B) - P( A n B )
= 0.63 + 0.37 - 0.233
= 0.766 ≈ 0.77
v) P( A' U B ) = P(A') + P(B) - P(A n B )
= 0.37 + 0.37 - 0.233
= 0.507 ≈ 0.51
4(x+9)=2x-6
Solve for x
Answer:
-21
Step-by-step explanation:
4(x+9) = 4x+36
4x+36 = 2x-6
-36 -36
minus 36 from both sides
4x = 2x-42
2x = -42
-42/2 = -21
x = -21
Hi there!
We are given the equation below:
[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]
1. Expand 4 in the expression.
When expand in the expression, it is like multiply everything in the expression. So when we expand 4 in x+9, it becomes 4(x)+9(4).[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]
Cancel the brackets.
[tex] \large{4x + 36 = 2x - 6}[/tex]
2. Isolate x-term and solve for the variable.
Think it easy. If you want to isolate x-term then what should you do? Well simply swap sides, and change the operator/sign.[tex] \large{4x - 2x = - 6 - 36}[/tex]
Finally, combine like terms.
[tex] \large{2x = - 42}[/tex]
Then divide both sides by 2 so we can finally leave only x-term.
[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]
3. Check the solution if it is right or wrong.
This step is optional but if you are not confident on your answer, this step is recommended.To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,
[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]
Since both sides are equal when substitute in x = -21.
4. Answer
Hence, the answer for this equation is x = -21.I hope this helps and let me know if you have any doubts!
The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at $2000. The students sold 2357 raffle tickets at $5 per ticket.
Required:
a. Kevin bought ten tickets. What is the probability that Kevin will win the spring break cruise to the Caribbean?
b. Expected earnings can be found by multiplying the value of the cruise by the probability that Kevin will win. What are Kevin's expected earnings?
c. How much did Kevin effectively contriute to the Samaritan Center for the Homeless?
Answer:
A) The probability that Kevin will win the spring break cruise is 0.42%.
B) Kevin's expected earnings are $ 8.4.
C) Kevin effectively contributed with $ 50.
Step-by-step explanation:
Since the college student senate is sponsoring a spring break Caribbean cruise raffle, and the proceeds are to be donated to the Samaritan Center for the Homeless, ya local travel agency donated the cruise, valued at $ 2000, and the students sold 2357 raffle tickets at $ 5 per ticket, to determine A) if Kevin bought ten tickets, what is the probability that Kevin will win the spring break cruise to the Caribbean; B) Kevin's expected earnings and C) how much did Kevin effectively contribute to the Samaritan Center for the Homeless; the following calculation must be performed:
A) 10/2357 = 0.0042 x 100 = 0.42
Therefore, the probability that Kevin will win the spring break cruise is 0.42%.
B) 2000 x 0.0042 = 8.4
Therefore, Kevin's expected earnings are $ 8.4.
C) 5 x 10 = 50
Kevin effectively contributed with $ 50.
Ahmad made $114 for 12 hours of work. At the same rate, how many hours would he have to work to make $108?
Answer:6
Step-by-step explanation:
The price of a 5-minute phone call is $1.75. What is the price of a 19-minute phone call?
Answer:
$6.65
Step-by-step explanation:
You could start by seeing the price of a 1 minute phone call. if you divide 1.75 by 5 it is 0.35. that means 1 minute costs $0.35. so the equation would be 0.35 times 19. which is 6.65 dollars.
5 minutes call = $1.75
1 minute call = $1.75/5 = $0.35
19 minutes call = $0.35 × 19 = $6.65
hello how are you today. Question 2(×+-5)+×=×+(-6)
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
2(x + -5) + x = x + (-6)
Step 2: Solve for x
[Distributive Property] Distribute 2: 2x - 10 + x = x - 6[Addition] Combine like terms (x): 3x - 10 = x - 6[Subtraction Property of Equality] Subtract x on both sides: 2x - 10 = -6[Addition Property of Equality] Add 10 on both sides: 2x = 4[Division Property of Equality] Divide 2 on both sides: x = 2Answer:
x=2 ( see Image below)
Step-by-step explanation:
cancel equal terms on both sides of the equation
2(x-5)=-6
move the constant to the right -hand side and change its sign
2x= -6 +10
Calculate the sum
2x=4
divide both sides of the equation by 2
x=2
2. Suppose the measures of the interior angles of a convex octagon are eight
numbers, each separated by a value of 1 degree from its neighbors. Find
the measure of the second smallest angle.
118°
131°
132.5°
142°
None of these answers are correct.
=====================================================
Explanation:
The interior angles are consecutive numbers such as 1,2,3,... or 7,8,9... and so on. The gap between any two adjacent neighbors is 1.
For any polygon with n sides, the interior angles add up to 180(n-2)
We have n = 8 sides so the interior angles sum to 180(n-2) = 180(8-2) = 1080 degrees.
Any octagon has its interior angles add up to 1080 degrees.
-----------------------------
Let x be the smallest angle. The next angle up is x+1. After that is x+2 and so on until we reach x+7 as the 8th angle.
Add up those 8 angles, set the sum equal to 1080 and solve for x
x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)+(x+7) = 1080
8x+28 = 1080
8x = 1080-28
8x = 1052
x = 1052/8
x = 131.5
This is the smallest angle. The next angle up or the second smallest angle is x+1 = 131.5+1 = 132.5 degrees (choice C)
The vector w=ai+bj is perpendicular to the line ax+by=c and parallel to the line bx−ay=c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
2x+5y=4, 7x+3y=8
Answer:
The angle between the liens is 135 degree.
Step-by-step explanation:
Equation of first line
2 x + 5 y = 4 ...... (1)
Equation of second line
7 x + 3 y = 8 ..... (2)
The slope of a line is given by
[tex]m = \frac{- coefficient of x}{coefficient of y}[/tex]
Slope of first line
[tex]m = -\frac {2}{5}[/tex]
Slope of second line
[tex]m'= - \frac{7}{3}[/tex]
The angle between the two lines is given by
[tex]tan\theta = \frac{m- m'}{1 + m m'}\\\\tan\theta = \frac{-\frac{2}{5}+\frac{7}{3}}{1+\frac{2}{5}\times \frac{7}{3}}\\\\tan\theta = -1 \\\\\theta = 135^o[/tex]
Given that abcd ~Jklm. Find the value of x, y, and z
Answer:
x = 7.2
y = 10
z = 6
Step-by-step explanation:
Since ABCD ~ JKLM, therefore, the ratio of their corresponding sides would be equal. Thus:
JK/AB = KL/BC = LM/CD = JM/AD
Substitute
12/x = y/6 = 15/9 = 10/z
✔️Find x:
12/x = 15/9
12/x = 5/3
Cross multiply
x*5 = 3*12
5x = 36
x = 36/5
x = 7.2
✔️Find y:
y/6 = 15/9
y/6 = 5/3
Cross multiply
y*3 = 5*6
3y = 30
y = 30/3
y = 10
✔️Find z:
15/9 = 10/z
5/3 = 10/z
Cross multiply
5*z = 10*3
5z = 30
z = 30/5
z = 6
Will Mark Brainlest. (find the domain of following relation for the given range) step by step
Step-by-step explanation:
I suppose you mean find the range for the following domain. Because when
g(x) is given the value of X
we are trying to solve the output value which is range.
If you want to solve for the domain, the question should give
g(x) = y
and provide the value of y.
X³+X²-X-2
Substitute
X=(-1)
-1+1-(-1)-2
= -1
g(-1)= -1
Substitute
X=(2)
8+4-2-2
=8
g(2)= 8
Substitute
X=(1)
1+1-1-2
=-1
g(1)= -1
g(2)+g(1)
=8-1
=7
ВС
2. In ATVW if VW is three meters longer than TV, TW
is 19 meters shorter than the sum of VW and TV,
and the perimeter of ATVW is 62 meters, find the length of VW.
20.75 m
15.75 m
25.5 m
21.75 m
None of the above
9514 1404 393
Answer:
21.75 m
Step-by-step explanation:
The given relations tell us that ...
VW = TV +3
TW = VW +TV -19
VW +TW +TV = 62
__
Solving the first equation for TW gives ...
TV = VW -3
Substituting that into the second equation gives ...
TW = 2VW -22
And using these expressions in the third equation, we have ...
VW +(2VW -22) +(VW -3) = 62
4VW = 87 . . . . . . . . collect terms
VW = 21.75 . . . . . . divide by 4
The length of VW is 21.75 meters.
Point D, not shown below, is one of the four (4) vertices of rectangle ABCD. Find its position and state the coordinate of point D.
Answer:
Hi im not got with graphs
Step-by-step explanation:
can someone tell me what the diffrence of 8 through 5 is
Answer:
The answer is 3.
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
Answer:
3
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
The ratio of girls to boys in a particular classroom is 8: 7. How many boys are in the class if there are 45 students?
Answer:
8+6=14
So , we can multiply 14 to 45 =630 in ratio 6:30
please help me...........
eople
Find the perimeter and area of the figure pictured below.
odules
fice 365
3.7 m
om
11.4 m
ades
2.3 m
9.2 m
Q
Perimeter
m
Area -
m2
Answer:
Perimeter: 41.2 m
Area: 54.83 m^2
Step-by-step explanation:
REFER TO THE IMAGE ATTACHED AS A
GUIDE.
PERIMETER:
(ADD UP ALL THE LENGTHS OF EACH SIDE)
Must be all 6 sides (see image, I solved for the two missing lengths)
3.7 + 9.1 + 11.4 + 9.2 + 2.3 + 5.5 = 41.2
perimeter is 41.2 m
AREA:
(See image again)
Shape is divided into two rectangles:
Top rectangle area: 11.4 x 3.7 = 42.18 m^2
Bottom triangle area: 5.5 x 2.3 = 12.65 m^2
ADD:
42.18 m^2 + 12.65 m^2 = 54.83 m^2
The area of the whole figure is 54.83 m^2
HOPE THIS HELPS
1. Cheryl Douglas works 43 hours in a week for an exempt salary of $1,827 per week. What are Cheryl's gross weekly earnings?
Answer:
$1827
Step-by-step explanation:
Since Cheryl is said to be paid an exempt salary. Then it can be said that Cheyk does not qualify for minimum wage or overtime pay, Hence, exempt payment is in terms or salary rather than wage. Similarly. Gross earning refers the amount a worker receives as income over a certain period of time. The gross income has not been subjected to tax charges or any form of deduction. Hence, it could be said to be the outright earning paid to an employee before any deduction is made.
Hence, Cheryl's gross weekly earning is $1827 per week.
The absolute value of -7
Answer:
7
Step-by-step explanation:
|-7| means find the distance from 0
We take the non negative value
|-7| = 7
PLEASE HELP MEEEEEEE EMERGENCY :(
Answer:
Ok ☺️✌️✌️✌️Ok ok ok ok
Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.
If she continues to read at the same rate, will she be able to complete this book in under 1 hour?
[ Select ]
If so, how much time will she have left? If not, how much more time is needed?
[ Select ]
Answer:
no
22.25 minutes
Step-by-step explanation:
First determine how long it will take her to read the entire book
20 pages 47 pages
-------------- = ----------------
35 minutes x minutes
Using cross products
20x = 35*47
20x=1645
Divide by 20
20x/20 = 1645/20
x =82.25 minutes
This is more than 1 hour ( 1 hour = 60 minutes)
82.25 minutes - 60 minutes = 22.25 minutes
She will need 22.25 more minutes
Which of the following is the square of a binomial?
Answer:
[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]
Step-by-step explanation:
U can reduce this into
[tex](4x + 3y) {}^{2} [/tex]
Which is a square.
Now,
16x^2 + 24xy + 9y^2
16x^2 + 12xy + 12xy + 9y^2
4x ( 4x + 3y ) + 3y ( 4x + 3y )
( 4x + 3y ) ( 4x + 3y )
( 4x + 3y )^2
I hope you understand...
Mark me as brainliest...
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.
a) dy/dx = (x − y)/x
b) (x + 1)dy/dx = −y + 20
c) dy/dx = 1/(x(x − y2))
d) dy/dx =(y^2 + y)/(x^2 + x)
e) dy/dx = 5y + y^2
f) y dx = (y − xy^2) dy
g) x dy/dx = ye^(xy) − x
h) 2xyy' + y^2 = 2x^2
i) y dx + x dy = 0
k) (x^2 + 2y/x) dx = (3 − ln x^2) dy
l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0
Here, we have to classify each differential equation based on their characteristics:
a) dy/dx = (x − y)/xThis is a separable differential equation because the variables can be separated on different sides of the equation.
It's of the form dy/dx = g(x) - f(y)/h(y), where g(x) = x/x and h(y) = 1.
b) (x + 1)dy/dx = −y + 20This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/(x + 1) and Q(x) = 20/(x + 1).
c) [tex]dy/dx = 1/(x(x - y^2))[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
d) [tex]dy/dx = (y^2 + y)/(x^2 + x)[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
e)[tex]dy/dx = 5y + y^2[/tex]This is a Bernoulli differential equation because it is of the form [tex]dy/dx = p(x)y + q(x)y^n[/tex], where p(x) = 0 and q(x) = 5x, n = 2.
f) [tex]y dx = (y - xy^2) dy[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
g) [tex]x dy/dx = ye^{(xy)} - x[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/x and [tex]Q(x) = e^{(xy)} - x^{(-1)[/tex].
h) [tex]2xyy' + y^2 = 2x^2[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -2/x and Q(x) = 2x.
i) y dx + x dy = 0This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
k) [tex](x^2 + 2y/x) dx = (3 - \text ln x^2) dy[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), although it's not immediately obvious what P(x) and Q(x) are.
l) [tex](y/x^2) dy/dx + e^{(2x^3)} + y^2 = 0[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where [tex]P(x) = -1/x^2[/tex] and [tex]Q(x) = -e^{(2x^3)} - y^2[/tex].
To know more about differential equation, visit:
brainly.com/question/1164377
#SPJ12
Please answer my question step be step
9514 1404 393
Answer:
z = 20
m∠A = 70°
Step-by-step explanation:
Step 0: read and understand the question. Identify the given information and the information requested.
Step 1: consult your knowledge of inscribed quadrilaterals to determine that opposite angles are supplementary.
Step 2: identify angles A and C as being marked with expressions in z.
Step 3: use those expressions and the relation in Step 1 to write an equation.
A + C = 180°
(4z -10)° +(10 +5z)°= 180°
Step 4: solve for z.
9z = 180 . . . . simplify, divide by °
z = 20 . . . . . . divide by 9
Step 5: use the relation between z and the measure of angle A to answer the question.
m∠A = (4z -10)° = (4·20 -10)°
m∠A = 70°
Step 6: check your answer. This can be done by making sure that angle C is supplementary to angle A.
C = (10 +5z)° = (10 +5·10)° = 110° = 180° -70° ∴ answer checks OK
Calculate the unit price. Round to the nearest cent, if necessary.
0.75 lb of salami for $2.65
$4.64 per lb of salami
$2.65 per lb of salami
$3.53 per lb of salami
$1.99 lb of salami
per
Answer:
$3.53 per lb of salami
Step-by-step explanation:
0.75 lb of salami for $2.65
The price per of salami will be :
0.75 lb = $2.65
1 lb = x
Using cross multiplication :
0.75 * x = $2.65 * 1
0.75x = $2.65
Divide both sides by 0.75
0.75x / 0.75 = $2.65 / 0.75
x = $3.533
This means that :
The price per unit of salami is $3.53
Answer:
0.75 lb of salami for $2.65 is $3.53 per lb of salami.
Solve the equation ln(x - 3) + ln(x + 1) = ln(x + 7)
x = 5, or x = ???
Answer:
x = 5 or x = - 2
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log (xy)
log x = log y ⇒ x = y
Given
ln(x- 3) + ln(x + 1) = ln(x + 7) , then
ln (x - 3)(x + 1) = ln (x + 7) , so
(x - 3)(x + 1) = x + 7 ← expand left side using FOIL
x² - 2x - 3 = x + 7 ( subtract x + 7 from both sides )
x² - 3x - 10 = 0 ← in standard form
(x - 5)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 2 = 0 ⇒ x = - 2
Solve this asap for me
Answer:
by using middle term break method
Step-by-step explanation:
9x^2 + 12x + 4
9x^2+ (6 + 6)x + 4
9x^2 + 6x + 6x + 4
3x(3x + 2) + 2(3x + 2)
(3x + 2)(3x + 2)
(3x + 2)^2
If you horizontally stretch the linear parent function, f(x) = x, by a factor of 3,
what is the equation of the new function?
A. g(x) = x - 3
B. g(x) = 3x
O C. g(x) = 3 - x
D. g(x) = 3 *
SUBMIT
Answer:
The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]
Step-by-step explanation:
Horizontally stretching a function:
Horizontally stretching a function f(x), by a factor of a, means that:
[tex]g(x) = f(\frac{x}{a})[/tex]
In this question:
[tex]f(x) = x[/tex], horizontally stretched by a factor of 3, so [tex]a = 3[/tex], and:
[tex]g(x) = f(\frac{x}{3}) = \frac{x}{3}[/tex]
The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]
the temperature at 6 pm in frost frozen antarctica was -37 if the tem dropped 8 1 /2 c uring the next hour what was the the temp at 7 pm
Answer:
-45 1/2
Step-by-step explanation:
x( 3x - 2y + 4z)x = -2, y = 4, and z = -3
Help. Urgent. Skenekeks
Answer:
D
Step-by-step explanation:
Plug in the numbers for the x-value and solve the equation.
| 3(80/3)/4 + 1 | = 16
| 3(-40/3)/4 + 1 | = 16
James hits a golf ball 145.7 yards Kayla hit a golf ball 122.95 yards how much farther does James hit a golf ball
