Answer:
0.1587
Step-by-step explanation:
Applying,
P(μ>40) = P(μ-(x-μ)/σ)............. Equation 1
Where P(μ>40) = probability of the age of the random subscriber more than 40 years μ = mean, σ = standard deviation, x = random subscriber
From the question,
Given: μ = 35 years, σ = 5 years, x = 40 years.
Therefore,
P(μ>40) = P(35-(40-35)/5) = P(35-(5/5)
P(μ>40) = 1-φ(1)
From the norminal probabilty table,
P(μ>40) = 1-0.8413
P(μ>40) = 0.1587
19. Students at a certain school can enroll in one elective course: painting, theater, choir, or band. This two-way frequency
table gives the number of male and female students enrolled in each class.
Male Female Total
Painting 17 16 33
Theater 15
18
33
Choir 21 25 46
Band 28
25
53
Total 81
84
165
Determine the conditional relative frequency that a student in the sample is enrolled in painting given that the student is
female.
O A. 19.0%
O B. 48.5%
O C. 9.7%
O D. 19.8%
Answer:
19.0%
Step-by-step explanation:
The probability that a student in the sample data is enrolled in painting Given that the student is female is a conditional probability and can be defined as :
Let,
F = Female ; P = painting
P(Painting Given female) = P(P|F) = (PnF) / F
From the table :
(PnF) = 16
F = 84
Hence,
P(P|F) = 16 / 84 = 0.19047 = 0.19047 * 100%
P(P|F) = 19.0%
Please help! I feel like I'm drowning :(
Answer:
1d = -3
2b = 2
2c = 1
3a = 3
3d = 4
Step-by-step explanation:
Polynomial 1: [tex]x^2-8x+15[/tex]
Multiply the leading coefficient, 1, and the last term, 15. You get: 15.
Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:
Factors of 15: -5 * -3
Addends of -8: -5 + -3
Replace the -8x with -5x - 3x:
[tex]x^2-5x-3x+15[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex](x^2-5x)-(3x+15)[/tex]
[tex]x(x-5)-3(x-5)[/tex]
[tex](x-5)(x-3)[/tex]
Looking at the answer (ax + b)(cx + d), d would correspond with -3.
Polynomial 2: [tex]2x^3-8x^2-24x[/tex]
First factor out the x:
[tex]x(2x^{2}-8x-24)[/tex]
Divide the polynomial inside by 2 and place the 2 outside with the x:
[tex]2x(x^2-4x-12)[/tex]
Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:
Factors of -12: -6 * 2
Addends of -4: -6 + 2
Replace the -8x with -6x + 2x:
[tex]2x(x^2-6x+2x-12)[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex]2x((x^2-6x)+(2x-12))[/tex]
[tex]2x(x(x-6)+2(x-6))[/tex]
[tex]2x((x+2)(x-6))[/tex]
[tex]2x(x+2)(x-6)[/tex]
Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.
Polynomial 3: [tex]6x^2+14x+4[/tex]
Divide the polynomial by 2:
[tex](2)(3x^2+7x+2)[/tex]
Find the factors of 3*2 and the addends of 7 and see which two numbers match:
Factors of 6: 6 * 1
Addends of 7: 6 + 1
Replace the 7x with 6x + x:
[tex](2)(3x^2+6x+x+2)[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex](2)((3x^2+6x)+(x+2))[/tex]
[tex](2)(3x(x+2)+(x+2))[/tex]
[tex](2)((3x+1)(x+2))[/tex]
[tex](2)(3x+1)(x+2)[/tex]
Then multiply the 2 with the (x+2) and here's your final answer:
[tex](3x+1)(2x+4))[/tex]
Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.
Hope that helps (●'◡'●)
(This took a while to write, sorry about that)
Which table represents a direct variation function?
9514 1404 393
Answer:
(b) the correct table is marked
Step-by-step explanation:
Direct variation is characterized by the ratio of y to x being a constant for all values in the table. That constant is the constant of proportionality. For the values in the second table (marked), the ratio is ...
y/x = 8/6 = 12/9 = 16/12 = 4/3
The constant of proportionality is 4/3.
where is the location of the incenter of triangle abc is
Answer:
The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter (denoted by I). The incircle (whose center is I) touches each side of the triangle.
Answer:
Step-by-step explanation:
we need a photo..
help e please i’ll give brainliest
Answer:
363,000,000
..........
(ar^b) ^4 = 16r^20 where a and b are positive integers work our a and b
Answer:
a = 2
b = 5
Step-by-step explanation:
Given :
(ar^b)^4 = 16r^20 ; a and b are positive integers :
Opening the bracket :
a^4r^4b = 16r^20
a^4 = 16 - - - - - (1)
r^4b = r^20 - - - (2)
a^4 = 16
Take the 4th root of both sides :
(a^4)^(1/4) = 16^1/4
a = 2
From (2)
r^4b = r^20
4b = 20
Divide both sides by 4
4b/4 = 20/4
b = 5
Hence ;
a = 2
b = 5
Use the coordinates of the labeled point to find a point-slope equation of the
line.
5
5
(-2,-5) 6.5
>
O A. y- 5 = -2(x - 2)
O B. y + 5 = 2(x + 2)
O C. y + 5 = -2(x + 2)
OD. y- 5 = 2(x - 2)
Answer:
B. [tex] y + 5 = 2(x + 2) [/tex]
Step-by-step explanation:
Point-slope equation is given as [tex] y - b = m(x - a) [/tex], where,
(a, b) = (-2, -5)
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line (-2, -5) and (0, -1),
Slope (m) = (-1 -(-5))/(0 -(-2)) = 4/2
m = 2
✔️To write the equation in point-slope form, substitute a = -2, b = -5, and m = 2 into [tex] y - b = m(x - a) [/tex]
Thus:
[tex] y - (-5) = 2(x - (-2)) [/tex]
[tex] y + 5 = 2(x + 2) [/tex]
Solve each inequality. Graph the solution on a number line.
Answer:
n>2 2/3
Draw a filled dot at a little more than 2 1/2 and continue the line to the right.
Step-by-step explanation:
Subtract 1/3 from both sides to get
2 2/3
Flip the inequality
n> 2 2/3
I hope this helps!
Find the perimeter of WXYZ. Round to the nearest tenth if necessary.
Answer:
C. 15.6
Step-by-step explanation:
Perimeter of WXYZ = WX + XY + YZ + ZW
Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.
✔️Distance between W(-1, 1) and X(1, 2):
Let,
[tex] W(-1, 1) = (x_1, y_1) [/tex]
[tex] X(1, 2) = (x_2, y_2) [/tex]
Plug in the values
[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]
[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]
[tex] WX = \sqrt{4 + 1} [/tex]
[tex] WX = \sqrt{5} [/tex]
[tex] WX = 2.24 [/tex]
✔️Distance between X(1, 2) and Y(2, -4)
Let,
[tex] X(1, 2) = (x_1, y_1) [/tex]
[tex] Y(2, -4) = (x_2, y_2) [/tex]
Plug in the values
[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]
[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]
[tex] XY = \sqrt{1 + 36} [/tex]
[tex] XY = \sqrt{37} [/tex]
[tex] XY = 6.08 [/tex]
✔️Distance between Y(2, -4) and Z(-2, -1)
Let,
[tex] Y(2, -4) = (x_1, y_1) [/tex]
[tex] Z(-2, -1) = (x_2, y_2) [/tex]
Plug in the values
[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]
[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]
[tex] YZ = \sqrt{16 + 9} [/tex]
[tex] YZ = \sqrt{25} [/tex]
[tex] YZ = 5 [/tex]
✔️Distance between Z(-2, -1) and W(-1, 1)
Let,
[tex] Z(-2, -1) = (x_1, y_1) [/tex]
[tex] W(-1, 1) = (x_2, y_2) [/tex]
Plug in the values
[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]
[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]
[tex] ZW = \sqrt{1 + 4} [/tex]
[tex] ZW = \sqrt{5} [/tex]
[tex] ZW = 2.24 [/tex]
✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56
≈ 15.6
Answer:CCCCCCCCCCCCCCCCC
Step-by-step explanation:
If I=square root-1 then i^2=
Answer:
i^−3 = i
i^−2 = −1
i^−1 = −i
i^0 = 1
i^1 = i
i^2 = −1
i^3 = −i
i^4 = 1
i^5 = i
i^ 6 = −1
See the pattern
Find surface area of this regular pyramid
Answer:
189 ft²
Step-by-step explanation:
Here is the formula...
1/2 * 6 * 36 + 81
Hope this helps
Solve x2 + 4x + 3 = 0 by completing the square.
options:
–6, –1
–3, –1
1, 3
–6, –2
Answer:
-3,-1
Step-by-step explanation:
x²+4x+3=0
x²+4x=-3
x²+4x+(2)²=-3+(2)²
(x+2)²=-3+4
(x+2)²=1
Take square root of both sides
x+2=±1
x=-2±1
x=-1 or-3
Solve the following differential equations using classical methods. Assume zero initial conditions.
a. dx/dy +7x = 5cos2t
b. d^2x/dt^2 + 6 dx/dt + 8x = 5sin3t
I'll use the integrating factor method for the first DE, and undetermined coefficients for the second one.
(a) Multiply both sides by exp(7t ):
exp(7t ) dx/dt + 7 exp(7t ) x = 5 exp(7t ) cos(2t )
The left side is now the derivative of a product:
d/dt [exp(7t ) x] = 5 exp(7t ) cos(2t )
Integrate both sides:
exp(7t ) x = 10/53 exp(7t ) sin(2t ) + 35/53 exp(7t ) cos(2t ) + C
Solve for x :
x = 10/53 sin(2t ) + 35/53 cos(2t ) + C exp(-7t )
(b) Solve the corresonding homogeneous DE:
d²x/dt ² + 6 dx/dt + 8x = 0
has characteristic equation
r ² + 6r + 8 = (r + 4) (r + 2) = 0
with roots at r = -4 and r = -2. So the characteristic solution is
x (char.) = C₁ exp(-4t ) + C₂ exp(-2t )
For the particular solution, assume an ansatz of the form
x (part.) = a cos(3t ) + b sin(3t )
with derivatives
dx/dt = -3a sin(3t ) + 3b cos(3t )
d²x/dt ² = -9a cos(3t ) - 9b sin(3t )
Substitute these into the non-homogeneous DE and solve for the coefficients:
(-9a cos(3t ) - 9b sin(3t ))
… + 6 (-3a sin(3t ) + 3b cos(3t ))
… + 8 (a cos(3t ) + b sin(3t ))
= (-a + 18b) cos(3t ) + (-18a - b) sin(3t ) = 5 sin(3t )
So we have
-a + 18b = 0
-18a - b = 5
==> a = -18/65 and b = -1/65
so that the particular solution is
x (part.) = -18/65 cos(3t ) - 1/65 sin(3t )
and thus the general solution is
x (gen.) = x (char.) + x (part.)
x = C₁ exp(-4t ) + C₂ exp(-2t ) - 18/65 cos(3t ) - 1/65 sin(3t )
What is the simplest form of 0.0115
23/200
Hope this helps! :)
Answer:
23/2000
Step-by-step explanation:
0.0115 can be written as 115/10000
=23/2000
Please mark me as brainliest.
what line will most likely have a slope of 10
Answer:
first one
Step-by-step explanation:
If p and q are whole numbers such that p×q=37, find the value of p+q
Answer:
6x6
Step-by-step explanation:
Find the value of x in each case:
Find the value of y.
Please help :(
The denominator of a fraction is three more than twice the numerator. if both numerator and denominator are degreased by seven, the simplified result is 4/13
orgnal fraction. (Don't simplify.)
Answer:
2/7
Step-by-step explanation:
d=2n+3
[tex]\frac{d-7}{2n-4} = \frac{4}{13}[/tex]
13(2n+3) -91 =8n - 16
26n+39 -91 = 8n-16
18n=36
n=2
d=7
HOW DO YOU SOLVE THIS PROBLEM
x = 100° (using definition of vertical angles)
if x can be divide by 7 and 9 without leaving a remainder, it can also divided by which number without leaving a remainder
Answer:
all counting numbers except one
BAC can be proved congruent to DEF by
Answer:
ASA
Step-by-step explanation:
∠ABC ≅ ∠EDF Angle
BC ≅ DF Side
∠C ≅ ∠F Angle
There are 10 students on the track team who compete in sprinting events. They make up 25% of the track team. How many students are on the track team?
Answer:
40
Step-by-step explanation:
10/x = 25/100
Cross multiply 10 and 100 = 1000.
Then, divide 1000 by 25 = 40.
10/40 = 0.25 = 25%
E. Engagement Time Frame: Dox2) Leaming Task 2: Mate lists of possible combinations of snacks in your notebook. Use O for Orange Juice, M for Mango Juice, B for Blue Lemonade, O for Oreo, s for Skyflakes and R for Rebisco. Juices Biscuit Orange Juice Oreo Mango Juice Skyflakes Blue Leronode Rebisco
Answer:
The maximum number of possible combinations are 9.
Step-by-step explanation:
There are three types of juices :
Orange, Mango and Blue lemonade
There are three types of biscuits:
Oreo, Skyflakes and Rebisco
So, the number of possible combinations are
= (3 C 1) x (3 C 1)
= 3 x 3 = 9
The maximum number of possible combinations are 9.
Which answers describe the shape below? Check all that apply.
A. Square
B. Quadrilateral
C. Rhombus
D. Trapezoid
E. Rectangle
F. Parallelogram
Answer:
b and f
Step-by-step explanation:
The population of a city this year is 200,000. The population is expected to increase by 2.5% per year over the next 10 years. Which exponential equation models this situation?
Answer:
[tex]A = 200,000(1+.025) ^{t}[/tex]
[tex]A = 200,000(1+.025) ^{10}[/tex]
Step-by-step explanation:
Which of these figures has rotational symmetry?
Hello!
The answer is a.
Good luck! :)
(3k + 5)(2k2 – 5k – 3)
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person.
Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents.
Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
Step-by-step explanation:
Part A.....let P be the number of people that will show up.....so....
The total amount of broccoli needed (in ounces) = 8P ounces
Part B
32 = 8P divide both sides by 8
4 = P so.....4 people can be fed.....!!!
Step-by-step explanation:
Can someone please help lol
Answer:
the range the score is 59 is the correct answer
Step-by-step explanation:
Range is the largest no minus the smallest no...so 59 is the largest minus 0 the smaller number