Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
1) Given P(A) = 0.3 and P(B) = 0.5, do the following.
(a) If A and B are mutually exclusive events, compute P(A or B).
(b) If P(A and B) = 0.2, compute P(A or B).
2) Given P(A) = 0.4 and P(B) = 0.2, do the following.
(a) If A and B are independent events, compute P(A and B).
(b) If P(A | B) = 0.7, compute P(A and B).
Answer:
1) a) 0.8
b) 0.6
2) a) 0.08
b) 0.14
Step-by-step explanation:
1) Given
[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]
Let us learn about a formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]
(a) If A and B are mutually exclusive i.e. no common thing in the two events.
In other words:
[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]
(b) P(A and B) = 0.2
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]
*************************************
1) Given
[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]
Let us learn about a formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex] for dependent events
[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.
(a) If A and B are independent events :
Using the above formula for independent events:
[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]
(b) [tex]P(A / B) = 0.7[/tex]
Using above formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]
if f(x)=3-2x and g(x)= 1/x+5 what is the value of (f/g) (8)
Answer:
Step-by-step explanation:
(f/g) = (3 - 2x ) / (1/x + 5) You could go to the trouble to simplify all of this, but the easiest way is to just put in the 8 where you see an x
(f/g)8 = (3 - 2*8) / (1/8 + 5)
(f/g)/8 = (3 - 16 / (5 1/8) 1/8 = 0.125
(f/g) 8 = - 13 / ( 5.125)
(f/g)8 = - 2.54
If the legs of an isosceles right triangle have a length of 15 StartRoot 2 EndRoot ft, what is the length of the hypotenuse?
Answer:
30 ft
Step-by-step explanation:
a² + b² = c²
(15sqrt(2))² + (15sqrt(2))² = c²
225 * 2 + 225 * 2 = c²
c² = 900
c = sqrt(900)
c = 30
Answer: 30 ft
Answer:
30 ft
Step-by-step explanation:
a² + b² = c²
(15sqrt(2))² + (15sqrt(2))² = c²
225 * 2 + 225 * 2 = c²
c² = 900
c = sqrt(900)
c = 30
Answer: 30 ft
please help me answer these questions :(
Answer:
a) ∠X = 67.4°
ii) ∠Y = 22.6°
b) Hypotenuse = 13 miles
ii) Length of each congruent = 4.33 miles
c) Distance of mall from point A = 5.21 miles
d) Distance os mall from point B = 8.17 miles
e) Difference = 2.96 miles
ii) Amount it will cost = $1,628,000
Step-by-step explanation:
Because of the length of the solution, I sent it as an attachment to this answer.
For each ordered pair, determine whether it is a solution to y=-9.
Is it a solution?
Yes or No
(1, -9)
(7,3)
(-9,4)
(0, -9)
Answer:
(1, -9) yes
(7,3) no
(-9,4) no
(0, -9) yes
Step-by-step explanation:
The y value must be -9
The x value can be any value to satisfy the equation y = -9
Find the area of the irregularly-shaped hexagon below
let each box length be 1
for white triangle
area = ½bh
=½(4)(2)
=4
for orange triangle
area=½(2)(3)
=3
for blue marked boxes
each of the box
area=l²
=(1)²
=1
there are 16 boxes
so the total area will be 16
total area of the hexagon = 4+3+16
=23 square units
[tex]A_1=\dfrac{1}{2}(3+5)\cdot 3=12\\A_2=1\cdot5=5\\A_3=\dfrac{1}{2}(5+1)\cdot 2=6[/tex]
So the area of the whole shape is [tex]12+5+6=23[/tex]
What is the radius of the circle whose center is the
origin and that passes through the point (5,12)?
Answer:
13 units
Step-by-step explanation:
Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.
Plug in the values and solve for r:
(5 - 0)² + (12 - 0)² = r²
25 + 144 = r²
169 = r²
13 = r
Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
What is the rectangular form of the polar equation?
0=-
57
y=x
V3
Oy= 32
y=-3x
Answer:
Option (1)
Step-by-step explanation:
From the picture attached,
tanθ = [tex]\frac{y}{x}[/tex]
Given : Polar equation as 'θ' = [tex]-\frac{5\pi }{6}[/tex]
Therefore, [tex]\text{tan}(-\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex]
[tex]-\text{tan}(\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex] [Since tan(-θ) = -tanθ]
[tex]\text{tan}(\pi -\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex] [Since -tanθ = tan(π - θ)]
[tex]\text{tan}\frac{\pi }{6}[/tex] = [tex]\frac{y}{x}[/tex]
[tex]\frac{y}{x}=\frac{\sqrt{3}}{3}[/tex]
y = [tex]\frac{\sqrt{3} }{3}x[/tex]
Therefore, y = [tex]\frac{\sqrt{3} }{3}x[/tex] will be the rectangular form of the polar equation.
Option (1) will be the correct option.
The value of 3 in 783.97
Answer:
place value of 3 in 783.97 is 3
Step-by-step explanation:
Answer:
Units
Step-by-step explanation:
The units start counting from 3 because after the point that is the 9 start counting tenth
An empty swimming pool is to be filled to the top. The pool is shaped like a rectangular prism with length 10m, width 8m , and depth 4m. Suppose water is pumped into the pool at a rate of 16m cubed per hour. How many hours does it take to fill the empty pool?
Answer:
20 hours
Step-by-step explanation:
10*8*4=320 (volume of the pool)
320/16=20 hours
Answer:
20 hours
Step-by-step explanation:
10x8x4 = 320
320 / 16 = 20
it takes 20 hours to fill the empty pool
Solve for x: −3x + 3 −1 b. x −3
Answer:
2/3
Step-by-step explanation:
Your −3x + 3 −1 is not an equation and thus has no solution.
If, on the other hand, you meant
−3x + 3 = 1
then -3x = -2, and x = 2/3
-50 POINTS- please help
Answer:
-13
-10
Step-by-step explanation:
A x = B
To find X
A ^ -1 A x = A ^ -1 B
x = A^ -1 B
x = -3/2 -5/2 2
-1 -2 4
Across times down
-3/2 * 2 + -5/2 *4 = -13
-1 *2 -2 * 4 = -10
The matrix is
-13
-10
Answer:
[tex]\Large \boxed{\bold{D.} \ \left[\begin{array}{ccc}-13\\ -10\end{array}\right]}[/tex]
Step-by-step explanation:
[tex]AX=B[/tex]
To find [tex]X[/tex]
[tex]X=A^{-1} \cdot B[/tex]
[tex]\displaystyle \left[\begin{array}{ccc}-\frac{3}{2} \cdot 2 + - \frac{5}{2} \cdot 4\\ -1 \cdot 2 + -2 \cdot 4\end{array}\right][/tex]
[tex]\displaystyle \left[\begin{array}{ccc}-3 + - 10\\ -2 + -8\end{array}\right][/tex]
[tex]\displaystyle \left[\begin{array}{ccc}-13\\ -10\end{array}\right][/tex]
find the value of X from the given picture
Answer:
x = 108
Step-by-step explanation:
The sum of a circle is 360
90 + x/2 + x+x = 360
Combine like terms
90 + 2x+x/2 = 360
90 + 5/2 x = 360
Subtract 90 from each side
5/2x = 270
Multiply each side by 2/5
5/2x * 2/5 = 270*2/5
x =108
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
Please help with this
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
In a lottery game, a player picks 6 numbers from 1 to 50. If 5 of the 6 numbers match those drawn, the player wins second prize. What is the probability of winning this prize
Answer:
1/254,251,200 Or 0.000000003933118
Step-by-step explanation:
1/50x1/49x1/48x1/47x1/46=1/254,251,200
Find the slope of the line whose x-intercept is 4 and the y- intercept is -9
Answer:
y = (9/4)x - 9
Step-by-step explanation:
The x-intercept is (4, 0) and the y-intercept is (0, -9).
As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9. Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:
y = (9/4)x - 9
A school newspaper reporter decides to randomly survey 15 students to see if they will attend Tet festivities this year. Based on past years, she knows that 24% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)
Answer:
0.70319018
Step-by-step explanation:
Given the following:
Number of students surveyed (n) = 15
Probability of attending tet festival (p) = 24% =0.24
Therefore,
Probability of not attending (1 - p) = (1 - 0.24) = 0.76.
The probability that at most 4 students will attend can be obtained using the binomial probability relation:
p(x) = nCx * p^x * (1 - p)^(n-x)
At most 4 students means:
p(x=0) + p(x=1) + p(x=2) + p(x=3) + p(x=4)
p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)
p(x=0) = 1 * 1 * 0.0004701 = 0.00047018
p(x=1) = 15C1 * 0.24^1 * 0.76^(14)
p(x=1) = 15 * 0.24 * 0.021448 = 0.07721
p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =
p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068
p(x=3) = 15C3 * 0.24^3 * 0.76^(12)
p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356
p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =
p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127
0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018
what is sum of all palindromic numbers from 1 to 100
Answer:
540
Step-by-step explanation:
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99
Answer:
540
Step-by-step explanation:
Hey there!
Well we need to first find all the palindromic numbers,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99
Add
= 540
Hope this helps :)
I suck at math, online school is really hard I need to find a tutor, can this be explained?
Answer:
its [c] if Bradley serves 4 tables he will earn an average of $25
Step-by-step explanation:
Answer two questions about Equations A and B:
A. 2x-1=5x
B. -1=3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Rewrite one side (or both) by
combining like terms
Rewrite one side (or both) using the distributive property
NEXT QUESTION
based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
A. Yes
B. No
Answer:
B: Add/subtract the same quantity to/from both sides
Next Question: Yes
Step-by-step explanation:
thats what the answer is dunno what else to tell you lol
Algebraic equations are mathematical equations that contain unknown variables.
To get Equation B from Equation A, we add/subtract the same quantity to/from both sides. Option A is the correct option. Equation A is equivalent to Equation BQuestion 1: We are given equation A as:2x - 1 = 5x .............Equation A
To get Equation B from A, we would subtract 2x from both sides of the equation.
2x - 2x - 1 = 5x - 2x
- 1 = 3x This is Equation B
Question 2: Based on the previous answer,2x - 1 = 5x is equal to -1 = 3x.
Hence, both Equation A and Equation B are equivalent expressions.
Therefore,
To get Equation B from Equation A, we add/subtract the same quantity to/from both sides. Option A is the correct option.Equation A is equivalent to Equation BTo learn more, visit the link below:
https://brainly.com/question/22299566
What would be the mass of a cube of tungsten (density of 19.3 g/cm), with sides of
3cm?
Answer:
M= 521.1 g
Step-by-step explanation:
1st. Find the volume of the cube: V=3³=27 cm³
As the weight of V= 1 cm³ cube is 19.3 g the weight of the cube=27 cm³ is
M=27*19.3= 521.1 g
A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
since there are 3 slots and each slot has 30 positions:
dial 1 can have a max of 30 possible outcomes, and so can dial 2 and 3
hence all the dial have 30 possible outcomes
total combinations = total outcomes of slot 1 X total outcomes of slot 2 X total outcomes of slot 3/ 3!
total combinations = 30 * 30 * 30 / 3 X 2 X 1
total combinations = 9000/3 X 2
total combinations = 1500
hence, there is a total of 1500 different combinations of the 3 slots
the combination required is 1 from the 1500
hence the odds are 1/1500
Answer:
1/27000
Step-by-step explanation:
30*30*30 =27000
each dial has to be in correct position so 1/27000 is correct
What is the simplified form of x minus 5 over x squared minus 3x minus 10⋅ x plus 2 over x squared plus x minus 12 ? (6 points) Select one: a. 1 over the quantity x minus 3 times the quantity x plus 4 b. 1 over the quantity x minus 3 times the quantity x plus 2 c. 1 over the quantity x plus 4 times the quantity x minus 5 d. 1 over the quantity x plus 2 times the quantity x minus 5
Answer:
[tex]\ \text{a. }\quad\dfrac{1}{(x-3)(x+4)}[/tex]
Step-by-step explanation:
Maybe you want the product ...
[tex]\dfrac{x-5}{x^2-3x-10}\cdot\dfrac{x+2}{x^2+x-12}=\dfrac{x-5}{(x-5)(x+2)}\cdot\dfrac{x+2}{(x-3)(x+4)}\\\\=\boxed{\dfrac{1}{(x-3)(x+4)}}[/tex]
__
Numerator factors of (x-5) and (x+2) cancel those in the denominator.
Marking as brainyest PLEASE HELP
How does f(x) = 9x change over the interval from x = 3 to x = 4? A) f(x) increases by 100% B) f(x) increases by 800% C) f(x) increases by 900% D) f(x) increases by 1000%
Answer:
C) f(x) increases by 900%
Step-by-step explanation:
The rate of change is
f(4) - f(3)
---------------
4-3
f(4) = 9*4 = 36
f(3) = 9*3 = 27
36 -27
---------------
4-3
9
-----
1
The rate of change is 9
To change to a percent, multiply by 100%
9*100% = 900%
Answer:
Increases by 900%
Step-by-step explanation:
● f(x) = 9x
The rate of change is:
● r = (36-27)/(4-3) = 9
So the function increses nine times wich is equivalent to 900%
what should be added to 66.778 get 78.2
Answer:
11.422
Step-by-step explanation:
[tex]78.2 - 66.778 \\ = 11.422[/tex]
Solve the equation for the given variable x/4=6/8
Answer:
x = 3
Step-by-step explanation:
This process is called cross multiplication.
Multiply 6 · 4 = 24
Divide 24 ÷ 8 = 3
x = 3
Answer:
x = 3
Step-by-step explanation:
x/4 = 6/8
Using cross products
x*8 = 4*6
8x = 24
Divide by 8
8x/8 = 24/8
x = 3
pls helpppp find the total area of the prism
Answer:
Total area = [tex](54+\frac{9\sqrt{3} }{2})[/tex] square inch
Step-by-step explanation:
Total area of the prism = Area of the rectangular sides (lateral sides) + area of the triangular bases
Area of the rectangular sides = 3 × (length × width)
= 3 × (3 × 6)
= 54 square inch
Area of the triangular bases = 2 × (Area of an equilateral triangle)
= 2 × [tex]\frac{\sqrt{3}}{4}(\text{Side})^2[/tex]
= [tex]\frac{\sqrt{3}}{2}(\text{Side})^2[/tex]
= [tex]\frac{\sqrt{3}}{2}(3)^2[/tex]
= [tex]9(\frac{\sqrt{3} }{2})[/tex]
= [tex]\frac{9\sqrt{3}}{2}[/tex] square inch
Total surface area = (54 + [tex]\frac{9\sqrt{3}}{2}[/tex]) square inch
The quotient of 8 and the difference of three and a number.
Answer: 8÷(3-x)
Answer:
Below
Step-by-step explanation:
● 8 ÷ (3-x)
Dividing by 3-x is like multiplying by 1/(3-x)
● 8 × (1/3-x)
● 8 /(3-x)
