Answer:
The growth rate was 5.87%
Step-by-step explanation:
Time interval is t=1999−1962=37 yearsInitial cost in 1962 was a=4 unit Final cost in 1999 was y=33 unit Exponential growth function :y=a(1+r)t;a>0,r>0,ris rate of growth in decimal form.y=a(1+r)tor33=4(1+r)37 or(1+r)37=334or(1+r)37=8.25 , taking log on bothsides we get, 37log(1+r)=log(8.25) orlog(1+r)=log(8.25)37orlog(1+r)≈0.24769(1+r)=100.24769or1+r≈1.0587∴r=0.0587 orr%=0.0587⋅100≈5.87%The growth rate was 5.87% [Ans]
A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B.
A coordinate plane with a circle drawn. The center of the circle is the origin, (0, 0). The circle has a diameter of 16 units. There is a line segment drawn from Point A at (8, 0), passing through (0, 4) to Point B at (negative 4, 6).
Which equation represents Grant’s path?
-Applications using z-scores-
(Note: draw the bell shape curve and convert data values to z-score)
A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr?
Answer: 16%
step explanation:
100 m/hr is ONE S.D. (10) above 90
z - score = .8413 (Form Z-score chart)
means 84 % of cars are travelling less than 100 m/hr
~ 16% are traveling 100 or more
Vigorous intensity physical activity target heart rate ranges between
A. 80-90%
B. 70-80%
C. 75-85%
D. 65-75%
100 POINTS
Solve x4 - 10x² + 9 = 0.
Answer:
[tex]x=\pm1 \:\textsf{or}\:x=\pm3[/tex]
Step-by-step explanation:
[tex]x^4-10x^2+9=0[/tex]
[tex]\textsf{let}\:x^2=y[/tex]
[tex]\implies y^2-10y+9=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find 2 two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
⇒ two numbers that multiply to 9 and sum to -10: -9 and -1
Rewrite [tex]b[/tex] as the sum of these 2 numbers:
[tex]\implies y^2-y-9y+9=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies y(y-1)-9(y-1)=0[/tex]
Factor out the common term [tex](y-1)[/tex]:
[tex]\implies (y-9)(y-1)=0[/tex]
[tex]\implies (y-9)=0 \implies y=9[/tex]
[tex]\implies (y-1)=0 \implies y=1[/tex]
Change [tex]y[/tex] back to [tex]x^2[/tex]:
[tex]\implies x^2=9\implies x=\pm3[/tex]
[tex]\implies x^2=1\implies x=\pm 1[/tex]
[tex]\textsf{So}\: x=\pm1 \:\textsf{or}\:x=\pm3[/tex]
Answer:
[tex]$x=\pm1\;\textrm{or}\;x=\pm3$[/tex]
Step-by-step explanation:
Substitute [tex]u = x^2[/tex] into the equation. This will make the quadratic formula easy to use.
[tex]\implies u^2 - 10u + 9 = 0[/tex]
Consider the form [tex]x^2 + bx + c = 0[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]c[/tex]. In this case, whose product is [tex]9[/tex]and whose sum is [tex]10[/tex]. And write the factored form using the integers.
[tex]\implies (u - 9)(u - 1) = 0[/tex]
If any individual factor on the left side of the equation is equal to [tex]0[/tex], the entire expression will be equal to [tex]0[/tex].
[tex]\implies \begin{cases}u - 9 = 0 \\ \\ u - 1 = 0\end{cases}[/tex]
Set [tex]u - 9[/tex] equal to [tex]0[/tex] and solve for [tex]u[/tex]. Similarly, Set [tex]u - 1[/tex] equal to [tex]0[/tex] and solve for [tex]u[/tex].
[tex]\implies \begin{cases}u = 9 \\ \\ u = 1\end{cases}[/tex]
Substitute the real value of [tex]u = x^2[/tex] back into the solved equation.
[tex]\implies \begin{cases}x^2 = 9 \\ \\ x^2 = 1\end{cases}[/tex]
Take the square root of both sides of the equations to eliminate the exponent on the left side.
[tex]\implies \begin{cases}x = \sqrt{9} \\ \\ x = \sqrt{1}\end{cases}[/tex]
Solve both the equations for the value of [tex]x[/tex].
[tex]\implies \begin{cases}x = \pm3 \\ \\ x = \pm1\end{cases}[/tex]
Hence, this is our required solution for this question.
[tex]\rule{300}{1}[/tex]
Additional information:
There are three ways to solve a quadratic equation:
FactoringComplete the SquareQuadratic FormulaFactoring uses the logic that the product of any number and zero is zero. Complete the square method uses square root, and the quadratic formula is the simpler method of it.
Quadratic Formula [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
50 points!!! Please help ASAP!!
The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -6
Answer:
Step-by-step explanation:
PLS HELP ILL MARK AS BRAINLEST
find the slope that goes through the following points
Answer:
The slope is 3
Step-by-step explanation:
The formula for slope is m = (y₂-y₁)/(x₂-x₁)
We assign
y₂ = -1y₁ = -4x₂ = 0x₁ = -1Note: You can choose any set of points as long as you assign y₂ and y₁ to y coordinates and x₂ and x₁ to x coordinates.
m = (-1+4)/(0+1) = 3/1 = 3
Answer:
D. 3 :)
Step-by-step explanation:
As the x value increases, so does the y value but in bigger jumps. It increases by 3 :)
Have an amazing day!!
Please rate and mark brainliest!!
pls helpp i need it i give 23 points
Shiho recorded the data below as she timed
how long it took for a car to go down a track.
Car Trial
Time
Trial 1
3.3 seconds
Trial 2
3.8 seconds
Trial 3
4.1 seconds
Trial 4
4.1 seconds
Trial 5
3.1 seconds
If Shiho wanted to determine the average time
it took the car to go down the track, which
measure should she find? (5 points)
A mean is an arithmetic average of a set of observations. The average time taken by Shiho to complete the track is 3.7 seconds.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
The reading of the 5 trials of Shiho is 3.3 seconds, 3.8 seconds, 4.1 seconds, 4.1 seconds, and 3.1 seconds. Therefore, the average or the meantime of Shiho can be written as,
[tex]\rm \text{Average Time} = \dfrac{\text{Sum of all observations}}{\text{Number of trials}}\\\\\text{Avrage Time} = \dfrac{3.3+3.8+4.1+4.1+3.1}{5}=\dfrac{18.4}{5}= 3.68\approx 3.7\ seconds[/tex]
Hence, the average time taken by Shiho to complete the track is 3.7 seconds.
Learn more about Mean:
https://brainly.com/question/16967035
#SPJ1
using appropriate property find -2/5 ×1/5 + 2/5 × 1/5
Answer:
simply cut 5 and solve if no property needed but if needed use distributive
What is the true solution to the logarithmic equation below?
log₂ (6x)-log₂ (√x)=2
answer: x = [tex]\\ \frac{4}{9\\}[/tex]
[tex]log_{2}[/tex] (6x) - [tex]log_{2}[/tex] ([tex]\sqrt{x}[/tex]) = 2
expand the expression:
[tex]log_{2}[/tex](6x) = [tex]log_{2}[/tex] (6) + [tex]log_{2}[/tex] (x)[tex]log_{2}[/tex] ([tex]\sqrt{x}[/tex]) = [tex]log_{2}[/tex] ([tex]x^{\frac{1}{2} }[/tex])transform the expression:
[tex]log_{2}[/tex] ([tex]x^{\frac{1}{2} }[/tex]) = [tex]\frac{1}{2}[/tex] * [tex]log_{2}[/tex] (x)calculate the difference:
[tex]log_{2}[/tex] (x) - [tex]\frac{1}{2}[/tex] * [tex]log_{2}[/tex] (x) = [tex]\frac{1}{2}[/tex] * [tex]log_{2}[/tex] (x)multiply both sides by 2:
[tex]log_{2}[/tex] (6) + [tex]\frac{1}{2}[/tex] * [tex]log_{2}[/tex] (x) = 2 is now 2 [tex]log_{2}[/tex] (6) + [tex]log_{2}[/tex] (x) = 4transform the expression:
2 [tex]log_{2}[/tex] (6) = [tex]log_{2}[/tex] ([tex]6^{2}[/tex])simplify the expression:
[tex]log_{2}[/tex] ([tex]6^{2}[/tex]) + [tex]log_{2}[/tex] (x) = [tex]log_{2}[/tex] ([tex]6^{2} x[/tex])evaluate the power:
[tex]log_{2}[/tex] ([tex]6^{2} x[/tex]) = [tex]log_{2} (36x)[/tex]convert the logarithm into exponential form:
[tex]log_{2}(36x) = 4[/tex] is now [tex]36x = 2^{4}[/tex]evaluate the power:
[tex]2^{4} = 16[/tex]divide both sides by 36:
[tex]\frac{36}{36}[/tex] x = [tex]\frac{16}{36}[/tex] which is x = [tex]\frac{4}{9}[/tex]A house on the market was valued at $396,000. After several years, the value increased by 8%. By how much did the house's value increase in dollars? What is the current value of the house?
Answer:
The value of the house increased $31,680.
The current value of the house is $427,680
Step-by-step explanation:
For a ride on a rental scooter, David paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for David's ride was $22.69. For how many minutes did David ride the scooter? minutes X
For $22.69 dollars I can ride the scooter for 179 minutes.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, A scooter ride has a starting fee of $3 and then 11 cents per mile.
Assuming with $22.69 I can ride x no. of minutes.
∴ 0.11x + 3 = 22.69.
0.11x = 19.69.
x = 19.69/0.11.
x = 179 minutes.
learn more about equations here :
https://brainly.com/question/29538993
#SPJ2
5 lb of apples at 2 lb for $0.80
Answer:
2 dollars for 5 lb
Step-by-step explanation:
^
Besides the actual mortgage payment, which also factors into the monthly payment on a home?
Please label your answer with the corresponding letter or you won't get brainliest. I like many others, hate having to sit through ads
A. repair costs
B. renters' insurance
C. property taxes
D. down payment
Answer:
C
Step-by-step explanation: Property taxes
For the quadratic function f(x) = x2 + 6x +11:
a. Use the idea of completing the square to write it in graphing form.
Step-by-step explanation:
Make f(x) = 0
[tex] {x}^{2} + 6x + 11 = 0[/tex]
First, we move the constant term to the right hand side of the equality sign.[tex] {x}^{2} + 6x = - 11[/tex]
Then, we half the coefficient of x and square our result.[tex]( \frac{6}{2} ) ^{2} = 3 ^{2} = 9[/tex]
Now, we add the result to the both sides of the equation.[tex] {x}^{2} + 6x + 9 = - 11 + 9[/tex]
We can see that x²+6x+9 = (x+3)² {Try factorizing}Therefore,(x+3)²= -2
(x+3)²+2= 0
f(x)= (x+3)²+2
Which is the f(x) in graphing form.
what is 3/5 - 3/10 = in simplest form
Answer:
3/10
Step-by-step explanation:
3/5 - 3/10 = 5×2 = 10 so 10 is the denominator
6/10 -3/10 = rewrite with a denominator of 10
(6-3)/10 = subtract numerators
3/10 already in simplest form
Answer:
3/5
Step-by-step explanation:
You don’t need a common denominator when subtracting
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Step-by-step explanation:
2*a*b + 2*a*c + 2*b*c = 2*8*2 +2*8*7 + 2*2*7 = 32 + 112 + 28 = 172 ft²
Answer:
172 ft2
Step-by-step explanation:
bxhxw= surface area
8x2x7=172
unit--> ft2
Choose the graph below that meets all three of the following requirements: Limit as x approaches 1 minusf(x) = 3 Limit as x approaches 1 plusf(x)= –1 Limit as x approaches 4f(x) = 2 On a coordinate plane, a horizontal line at y = 3 goes to open circle (1, 3). It then goes down to point (2, negative 1) and up to open circle (4, 2). It then increases through (7, 4). On a coordinate plane, a horizontal line starts at open circle (negative 1, 3) and decreases through (negative 3, 0). A curve starts at closed circle (1, negative 1), curves up to (4, 2), and curves down through (6, 0). On a coordinate plane, a line starts at (1, 3) and increases through (0, 4). A line starts at closed circle (4, 3) and decreases through (5, 2). A horizontal line starts at (1, negative 1) and goes to open circle (4, negative 1). On a coordinate plane, a curve starts at open circle (1, 3), increases to (0, 4), and curves down through (negative 2, 1). A line starts at closed circle (1, negative 1) and goes up through (4, 2).
Graph D (last one)
Step-by-step explanation:
edge
Answer:
the last graph is d
Step-by-step explanation:
same homework. different question.
Answer:
Answer = B. Obtuse.
Step-by-step explanation:
Ye Li drew another quadrilateral it is a parallelogram and has four right angles can it be rhombus?
Answer:
A rhombus is both a rectangle and a rhombus. All the sides are equal and each angle measure 90 degrees. So yes it can be a rhombus.
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
A squares angles are all 90 degree, a rhombus however, has perpendicular angles crossing each other that are equal to 90 degress.
3)
A mobile phone company uses the formula C = 10t + 20m to calculate the total cost
of a bill.
C is the total cost of the bill in pence
t is the number of text messages
m is the number of minutes of call time
Calculate the total cost for 150 texts and 50 minutes of call time.
р
Answer:
2500 pence (C = 2500)
Step-by-step explanation:
[tex]C = 10t + 20m[/tex]
From the given information, t is the number of texts so essentially you will plug in the number of texts provided (150) in the place of the variable t.
[tex]C = 10(150) + 20m[/tex]
Apply the same thing to minutes, plug in the number of minutes (50) in the place of the variable m.
[tex]C = 10(150) + 20(50)[/tex]
Now multiply the substitutes with the co-efficient.
[tex]C = 1500 + 1000[/tex] (10*150=1500 & 20*50=1000)
Add the addends
C = 2500
What is value of 5 in 2 500.7 please will like it to see how is solved without explaining,am really confused
Answer:
If there is no space between 2 and 5 then 5 is in the hundredths place
Step-by-step explanation:
For what values of b will F(x) log, xbe a decreasing function?
O A. 0> b>-1
B. b> 0
O C. b<0
O D. 0 < b<1
Step-by-step explanation:
Have a Great day✧◝(⁰▿⁰)◜✧The correct values for b is,
⇒ 0 < b < 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
F (x) = [tex]log_{b} x[/tex]
Now, We know that;
As the logarithm of a negative number is undefined, b should be a positive number (b>0 ).
Therefore, the value of b must be in the range of 1 > b > 0 for the function to be a decreasing function.
Thus, The correct values for b is,
⇒ 0 < b < 1
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ5
After arguing for two weeks, Seth convinced his parents to have his birthday party at FlyZone trampoline park. As soon as he gets there, Seth spends time practicing flips on the trampolines. Then, he spends
1/2
of an hour eating birthday cake with his friends. In all, Seth spends 1 1/4
hours at FlyZone.
Which equation can you use to find the amount of time t Seth practices flips?
Answer:
[tex]t + \frac{1}{2} = 1 \frac{1}{4} [/tex]
Trey caught a 3 1/4 pound fish. How much did it weigh in ounces?
Answer: 52 ounces
multiply the mass value by 16
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
m A equal 14 the second one is 11
Step-by-step explanation:
Each set of ordered pairs ( x , y ) represents a relationship with input x and output y . Which relationships do not represent a function? Select two correct answers. A. { ( ¯ 3 , 9 ), ( ¯ 1 , 1 ), ( 1 , 1 ), ( 3 , 9 ) } B. { ( ¯ 6 , 8 ), ( ¯ 6 , 4 ), ( 0 , 0 ), ( 3 , ¯ 4 ) } C. { ( 9 , ¯ 8 ), ( 8 , ¯ 9 ), ( ¯ 9 , 8 ), ( ¯ 8 , 9 ) } D. { ( ¯ 5 , ¯ 2 ), ( ¯ 1 , 3 ), ( 4 , 8 ), ( ¯ 1 , 13 ) } E. { ( ¯ 9 , ¯ 2 ), ( ¯ 5 , 11 ), ( 4 , ¯ 6 ), ( 1 , 17 ) }
Answer:
B and D
Why?
Well when looking for a function you have to look at the X Values. Why the X values? Well if they are different it is considered a function. If it is the same it will NOT be considered a function
5* 3 1/3 I have to have my math done in an hour and I don’t know this
16.65... .... ..... ...
Answer: 16.65
Step-by-step explanation:
1/3 is equivalent to the decimal value .33
so, use the equation:
5x(3+.33) or 5x3.33, which equals 16.65
. If 27 and 45 are two lengths of a right triangle, what is the third length of the right triangle?'
Answer:
36 ( or possibly sqrt (2754) )
Step-by-step explanation:
Use the Pythagorean Theorem to find the missing side (you will have to try two different times because you do not know what is missing....a leg or the hypotenuse)
27^2 + 45^2 = x^2 x = sqrt2754=52.4786 although this is one true answer, I do not think it is what the question seeks
let's try
27^2 + x^2 = 45^2 x = 36 Check !
Katie's earnings, E , for a week are given by the equation E = 18h, where H is the number of hours that Katie works during the week. If Katie works 40 hours per week for 4 weeks, how much money will she earn during the 4-week period?
Answer:
$2,880
Step-by-step explanation:
18 x 40 = 720 earned per week
720 x 4 (weeks) = 2880 earned in 4 weeks