Answer:
The common ratio is - 3Step-by-step explanation:
To find the common ratio between the terms of the sequence divide the previous term by the next term.
That's
[tex] - 2 \div \frac{2}{3} = - 2 \times \frac{3}{2} = - 3[/tex]Or
[tex] \frac{6}{ - 2} = - 3[/tex]Therefore the common ratio of the sequence is - 3
Hope this helps you
Answer:
-3
Step-by-step explanation:
A package of 8-count AA batteries costs $6.40. A package of 20-count AA batteries costs $15.80. Which statement about the unit prices is true?
Answer:
The unit price of the 20 pack is $0.79 and the unit price for the 8 pack is $0.80.
Step-by-step explanation:
Simply Take the price of the pack of batteries divided by the number within the pack.
$6.40 / 8 == $0.80
$15.80 / 20 == $0.79
Cheers.
The question is incomplete. You can find the missing content below.
A package of 8-count AA batteries costs $6.40. A package of 20-count Of batteries costs $15.80. Which statement about the unit prices is true?
A) The 8-count pack of AA batteries has a lower unit price of $0.79 per battery.
B) The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.
C) The 8-count pack of AA batteries has a lower unit prices of $0.80 per battery.
D) The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.
The correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.
What is inequality?Inequality is the relation between two numbers or variables or expressions showing relationships like greater than, greater than equals to, lesser than equals to, lesser than, etc.
For example 2<9
A package of 8-count AA batteries has cost = $6.40.
cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries
= $6.40/8= $0.8
A package of 20-count AA batteries has cost = $15.80.
cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries
= $15.80/20= $0.79
As 0.79<0.8
cost of 20-count AA batteries < cost of 8-count AA batteries
Therefore the correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.
Learn more about inequality
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The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
Find the first term in the sequence when u(subscript)31=197 and d= 10.
Answer:
197 = 10(31-1) + a
197 = 300 + a
-103 = a
6(x + 2) = 30Solve the following linear equation
Answer:
[tex]\huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]6(x+2)=30[/tex]
[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]
[tex]x+2=5[/tex]
[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]
[tex]x=3[/tex]
Answer:
3
Step-by-step explanation:
30 = 6(x+2)
30/6 = 5
5 = x+2
5-2 = 3
3=x
This is a pretty simple question and I tried to make it as simple as possible when explaining it.
paul worked 50 hours last week. if he earns $10 per hour plus time-and-a-half for any hours worked beyond 40 in a week, how much did he earn last week?
Answer: 4150
Step-by-step explanation:
You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!
4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25
Answer:
a) Means: 24 and 2; Extremes: 4 and 12
b) Means: 6 and 16; Extremes: 24 and 4
c) Means: 8 and 8; Extremes: 4 and 16
d) Means: 50 and 3; Extremes: 6 and 25
Step-by-step explanation:
The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:
a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.
The Means are the values that appear in the middle of the one line expression, that is: b and c.
Recall as well that the proportion can also be written with fractions:
a : b = c : d is the same as: a / b = c / d
so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.
A circle has center (3, -5) and the point (-1, -8) lies on the circumference of the circle. What is the equation of the circle in Standard Form?
Answer:
[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]
Step-by-step explanation:
First find the radius
Which is the distance between the 2 points.
Radius =5
The answer in the standad form is above.
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
The standard equation of a circle is given as:
(x - a)² + (y - b)² = r²
where (a, b) is the center of the circle and r is the radius of the circle.
Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:
[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]
hence:
(x - 3)² + (y - (-5))² = 5²
(x - 3)² + (y + 5)² = 25
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
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Which of the following could be the equation of the line passing through (8, 3) parallel to y = -2.
Answer:
y = 3 passes through (8, 3) and is therefore parallel to y = -2
Step-by-step explanation:
Any line parallel to y = -2 is a horizontal one, and it has the same slope (zero) as does y = -2.
We could invent the horizontal line y = 3 (which comes from the point (8, 3) and surmise that it is parallel to the given line y = -2.
Thus, y = 3 passes through (8, 3) and is therefore parallel to y = -2.
In the future, please share any answer choices that are give you. Thank you.
Please answer this correctly without making mistakes
Answer:
151 9/19
Step-by-step explanation:
Step-by-step explanation:
Option A is the correct answer because it is equal to 151.47
The range of values for x?
Answer:
x = 32
but
I would say anything from 30 to 33
but truly i have no clue about the range
Step-by-step explanation:
3x-9=87 (because 180 -93 =87)
3x = 96
x = 32
Answer:
it is 32
Step-by-step explanation:
In a genetics experiment on peas, one sample of offspring contained green peas and yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of that was expected? 350 127 3 4 The probability of getting a green pea is approximately . (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to ? Choose the correct answer below. 3 4 A. No, it is not reasonably close. B. Yes, it is reasonably close.
Complete Question
In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?
Answer:
The probability is [tex]P(g) =0.72[/tex]
Yes the result is reasonably close
Step-by-step explanation:
From the question we are told that
The number of of green peas is [tex]g = 436[/tex]
The number of yellow peas is [tex]y = 171[/tex]
The sample size is [tex]n = 171 + 436 = 607[/tex]
The probability of getting an offspring pea that is green is mathematically represented as
[tex]P(g) = \frac{g}{n}[/tex]
[tex]P(g) = \frac{436}{607}[/tex]
[tex]P(g) =0.72[/tex]
Comparing [tex]P(g) =0.72[/tex] to [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close
what are the comparison symbols for 5/6 and 2/5, 4/10 and 7/8, and 3/12 and 1/4
Answer like this: Example
=
<
>
Answer:
5/6 > 2/44/10 < 7/83/12 = 1/4Step-by-step explanation:
The comparison will be the same if you subtract the right side and compare to zero:
a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol
a/b - c/d ?? 0 . . . . subtract the fraction on the right
(ad -bc)/bd ?? 0 . . . combine the two fractions
ad - bc ?? 0 . . . . . . multiply by bd to make the job easier
__
5/6 and 2/5
5(5) -6(2) = 25 -12 > 0 ⇒ 5/6 > 2/5
4/10 and 7/8
4(8) -10(7) = 48 - 70 < 0 ⇒ 4/10 < 7/8
3/12 and 1/4
3(4) -12(1) = 0 ⇒ 3/12 = 1/4
_____
Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.
0.833 > 0.400
0.400 < 0.875
0.250 = 0.250
What is the best way you learn math?
Answer:
to provide interest in the subject
As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c
Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.
Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.
if you're next to your exams then just one thing, Start now!!
hope this helps!
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
In the multiplication below, each of A, B and
C represents a different digit. What is ABC?
A B C
X
3
В В В
Answer:
ABC = 148, 3*148 = 444
Step-by-step explanation:
We know that 111 = 3* 37, so all numbers of the form BBB has the factor 37.
So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.
Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.
So ABC is 148.
A Ferris wheel has a diameter of 42 feet it rotates 3 times per minute approximately how far will a passenger travel during a 5 minute ride
Answer:
1978.2 or 630π feet
Step-by-step explanation:
The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.
6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12
Answer:
x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
6x - 10 = 4(x+3)
6x - 10 = 4*x + 4*3
6x - 10 = 4x + 12
6x - 4x = 12 + 10
2x = 22
x = 22/2
x = 11
check:
6*11 - 10 = 4(11+3)
66 - 10 = 4*14 = 56
If the item regularly cost d dollars and is discounted 12percent which of the following represents discount price dollar
Answer:
-12
Step-by-step explanation:
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
3 x times the fraction 1 over x to the power of negative 4 => 3x * 1/x^-4
= 3x *x^4 = 3x^5
times x to the power of negative 3 => x^-3
3x^5 * x^-3 = 3x^2
Answer:
3x^2
Step-by-step explanation:
i got it right on the test on god!
The coffee cups can hold 7/9 of a pint of liquid. If Emily pours 2/3 of a pint of coffee into a cup,how much milk can a customer add? PLZ HELP!
Answer:
1/9
Step-by-step explanation:
easy 2/3 is equivalent to 6/9. So there is 1/9 of a pint left
Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
Answer:
17h+1.75m=522 m=40h
Step-by-step explanation:
Let h= {the number of hours the driver drove}
Let m= the number of miles driven
The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:
17h+1.75m=522
17h+1.75m=522
Since the driver drove an avearge of 40 miles per hour, if the driver drove hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:
m=40h
m=40h
Write System of Equations:
17h+1.75m= 522
m=40h
The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
The following are the different costs of the truck that Luke must be pay while running a truck:
Luke must pay the driver $17 per hour of driving.A truck has an expense of $1.75 per mile driven for gas and maintenance.Let ' x ' be the total time of driving a truck in hours.
and ' y ' be the total mile distance that is covered by the truck.
Therefore, the system of the equation for the overall running cost for a truck is given below.
[tex]\rm{Cost}=17x+1.75y[/tex]
Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.
Thus,
The total distance traveled by truck is 40x.
That is,
[tex]y=40x[/tex]
Substitute the values and solve them further.
[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]
Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
To know more about variables, please refer to the link:
https://brainly.com/question/14393109
Select the correct answer from each drop-down menu.
Nirja has 24 marbles. The number of marbles Nirja has is 6 more than the number of marbles Tim has.
If Tim has x marbles, the equation that represents the situation is
The value of x that makes the equation true is
Reset
Next
Answer:
24 = x+6
x = 18
Step-by-step explanation:
N = 24
T = x
N = x+6
24 = x+6
Subtract 6 from each side
24-6 = x+6-6
18 = x
Time has 6 marbles
Nirja has 6 more than Tim,
So you can subtract 6 from 24 to find x:
24-6 = x
Or you can add 6 to x to equal 24:
x + 6 = 24
You don't list the choices but it should be one of these.
Solve:
24 - 6 = x
x = 18
can you please help ?
Answer:
69
Step-by-step explanation:
The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.
We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.
[tex]\frac{5(x)}{2} -6[/tex]
[tex]\frac{5(30)}{2}-6[/tex]
[tex]\frac{150}{2}-6[/tex]
[tex]75-6[/tex]
[tex]69[/tex]
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 3 − 5 x y^=3-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:
1.) When amount of schooling increases by one year, the number of pregnancies decreases by 4.
2.) When amount of schooling increases by one year, the number of pregnancies increases by 4.
3.) When amount of schooling increases by one year, the number of pregnancies increases by 5.
4.) When amount of schooling increases by one year, the number of pregnancies decreases by 5.
Answer:
1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.
Step-by-step explanation:
Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4
Please answer asap this person made a mistake what is the error and correct solution to this problem
Answer:
6
Step-by-step explanation:
Hello, please consider the following.
[tex](4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2[/tex]
So the correct equation becomes.
[tex]x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=\dfrac{45}{8}=6[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
Error : The expression ( 4 + x )² was expanded incorrectly.
Correct Solution : x = 6
Step-by-step explanation:
The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.
PQ² + QO² = PO²,
x² + 8² = ( 4 + x )²,
x² + 8² = 16 + 8x + x²,
64 = 16 + 8x,
48 = 8x,
x = 48 / 8 = 6, x = 6
As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2 [tex]*[/tex] 4 [tex]*[/tex] x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.
Answer:
F = 32.2mStep-by-step explanation:
According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e
F = mg where;
F is the force of gravity
m is the mass of the body
g is the proportionality constant known as the acceleration due to gravity.
If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;
F = m*32.2
F =32.2m
Hence the required equation is F = 32.2m
In a survey of 200 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2. When testing the hypothesis (at the 5% level of significance) that the average price-earnings ratio has increased from the past value of 16.8, the null and alternative hypotheses would be:________
Answer:
Null Hypothesis: H0:μ ≤ 16.8
Alternative Hypothesis: Ha: μ > 16.8
Step-by-step explanation:
We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.
It means that the past value was not more than 16.8.
This follows that the null hypothesis is given as;
H0:μ ≤ 16.8
And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;
Ha: μ > 16.8
