The equation of the number of pages is y = 40 + 10x and for 9 days, you read 130 pages
How to determine the equation of the number of pages?From the question, we have
Initial number of pages = 40
Rate per day = 10 pages per day
The equation of the number of pages is then represented as
y = Initial number of pages + Rate per day x Number of days
Substitute the known values in the above equation, so, we have the following representation
y = 40 +10 * x
Evaluate
y = 40 + 10x
For 9 days, we have
x = 10
This gives
y = 40 +10 * 9
Evaluate
y = 130
Hence, the number of pages is 130
Read more about linear equations at
https://brainly.com/question/13738662
#SPJ1
Rahul invested $1,100 in an account paying an interest rate of 3 3/8% compounded
quarterly. Caleb invested $1,100 in an account paying an interest rate of 3 1/4%
compounded daily. After 8 years, how much more money would Rahul have in his
account than Caleb, to the nearest dollar?
Answer:
$13
Step-by-step explanation:
You want to know how much more Rahul's investment of $1100 at 3 3/8% compounded quarterly for 8 years is worth than Caleb's investment of $1100 at 3 1/2% compounded daily for 8 years.
Rahul's accountThe amount in Rahul's account is given by ...
A = P(1 +r/n)^(nt) . . . . . P invested at rate r compounded n times per year
A = $1100(1 +0.03375/4)^(4·8) = $1100(1.0084375^32) ≈ $1439.33
Caleb's accountThe same formula is used for Caleb's account, but with different numbers.
A = $1100(1 +0.0325/365)^(365·8) ≈ $1426.61
DifferenceThe difference in account values is ...
Rahul's - Caleb's = $1439.33 -1426.61 = $12.72 ≈ $13
Rahul will have about $13 more in his account.
<95141404393>
question a fair die with its faces numbered from 1 to 6 will be rolled. which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ? responses for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 13. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is one third . for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 12. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is one half . for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 23. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is two thirds . for three rolls of the die, a number less than 3 will land face up one time. for three rolls of the die, a number less than 3 will land face up one time. it will take three rolls of the die before a number less than 3 lands face up for the first time.
For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
Given that,
Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.
The best way to interpret the data is thus,
For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.
Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
Learn more about relative frequency:
brainly.com/question/16832475
#SPJ4
factor -1/2 out of 1/2x+6.
Answer:
-1/2(x - 12). Hope this helped out for you!
2. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.
CPCTC
Corollary 1 to the Isosceles Triangle Theorem
Corollary 2 of the Isosceles Triangle Theorem
Isosceles Triangle Theorem
Converse to the Isosceles Triangle Theorem
The theorem (A) CPCTC represents the given condition of the triangle.
What is CPCTC?According to the formula CPCTC, which stands for "corresponding portions of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.
When demonstrating the congruence of triangles or other shapes, the term CPCT is employed.
When a student is asked to demonstrate that two angles or two sides are congruent, CPCTC is frequently employed at the end of the proof or close to it.
So, in the given triangle:
The angles are bold and the lines are not bold.
This represents that it is proved first that the angles are congruent.
And through CPCTC, we are concluding that the sides of the triangles are also congruent.
Therefore, the theorem (A) CPCTC represents the given condition of the triangle.
Know more about CPCTC here:
https://brainly.com/question/6076251
#SPJ1
The price of a football season ticket is £1200 Next season the price will increase by 6% Work out how much the season ticket will cost next season.
Answer:
Step-by-step explanation:
34567
Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
2. x-int: (-4,0) , (-10, 0)
P (-6,-12)
Answer:
y = 1.5(x + 4)(x + 10)=========================
Givenx- intercepts (-4, 0) and (-10, 0),Point P (- 6, - 12).SolutionThe given translates as:
p = - 4, q = - 10, x = - 6, y = - 12Use given x - intercepts to get the equation:
y = a(x + 4)(x + 10)Use the coordinates of P to find the value of a:
- 12 = a(-6 + 4)(-6 + 10)- 12 = a*(-2)*4- 12 = - 8aa = - 12 / - 8a = 1.5The equation of this parabola is:
y = 1.5(x + 4)(x + 10)Answer:
[tex]\textsf{Intercept form}: \quad y=\dfrac{3}{2}(x+4)(x+10)[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{3}{2}x^2+21x+60[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-4, 0) and (-10, 0) then:
p = -4q = -10Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-4))(x-(-10))[/tex]
[tex]\implies y=a(x+4)(x+10)[/tex]
To find a, substitute the given point on the curve P (-6, -12) into the equation:
[tex]\implies -12=a(-6+4)(-6+10)[/tex]
[tex]\implies -12=a(-2)(4)[/tex]
[tex]\implies -12=-8a[/tex]
[tex]\implies a=\dfrac{-12}{-8}[/tex]
[tex]\implies a=\dfrac{3}{2}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=\dfrac{3}{2}(x+4)(x+10)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=\dfrac{3}{2}(x^2+14x+40)[/tex]
[tex]\implies y=\dfrac{3}{2}x^2+21x+60[/tex]
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
30k-30k +2j
Answer:
2j
Step-by-step explanation:
30k-30k = 0
0 + 2j = 2j
eight points are in/on the circle of radius 1cm. show that distance between some two points is less than 1cm.
According to the circle, if 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm.
Circle:
Circle refers the round shape that has no corners or line segments. And it is a closed curve shape in geometry.
Given,
Eight points are in/on the circle of radius 1cm.
Here we need to show that distance between some two points is less than 1cm.
Let us consider the points be p1,p2,…,p8
Noe, we have to place the point p8 at the center of the circle and placing other seven points on the periphery of the circle, at equal distances
Here we have to remember that we are required to prove that there are at least a pair of points whose distance from each-other is less than 1cm.
So, now we have one point at the center and seven at the periphery of the circle.
Based on this the heptagon which will be formed by joining the seven points on the circle will have all its side equal in length.
Then the length of the side of the heptagon is less than 2π/7 cm which is less than 1cm.
Therefore, if we replace the position of any point then too we get a pair of points whose distance from each-other is less than 1cm.
To know more about Circle here.
https://brainly.com/question/11833983
#SPJ4
At a water park, 26 out of 52 tickets sold were child tickets. What percentage of the tickets
were child tickets?
Answer:
50%
Step-by-step explanation:
[tex]\frac{26}{52}[/tex] x 100 = 50
ANSWER
1. Your friend decides you should go to a clothes store next. Your friend has one hundred dollars. They pick out 10 items. The first three are $15.99, the second three are $10.40 and the last four are $4.50. Explain how you would estimate if your friend has enough money to buy all the items. Then setup an expression to find out if your friend has enough money to buy all the items. Lastly, find the total from your expression.
2. The weather man says the temperature will increase by 32 degrees by 12 pm then decrease by 14 degrees at 6pm where it remains constant. Setup an expression for finding temperature throughout the day. Find the final temperature from your expression.
In order to determine if your friend has enough money to buy all the items, the total cost of the items have to be determined. The total cost is the sum of all the items bought.
Total cost = total cost of the first three items + total cost of the second three + total cost of the last three
Total cost = (3 x 15.99) + (3 x 10.40) + (4 x 4.50)
Total cost = $47.97 + $31.20 +18
Total cost = $97.17
An increase in temperature would be represented with a positive number. While, a decrease in temperature would be represented with a negative number. The final temperature can be determined by adding the temperature increase and decease together.
Final temperature = increase in temperature - decrease in temperature
Final temperature = 32 - 14 = 18 degrees
To learn more about temperature, please check: https://brainly.com/question/136550
#SPJ1
ayo can sm help me w this question?
Answer: [tex]2^{-3}[/tex]
Step-by-step explanation:
[tex]4^{-6} *4^4*(2^3*2^{-4} )^{-1}\\=(2^2)^{-6}*(2^2)^4*(2^{3-4})^{-1}\\=2^{-12}*2^8*(2^{-1})^{-1}\\=2^{-12+8}*2^1\\=2^{-4}*2^1\\=2^{-4+1}\\=2^{-3}[/tex]
10.) Christina cuts 4 squares with side length x inches from the corners of a 5 inch by 10 inch cardboard
rectangle. She folds the remaining cardboard to make a tray that is x inches high.
Write and simplify a polynomial function for the volume V of the tray in terms of x.
The polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.
According to the question,
We have the following information:
Christina cuts 4 squares with side length x inches from the corners of a 5 inch by 10 inch cardboard rectangle. She folds the remaining cardboard to make a tray that is x inches high.
Now, the length of the tray will be (10-2x) inches and the breadth of the tray will be (5-2x) inches.
Volume of tray = length*breadth*height
Volume of tray = (10-2x)(5-2x)x
Volume of tray = x(50-20x-10x+4[tex]x^{2}[/tex])
Volume of tray = x(4[tex]x^{2}[/tex]-30x+50)
Volume of tray = [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches
Hence, the polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.
To know more about volume of the tray here
https://brainly.com/question/17456220
#SPJ9
can someone help me really quick
A line parallel to the line produced by 6x-2y=25 has what gradient?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]6x-2y=25\implies -2y=-6x+25\implies y=\cfrac{-6x+25}{-2} \\\\\\ y=\cfrac{-6x}{-2}+\cfrac{25}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{3}x-\cfrac{25}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}[/tex]
big ben, the nickname for the clock in elizabeth tower (named after the queen in 2012) in london, has an hour hand 2.70 m long with a mass of 60.0 kg and a minute hand 4.50 m long with a mass of 100 kg (figure). calculate the total rotational kinetic energy of the two hands about the axis of rotation. (you may model the hands as long, thin rods rotated about one end. assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)
The hour hand is 2.70 m long and minute hand is 4.50m long with mass of 60 kg and 100 kg. Therefore. Total angular momentum is 1.2 kgm²/s.
Mass of Hour hand = 60 kg
length of hour hand = 2.70 m
Now,
Moment of inertia of the hour hand is given by:
I = mL²/ 3
I = 60(2.70)²/3
I = 145.8 kgm²
Now,
The angular speed of hour hand is:
ω = 2π/ T
⇒ ω = 2π / 12×3600
⇒ ω = 1.45 × 10⁻¹ rad/s
Now,
Angular momentum is given as:
L₁ = Iω = 145.8 × 1.45× 10⁻¹
= 0.021 kgm²/s
Mass of minute hand = 100 kg
length of minute hand = 4.50 m
Now,
Moment of inertia of the minute hand is given by:
I = mL²/ 3
I = 100(4.50)² /3
I = 675 kgm²
Now,
The angular speed of minute hand is
ω = 2π/ T
ω = 2π / 60× 60
ω = 1.74 × 10⁻³ rad/s
Now,
Angular momentum is given as:
L₂ = Iω = 675 × 1.74 ×10⁻³
= 1.178 kgm²/s
Total angular momentum is given as
L = L₁ + L₂
= 0.021 + 1.178
= 1.2 kgm²/s
Learn more about Angular momentum:
https://brainly.com/question/15104254
#SPJ4
Can Someone Please Help Me? Thanks!
Find the opposite of the polynomial.
−5a²b⁴c
A. 10a²b⁴c
B. 5a²b⁴c
C. −2.5a²b⁴c
D. −5a²b⁴c
What is the function of the following graph?
Answer:
I can't see the graph anywhere.
Step-by-step explanation:
Compare -2.655 and 4 square root
Answer:
-2.655 < -√4
Step-by-step explanation:
-√4 = -2
-2.655 < -2
I assume that's what the question is asking for?
What is the equation of the line that passes through the point (-4,5) and has a slope of 3/4
Answer:
y = 3/4 x + 8
Step-by-step explanation:
y-5 = 3/4 (x-(-4)
y - 5 = 3/4 (x+4)
y - 5 = 3/4 x + 3
Y = 3/4 x + 3 + 5
y = 3/4 x + 8
Answer:
(-4,5) x = -4 and y = 5
use y = mx + c formula
so 5 = 3/4 (-4) +c
5 = -3 + c
5 + 3 = c
so c = 8
y = 3/4x + 8
Some students in Grade 7 and Grade 8 take a survey about whether they would prefer to join
a dance club or a hiking club. The table shows the results. The students want to make
25 POINTS
The completion for the row of the table will be:
Grade 8
Dance club: 0.25
Hiking club: 0.75
Total : 1
Grade 9:
Dance club: 0.40
Hiking club: 0.60
Total : 1
How to calculate the values?The dance club for grade 8 will be calculated as:
= Number of dancers / Total number
= 5/20
= 0.25
The hiking club will be:
= 15/20
= 0.75
The dance club for grade 9 will be calculated as:
= Number of dancers / Total number
= 20/50
= 0.4
The hiking club will be:
= 30/50
= 0.6
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
Halla dos números enteros consecutivos tales que el triple del primero menos el doble del segundo seas 119
Answer:
121; 122
Step-by-step explanation:
x
x+1
3x-2(x+1) = 119
3x-2x-2 = 119
x = 119 +2
x = 121
x+1 = 122
Let f(x)=1/2x-3 Suppose you subtract 6 from the input of f to create a new function g, and then multiply the input of function g by 4 to create a function h. What equation represents h?
The value of h(x)= 2x- 36.
What is function?
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)=[tex]\frac{1}{2x}[/tex]-3
Now, subtract 6 from the input of f to create a new function g
g(x)= [tex]\frac{1}{2x}[/tex]-3 -6
g(x)= [tex]\frac{1}{2x}[/tex] -9
and, multiply the input of function g by 4
h(x)= 4([tex]\frac{1}{2x}[/tex] -9)
h(x) = 2x- 36
Hence, the value of h(x)= 2x- 36.
Learn more about function here:
https://brainly.com/question/29388264
#SPJ9
If I were to start with $50 and add $20 each week for 12 weeks, what is an equation that represents the relationship between the dollar amount and the number of weeks?
Answer:
This is a function y = mx + b:
You start with $50, so the y-intercept(b) is 50.Adding $20 a week means that the slope(m) is 20.So, the function would be y = 20x + 50, where y is the dollar amount after x weeks and x cannot be greater than 12.
HELLP ME LOL PLEASE THHANK
Answer:
Clara will call 1 more person than Toby
Step-by-step explanation:
Every 10 phones call is 4 people so 40 phone calls will be 16 people
If every 8 phones calls is 3 people then 40 phones calls will be 15 people
By 1 person
Sorry about previous answer I read question wrong
Hopes this helps please mark brainliest
Answer:
if times 40 it is clara by 40
Step-by-step explanation:
Charlie is making copies of fliers to advertise his new club at school. The cost for 25 copies is $3.75. What is c, the total cost Charlie will pay for 40 copies?
The total cost for Charlie to make 40 copies of flyers is $6
Given the fact that 25 copies of flyers is costing him $3.75, we will then need to find the cost of each copy of the flyer. The figure is calculated using unit rates as follows:
25x = 3.75
x = 3.75/25
x = 0.15
so each copy of a flyer will cost him $0.15
To make 40 copies of flyers, Charlie will need to spend:
$0.15 × 40 = $6
So the amount of money Charlie will have to spend in order to make a copy of 40 flyers is $6
To learn more about unit rates visit: https://brainly.com/question/4895463
#SPJ1
Answer: Charlie will pay 6$.
Step-by-step explanation:
The sum of 4 consecutive even integers is 284. What is the value of the greatest integer?
Answer: 74
Step-by-step explanation:
Lets say the four even numbers are 2x - 4, 2x - 2 , 2x , 2x + 2
The sum would be
8x - 4 = 284
x = 36
Therefore, the smallest number is 2 * 36 - 4 = 68
The consecutive even numbers are 68, 70, 72, 74 and 74 is the largest.
4. because we are using a coin flip app, this experiment really tests only that app inventor's random integer block generates 1 around half the time. is this a sufficient test for app inventor's prng? what other experiments might you do to increase your confidence in app inventor's prng?
App inventor's random integer block test is sufficient for app inventor's prng . but to increase our confidence in app inventor's prng we can do other tests like random fraction test and random set speed test.
The Coin Flip Experiment app allows you to run experiments aimed at determining how "good" the App Inventor PRNGs are. The app allows the user to "flip a coin" her N times and the results are displayed. They should record and count the results and calculate the average head percentage. The expectation of should reach 50% on average as N increases.
To properly test an App Inventor PRNG, you must test both the Random Integer and Random Fraction blocks along with the Random Fraction and Random set speed to blocks. Create dice simulations to get better than 50/50 predictions and reuse dice simulators for all combinations of different App Inventor random blocks. If such a combination yields the same results, then you can be confident that her PRNG in App Inventor provides a good model of randomness from all angles.
To learn more about Coin flip app , refer:
https://brainly.com/question/28688416
#SPJ4
9.- Suma de fuerzas
4
45N + SON + 25N
4
4
127N 200N + 1250N
4
1
355N + 40N + 30N + 20N
Answer:
multiply
Step-by-step explanation:
2345567 in the subtract 578431111
HELPPPP :Solve for x. (23x-3) degrees and 78 degrees
Arc & Angle measure formed by Chords, Secants, & Tangents
The value of x in the intersecting chords SP and PB is determined as 3.52.
What is the value x?The value of x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc SB = m∠SPB
From the diagram, we have arc SB = 78⁰
m∠JNK = 78 (interior angles of intersecting secants)
23x - 3 = 78
23x = 78 + 3
23x = 81
x = 81/23
x = 3.52
Thus, the value of x in the intersecting chords SP and PB is determined as 3.52.
Learn more about chord angles here: brainly.com/question/23732231
#SPJ1
the correlation between variables x and y is .50. You compute a least squares regression line wit this bivariata data. Which of the following is true?
a. the r^2 is greater than .50
b. the regression constant is positive
c. the regression coefficient is positive
d. the slope of the regression line is negative
e. all of the above
The correlation between variables x and y is 0.50 . The true option is option (c) .
that's the regression coefficient is positive for given bivariata.
Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The
sample correlation coefficient r quantifies the strength of the relationship.
Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.
Here:
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at allPearson's correlation coefficient is denoted by "r" and is
r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)
We have given that correlation between x and y is 0.50.
cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2
=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)
Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.
Symbolically it can be expressed as:
bₓᵧ= r σ ₓ /σ ᵧ
where x and y are correlated
σ ₓ --> standard deviation of X
σᵧ ---> standard deviation of y
We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.
Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.
Hence, Regression cofficient is positive.
To learn more about Regression and Correlation, refer :
https://brainly.com/question/16814950
#SPJ4