Answer: 18/25 chapters / hour
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit rate.
A unit rate is a rate with 1 in the denominator.
In simple words, the unit rate is something per one thing. For example, when you go to a store, you bought a book that is priced at $10. In actually meaning, it is $10 per book, or $10/book.
Solve:
Given formula
Unit rate = Number of chapters / Hours
Substitute the value into the formula
Unit rate = (3/5) / (5/6)
Convert to multiplication by taking the reciprocal of the divisor
Unit rate = (3/5) · (6/5)
Numerator times numerator / denominator times denominator
Unit rate = (3 × 6) / (5 × 5)
Unit rate = 18 / 25 chapter / hour
Hope this helps!! :)
Please let me know if you have any questions
The unit rate is 18/25 chapters per hour. This means Maria is reading at a rate of 18/25 chapters in one hour.
How to determine the unit rateTo calculate the unit rate, we're trying to find out how much of something (in this case, chapters) happens in a single unit of another thing (time, in hours).
In this scenario, Maria reads 3 out of 5 chapters in 5 out of 6 hours. To find the unit rate, we divide the chapters read (3/5) by the time taken (5/6 hours):
Unit Rate = Chapters Read / Time Taken
= (3/5) / (5/6)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Unit Rate = (3/5) * (6/5)
= (3 * 6) / (5 * 5)
= 18 / 25
So, the unit rate is 18/25 chapters per hour. This means Maria is reading at a rate of 18/25 chapters in one hour.
Learn more about unit rate at https://brainly.com/question/19493296
#SPJ3
Write y=2/3x+7 in standard form using intergers
Answer:
a.
Step-by-step explanation:
y = 2/3 x + 7
3 * y = 3 * (2/3 x + 7)
3y = 2x + 21
2x - 3y = -21
-2x + 3y = 21
Answer: a.
If f(x)=5(x+3)^3-2. What does f^-1(x) equal?
9514 1404 393
Answer:
C ∛((x+2)/5) -3
Step-by-step explanation:
To find the inverse function, solve for y:
x = f(y)
x = 5(y +3)³ -2 . . . . . . substitute f(y)
x +2 = 5(y +3)³ . . . . . add 2 -- already you know C is the answer
(x +2)/5 = (y +3)³ . . . . divide by 5
∛((x +2)/5) = y +3 . . . . take the cube root
∛((x +2)/5) -3 = y . . . . subtract 3
f^-1(x) = ∛((x +2)/5) -3 . . . . matches expression C
Geo-net, a cellular phone company, has collected the following frequency distribution for the length of calls outside its normal customer roaming area: Length (min.) Frequency 0<5 260<5 75 5<10 13910<15 10515<20 3720<25 1825+ 400 The sample mean(x) for this distribution is 14.3 minutes, and the sample standard deviation is 3.7 minutes. Determine whether these data are normally distributed (a = .05).
Answer:
Reject H0 ; and conclude that call length does not follow a normal distribution.
Step-by-step explanation:
Given :
The hypothesis :
H0: Call lengths outside normal customer roaming areas follows normal distribution
H1: Call lengths outside normal customer roaming areas do not follows normal distribution
Mean, μ = 14.3
Standard deviation, σ = 3.7
From the frequencies Given :
Expected values can be calculated :
Observed values :
16, 75, 139, 105, 37, 18 ; Total = 400
P(Z < (x - μ) / σ)) * total frequency
x = frequency
For x = 5 ;
P(Z < (5 - 14.3) / 3.7)) * 400 = 2.391
For x = 10;
P(Z < (10 - 14.3) / 3.7)) * 400 = 46.644
For x = 15;
P(Z < (15 - 14.3) / 3.7)) * 400 = 180.960
For x = 20;
P(Z < (20 - 14.3) / 3.7)) * 400 = 145.32
For x = 25;
P(Z < (25 - 14.3) / 3.7)) * 400 = 23.92
For x = 30;
P(Z < (30 - 14.3) / 3.7)) * 400 = 0.766
χ² = Σ(O - E)²/E
O = observed values
E = Expected values
χ² = (26-2.391)^2 / 2.391 + (75-46.644)^2 / 46.644 + (139-180.96)^2 / 180.96 + (105-145.32)^2 / 145.32 + (37-23.92)^2 / 23.92 + (18-0.766)^2 / 0.766 = 666.17
χ² = 666.17
The critical value "; df = n - 1= 6-1 = 5
α = 0.05
χ²critical(0.05 ; 5) = 11.07
χ²statistic > χ²critical ; Reject the Null, H0 ; and conclude that call length does not follow a normal distribution.
find the area of the circle whose equation is x2+y2=6x-8y
Answer:
Given that the equation of a circle is :
[tex] \green{ \boxed{\boxed{\begin{array}{cc} {x}^{2} + {y}^{2} = 6x - 8y \\ = > {x}^{2} + {y}^{2} - 6x + 8y = 0 \\ = > {x}^{2} + {y}^{2} + 2 \times ( - 3) \times x + 2 \times 4 \times y = 0 \\ \\ \sf \: standard \: equation \: o f \: circle \: is : \\ {x}^{2} + {x}^{2} + 2gx + 2fy + c = 0 \\ \\ \sf \: by \: comparing \\ \\ g = - 3 \\ f = 4 \\ c = 0 \\ \\ \sf \: radius \: \: r = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ {( - 3)}^{2} + {4}^{2} - 0 } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5 \: unit \\ \\ \bf \: area \: = \pi {r}^{2} \\ = \pi \times {5}^{2} \\ =\pink{ 25\pi \: { unit }^{2} }\end{array}}}}[/tex]
A. If x:y= 3:5, find = 4x + 5 : 6y -3
Answer:
17 : 27
Step-by-step explanation:
x=3
y=5
4(3)+5 : 6(5)-3
= 12+5 : 30-3
= 17 : 27
Jan gives Ted a loan at 4% effective to be repaid by 10 annual payments of 100, followed by 5 annual payments of 200. Just after Ted makes the 5th payment, Jly and Ted discover that each of the 15 payments should have been 10% higher than they were originally scheduled. They agree that Ted will make increased payments of K in the 6th through 10th years to adjust for the error. The payments of 200 in the 11th through 15th years will not change. Determine K.
a. 129
b. 113
c. 145
d. 139
e. 149
Answer:
139 ( D )
Step-by-step explanation:
Interest rate on loan = 4% = 0.04
Number of payments = 15
First 10 payments = 100 each
last 5 payments = 200 each
Calculating the value of K
K = [ ( 100 / 0.04 * ( 1-1 / 1.04^10 ) + 200/0.04 * ( 1-1 / (1 +0.04)^5)* 1 /1.04^10)
* 1.1 - 100 / 0.04 * ( 1-1 / (1+0.04)^5 ) - 200/0.04 * (1-1 /1.04^5) * 1/1.04^10)*0.04 / ( 1-1 / 1.04^5) * (1 + 0.04)^5
= 138.6051 ≈ 139
What is the axis of symmetry of the
parabola graphed below?
O x=4
Oy=2
Oy=4
Ox=2
Other:
Answer:
A
Step-by-step explanation:
i think so..sorry if im wrong
What is 5 (x-4) + 3x - 9x + 7?
Answer:
-x - 13
Step-by-step explanation:
5(x-4) + 3x - 9x + 7
First we use the distributive property to remove the parenthesis
5x -20 + 3x - 9x + 7
then we combine the like terms
-x - 13
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
Step-by-step explanation:
I really need help please
what is this?
Answer:
431.2
Step-by-step explanation:
Area of a regular polygon = # of sides * side length of 1 side * apothem
We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters
So # of sides = 7
apothem = 8
side length = 7.7
so the area would equal 7 * 8 * 7.7 = 431.2
It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth
Answer:
That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2
15.6
Step-by-step explanation:
Cos(x)=0.35 all solutions
Step-by-step explanation:
you have to type shift an cos button together at one time and then write 0.35 youwill get answer
Which formula can be used to describe the sequence?
Answer:
B could be used to show the formula to describe the sentence
Given the exponential function g(x)= 1∕2(2)^x, evaluate ƒ(1), ƒ(3), and ƒ(6).
A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32
B) ƒ(1) = 2, ƒ(3) = 9, ƒ(6) = 64
C) ƒ(1) = 1, ƒ(3) = 2, ƒ(6) = 8
D) ƒ(1) = 4, ƒ(3) = 16, ƒ(6) = 128
Answer:
A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32
Step-by-step explanation:
f(x)= 1∕2(2)^x,
Let x = 1
f(1)= 1∕2(2)^1 = 1/2 ( 2) = 1
Let x = 3
f(3)= 1∕2(2)^3 = 1/2 ( 8) = 4
Let x = 1
f(6)= 1∕2(2)^6 = 1/2 ( 64) = 32
Answer:
A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32
Step-by-step explanation: I took the test
5) If the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game. If they lose this game, they have a 1/2 chance of winning their next game.
A) Make a Markov Chain for this problem; give the matrix of transition probabilities and draw the transition diagram.
B) If there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game?
C) If they won today, what are the chances of winning the game after the next?
Answer:
If they win today's game, the probability to win the next game = 2/3
Therefore the probability that they lose the next game when they win today's game = 1-(2/3) =1/3.
If they lose today's game, the probability to win the next game = 1/2
so, the probability to lose is 1/2.
a) [tex]\begin{bmatrix} \frac{2}{3}&\frac{1}{2} & \\\\ \frac{1}{3}&\frac{1}{2} & \end{bmatrix}[/tex]
b) [tex]p=\begin{bmatrix} \frac{1}{2}\\\\ \frac{1}{2} \end{bmatrix}[/tex]
[tex]p^{'} =\begin{bmatrix} \frac{7}{12}\\\\ \frac{5}{12} \end{bmatrix}[/tex]
c) Let them win today's game
[tex]p=\begin{bmatrix} 1\\ 0 \end{bmatrix}\\\\\\p^{'} =\begin{bmatrix} \frac{2}{3}\\\\\frac{1}{3} \end{bmatrix}[/tex]
[tex]p^{''}= \left[\begin{array}{c}\frac{11}{18} \\\\\frac{7}{18} \end{array}\right][/tex]
The chances that they win their next game are 58.33%, while if they won today, the chances of winning the game after the next are 38.88%.
ProbabilitiesGiven that if the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game, while if they lose this game, they have a 1/2 chance of winning their next game, to determine, if there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game, and determine, if they won today, what are the chances of winning the game after the next, you must perform the following calculations:
(2/3 + 1/2) / 2 = X1,666 / 2 = X0.58333 = X((2/3 + 1/2 / 2) x 2/3 = X0.58333 x 0.666 = X0.3888 = XTherefore, the chances that they win their next game are 58.33%, while if they won today, the chances of winning the game after the next are 38.88%.
Learn more about probabilities in https://brainly.com/question/10182808
Write the quadratic function in the form g(x) = a (x-h)^2 +k.
Then, give the vertex of its graph.
g(x) = 2x^2 + 8x + 10
9514 1404 393
Answer:
g(x) = 2(x +2)² +2
vertex: (-2, 2)
Step-by-step explanation:
It is often easier to write the vertex form if the leading coefficient is factored from the variable terms:
g(x) = 2(x² +4x) +10
Then the square of half the x-coefficient is added inside parentheses, and an equivalent amount is subtracted outside.
g(x) = 2(x² +4x +4) +10 -2(4)
g(x) = 2(x +2)² +2
Comparing to the vertex form, we see the parameters are ...
a = 2, h = -2, k = 2
The vertex is (h, k) = (-2, 2).
Which function has exactly one real solution? A. f(x) = -4x2 + 9x B. f(x) = 2x2 + 4x – 5 C. f(x) = 6x2 + 11 D. f(x) = -3x2 + 30x – 75
Answer:
A.
[tex]{ \tt{f(x) = - 4 {x}^{2} + 9x }}[/tex]
Step-by-step explanation:
[tex]{ \tt{f(x) = x( - 4x + 9)}}[/tex]
In the equation z/6 =
36, what is the next step in the equation solving sequence?
Isolate the variable
using inverse operations.
Combine like terms.
Identify and move the coefficient and variable.
Move all numbers without a variable.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"Isolate the variable using inverse operations."
»»————- ★ ————-««
Here’s why:
To solve for a variable, we would have to isolate it on one side.
To isolate it, we would use inverse operations on both sides on the equation until the variable is isolated.
There are no like terms in the given equation.
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'z'...}}\\\\\frac{z}{6} = 36\\-------------\\\rightarrow (\frac{z}{6})6 = (36)6\\\\\rightarrow \boxed{z = 216}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
First option: Isolate the variable using inverse operations
Step-by-step explanation:
z/6 = 36
Since we already have the equation set up and cannot simplify any further, we must try to isolate the variable, z, by using inverse operations.
The inverse operation of division is multiplication, so to isolate z, we multiply 6 on each side:
z/6 · 6 = 36 · 6
z = 216
sin x - cos x - 1/√2 = 0
Find the value of x
Answer:
Step-by-step explanation:
Claims from Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. Claims from Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. All claim amounts are independent of the other claims. Fifty claims occur in each group. Find the probability the total of the 100 claims exceeds 1,530,000.
Answer:
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n instances of a normal variable:
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Sum of normal variables:
When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.
Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.
This means that:
[tex]\mu_A = 10000*50 = 500000[/tex]
[tex]s_A = 1000\sqrt{50} = 7071[/tex]
Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.
This means that:
[tex]\mu_B = 20000*50 = 1000000[/tex]
[tex]s_B = 2000\sqrt{50} = 14142[/tex]
Distribution of the total of the 100 claims:
[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]
Find the probability the total of the 100 claims exceeds 1,530,000.
This is 1 subtracted by the p-value of Z when X = 1530000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]
[tex]Z = 1.9[/tex]
[tex]Z = 1.9[/tex] has a p-value of 0.9713
1 - 0.9713 = 0.0287
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
A student writes
1 1/2 pages of a report in 1/2
an hour. What is her unit rate in pages per hour?
Answer:
3 pages per hour
Step-by-step explanation:
Take the number of pages and divide by the time
1 1/2 ÷ 1/2
Write the mixed number as an improper fraction
3/2÷1/2
Copy dot flip
3/2 * 2/1
3
9514 1404 393
Answer:
3 pages per hour
Step-by-step explanation:
To find the number of pages per hour, divide pages by hours.
(1.5 pages)/(0.5 hours) = 3 pages/hour
find the area of this unusual shape
Answer:
38 ft²
Step-by-step explanation:
The shape consists of a rectangle and two triangles.
Area of the shape = area of rectangle + area of the two triangles
✔️Area if the rectangle = L × W
L = 8 + 2 = 10 ft
W = 3 ft
Area of rectangle = 10 × 3 = 30 ft²
✔️Area of the large triangle = ½ × bh
b = 4 ft
h = 3 ft
Area of large triangle = ½ × 4 × 3 = 6 ft²
✔️Area of the small triangle = ½ × bh
b = 2 ft
h = 2 ft
Area of large triangle = ½ × 2 × 2 = 2 ft²
✅Area of the shape = 30 + 6 + 2 = 38 ft²
Suppose a classmate got 12+ 2x as
the answer for Example D instead of
2x + 12. Did your classmate give a
correct answer? Explain.
Answer:
Yes
Step-by-step explanation:
Using the commutative property (a + b = b + a), we can easily calculate that 12 + 2x is equal to 2x + 12.
4) A box has dimensions of 14 inches long, 1.4 feet wide,
and 9 inches high. What is the volume of the box?
The formula for the volume is V=1.w.h.
Answer:
2116.8 in^3
Step-by-step explanation:
V = l*w*h
All the units need to be the same
Convert 1.4 ft to inches
1.4 ft * 12 inches/ ft = 16.8 inches
V = 14 * 16.8 * 9
= 2116.8 in^3
Quick can someone plot these in a scatter plot
(9.2,2.33)
(19.5,3.77)
(15.5,3.92)
(0.7,1.11)
(21.9,3.69)
(0.7,1.11)
(16.7,3.5)
(0.7,1.11)
(18,4)
(18,3.17)
The scatterplot is below.
I used GeoGebra to make the scatterplot. Though you could use other tools such as Excel or Desmos, or lots of other choices.
Side note: I'm not sure why, but you repeated the point (0.7,1.11) three times.
The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3
Answer:
0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3
Step-by-step explanation:
We have the mean, which means that the poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily.
This means that [tex]\mu = 6.3[/tex]
What is the probability that, for any day, the number of special orders sent out will be exactly 3?
This is P(X = 3). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-6.3}*6.3^{3}}{(3)!} = 0.0765[/tex]
0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3
Dan's car depreciates at a rate of 6% per year. By what percentage has Dan's car depreciated after 4 years? Give your answer to the nearest percent
Answer:
it's easy you need to do 6%×4 it's 24%
The edge roughness of slit paper products increases as knife blades wear. Only 2% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 4% of products slit with worn blades exhibit roughness. If 25% of the blades in the manufacturing are new, 60% are of average sharpness, and 15% are worn, what is the proportion of products that exhibit edge roughness
Answer:
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
Step-by-step explanation:
Proportion of products that exhibit edge roughness:
2% of 25%(new blades).
3% of 60%(average sharpness).
4% of 15%(worn). So
[tex]p = 0.02*0.25 + 0.03*0.6 + 0.04*0.15 = 0.029[/tex]
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard deviation of 0.292 grams. Find the probability of randomly selecting a cigarette with 0.37 grams of nicotine or less. Round your answer to four decima
Let X be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.
P(X ≤ 0.37) = P((X - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(Z ≤ -2)
where Z follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform X to Z using the rule Z = (X - mean(X))/sd(X).)
Given the required precision for this probability, you should consult a calculator or appropriate z-score table. You would find that
P(Z ≤ -2) ≈ 0.0228
You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,
P(-2 ≤ Z ≤ 2) ≈ 0.95
which means
P(Z ≤ -2 or Z ≥ 2) ≈ 1 - 0.95 = 0.05
The normal distribution is symmetric, so this means
P(Z ≤ -2) ≈ 1/2 × 0.05 = 0.025
which is indeed pretty close to what we found earlier.
Jason collects baseball cards. He bought one card for $25. Its current value is represented by the expression 25(1.02)t, where t is the number of years Jason has owned the card. Is Jason’s baseball card going up or down in value?
Which of the following is the graph of
(x - 1)^2 + (y + 2)^2 = 4 ?
Answer:
a
Step-by-step explanation:
The correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given equation is ( x-1 )² + ( y + 2 )² = 4
The graph of the equation is attached with the answer below when we plot the graph we will get the circle that is lying in the third and the fourth quadrant.
Therefore the correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
To know more about graphs follow
https://brainly.com/question/25020119
#SPJ2
