The tables show the books read by two different students. Explain how to determine which student read faster.
Answers
The first student read faster than the second student.
Step-by-step explanation:
Step 1:
To determine how long each student takes to read a book, we divide the time taken to read by the number of books read in that period.
Time taken to read a book = [tex]\frac{time taken to read}{number of books read in that period}[/tex].
In the given table, the second column values are times taken to read and the first column represents the number of books read in that period.
Step 2:
For the first student, the time taken is calculated.
The first student's time taken to read a book = [tex]\frac{30}{3}[/tex] = [tex]\frac{50}{5}=\frac{70}{7}[/tex] = 10 minutes to read a book.
Step 3:
Similarly, the time taken to read a book is calculated for the second student.
The first student's time taken to read a book = [tex]\frac{24}{2}=\frac{48}{4}=\frac{72}{6}[/tex] = 12 minutes to read a book.
Step 4:
Now we compare the times taken. The first student read a book in 10 minutes while the second student took 12 minutes for a book. So the first student read faster.
Related Questions
cos^2x-sin^2x/sin^2x+sinxcosx=cotx-1
Answers
Answer:
[tex]\bold{\frac{(cosx-sinx)}{(sinx)}}=\bold{\frac{cosx-sinx}{sinx}}[/tex]
Step-by-step explanation:
[tex]\frac{cos^2x-sin^2x}{sin^2x+sinxcosx}=cotx-1[/tex]
We're going to start by manipulating the left side of the equation and making it the same form as [tex]cotx-1[/tex].
Start by applying the difference of two squares formula to the numerator, like so:
[tex]\frac{(cosx+sinx)(cosx-sinx)}{sin^2x+sinxcosx}[/tex]Now simplify the denominator by expanding the [tex]sin^2x[/tex].
[tex]\frac{(cosx+sinx)(cosx-sinx)}{(sinx)(sinx)+sinxcosx}[/tex]The denominator can even be further simplified since both addends (when added together = a sum) have the common factor of [tex]sinx[/tex]. Factor it out.
[tex]\frac{(cosx+sinx)(cosx-sinx)}{(sinx)(sinx+cosx)}[/tex]Cancel out the common factor [tex](cosx+sinx)[/tex].
[tex]\bold{\frac{(cosx-sinx)}{(sinx)}}[/tex]Since this is the furthest simplified that the left side can be manipulated, let's see if can try to manipulate the right side to also look like [tex]\frac{(cosx-sinx)}{(sinx)}[/tex].
Start by expressing [tex]cotx-1[/tex] with [tex]sinx[/tex] and [tex]cosx[/tex], since we know that cotangent is simply [tex]\frac{x}{y} \rightarrow\frac{cosx}{sinx}[/tex].
[tex]\frac{cosx}{sinx}-1[/tex]We can simplify this expression to look like our expression we found by manipulating the left side [tex](\frac{(cosx-sinx)}{(sinx)})[/tex] by making the 1 have a common denominator of [tex]sinx[/tex].
To do this, multiply 1 by [tex]\frac{sinx}{sinx}[/tex]. Now the expression should look like:
[tex]\frac{cosx}{sinx}-\frac{sinx}{sinx}[/tex]Since they have a common denominator we can write the expression under one fraction, like so:
[tex]\bold{\frac{cosx-sinx}{sinx}}[/tex]This looks exactly the same as what we manipulated the left side to be [tex](\frac{(cosx-sinx)}{(sinx)})[/tex], just without parentheses. I put both expressions in bold. Therefore, this identity proves to be true as we just proved it.
which equation represents the distributive property
Answers
Answer:
u didnt give all the info
Step-by-step explanation:
Simplify the expressions 4k9×8k3×k
Answers
Answer:
32k13
Step-by-step explanation:
32k13 Multiply the number add the the exponent
To simplify the expression 4k9×8k3×k, combine the coefficients and add the exponents of the same variable k to get 32k13.
Explanation:To simplify the expression 4k9×8k3×k, we can combine the coefficients and add the exponents of the same variable k.
4k9×8k3×k = (4×8)k(9+3+1) = 32k13
Therefore, the simplified expression is 32k13.
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20 points!!! (PLEASE ANSWER ALL, AND ALL CORRECTLY!!) this test is already late!
At the zoo, the ratio of mammals to reptiles is 4:3. There are 20 mammals in the zoo.
(a) How many reptiles are in the zoo?
(b) If the zoo adds 12 more mammals to its collection, how many more reptiles will they have to add to keep the ratio the same?
(c) A zoo in a different city has a ratio of mammals to reptiles of 6:5. Which zoo has the larger ratio of mammals to reptiles?
Thank you!
Answers
Answer: im not sure but a)15 B)24 c)zoo in a different city
Step-by-step explanation:
There are 15 reptiles in the zoo. To keep the ratio 4:3, if the zoo adds 12 more mammals, they will need to add 9 more reptiles. The first zoo has a larger ratio of mammals to reptiles (4:3) compared to the second zoo (6:5).
To answer the question, let's solve each part step by step:
Given the ratio of mammals to reptiles is 4:3 and there are 20 mammals, we can set up a proportion to find the number of reptilesIf the zoo adds 12 more mammals, to keep the same ratio of 4:3, we calculate the number of reptiles to add. We can find this by multiplying the 12 additional mammals by 3/4, which results in 9 more reptiles.To compare the ratios of the zoos, we can turn them into comparable fractions: 4/3 for the first zoo and 6/5 for the second zoo. By finding a common denominator or comparing their cross-multiplication products, we can determine which ratio represents a larger number of mammals to reptiles. Here, 4/3 is larger than 6/5, so the first zoo has a larger ratio of mammals to reptiles. This can be confirmed by cross multiplication: 4*5=20 and 6*3=18, since 20 is greater than 18, the first zoo has a larger ratio.2). A bag contains 50 pieces of gum flavored cherry, grape, and watermelon.
• William will randomly pick a piece of gum.
• The probability of picking cherry is 5.
• The probability of picking watermelon is 10.
3
What is the probability William will pick a piece of grape gum?
Answers
Answer:
37 (i think)
Step-by-step explanation:the probability means the amount of (in this case) the cherry gum or watermelon gum. Add the amount and then subtract the total from the WHOLE number of the WHOLE of the group
(hopefully that made sense)
Y=5x+20
Y=-7x-16
Solve each system by substitution
Answers
Answer:
x=3
y=35
Step-by-step explanation:
5x+20=-7x-16
-16+20=4
5x=-7x+4
5x+7x= 12x
12x=4
12/4=3
Answer: x = -3 ; Y = 5
Step-by-step explanation:
Y=5x+20
Y=-7x-16
5x+20 = -7x-16
5x+ 7x = -16 - 20
12x = - 36
x = -36 / 12
x = -3
Y=5x+20
Y = 5.(-3) + 20
Y = - 15+20
Y = 5
Can the number of students who completed their homework be represented as a function of the homework's
size?
Answers
It would be a positive, linear graph
i need 4 7 and 10
pleaseee
Answers
Step-by-step explanation:
4.
22+4x= 90
4x=90-22
4x=68
x°=17°
7.
(x-5)°+29°=180°
x-5+29=180
x= 180-24
x=156°
10.
(x+3)°+49°=90°
x= 90-52°
x=38°
multiplicative inverse of 9 ^3
Answers
Solution:
Given that,
We have to find the multiplicative inverse of [tex]9^3[/tex]
By multiplicative inverse,
The product of a number and its multiplicative inverse is 1
Given number is: [tex]9^3[/tex]
Let "x" be the required multiplicative inverse
Therefore,
[tex]9^3 \times \text{ multiplicative inverse of } 9^3 = 1[/tex]
[tex]9^3 \times x = 1\\\\x = \frac{1}{9^3}[/tex]
Thus the multiplicative inverse of [tex]9^3[/tex] is [tex]\frac{1}{9^3}[/tex]
The dot plot below shows 6 data points with a mean of 16.
A dot plot going from 11 to 20. 1 dot is above 12, 13, 15, 17, 19, 20.
What is the absolute deviation at 19?
Answers
Answer:I think its C
Step-by-step explanation:
Answer: the answer is c
Step-by-step explanation:
What is the area of this trapezoid
Answers
Answer:
[tex]A = 80[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
Given Data:
a = 7+3+7 =17 units
b = 3 units
h = 8 units
To Find Out:
Area of trapezoid = ?
Formula:
[tex]A = \frac{a+b}{2}h[/tex]
Solution:
[tex]A = \frac{a+b}{2}*h[/tex]
[tex]A = \frac{17+3}{2}*8[/tex]
[tex]A = \frac{20}{2}*8[/tex]
[tex]A =10*8[/tex]
[tex]A = 80[/tex] [tex]units^{2}[/tex]
Find the value of 6+x when x = 15.
Answers
Answer:
Step-by-step explanation:
Given the function f(x)=6+x
F(x) is dependent on x,
When x=1
f(x)=6+x
f(x)=6+1,
f(x)=7
When x=2
f(x)=6+x
f(x)=6+2
f(x)=8.
This will continue like this till we get to x=15
So when x=15
We will substitute x=15 into the function f(x)
f(x)=6+x
f(x)=6+15
f(x)=21
Then, the answer is 21.
Answer: 17
Step-by-step explanation:
To solve 6+x when x = 15,
Step 1: Substitute 15 into x
Step 2: Sum 6 and 15
6+15= 17.
Rectangle with length 8 1/2 in. And width 6in
Answers
Answer:
51 inches
Step-by-step explanation:
area = base x height
8.5 x 6 = 51
51 inches
Can there be two modes in a data set?? for example 2,5,6,7,9,9,11,11,12,13
Answers
Final answer:
Yes, a data set can have two modes, which occurs when two different values appear with equal and highest frequency, making the set bimodal.
Explanation:
Yes, there can be two modes in a data set. The mode is the most frequent value or values in a set of data. When a data set has exactly two modes, it is called bimodal. This phenomenon occurs when two different numbers appear with equal frequency and more often than any other numbers in a set. For example, in the data set 2,5,6,7,9,9,11,11,12,13, both 9 and 11 appear twice and more frequently than any other values, making them both modes of the data set.
Find the cost price if the selling price is $1800 and profit is $10%
Answers
Answer:$1636.4
Step-by-step explanation:
Selling price(sp)=$1800
Profit%=10%
Cost price(cp)=?
Profit%=(sp-cp)/cp x 100
10=(1800-cp)/cp x 100
Cross product
10cp=100(1800-cp)
Open brackets
10cp=180000-100cp
Collect like terms
10cp+100cp=180000
110cp=180000
Divide both sides by 110
110cp/110 = 180000/110
cp=1636.4
Cost price is $1636.4
Answer: Cost Price = $1, 636.36
Step-by-step explanation:
Given from the question Selling price (SP)= $1800; Profit%= 10%= 10/100 = 0.1
Cost price(CP)= ??
Profit% is derived by the formula
=(SP-CP)/ CP x 100
0.1 = (1800 - CP)/CP x 100
Then we cross multiply
0.1 x 100 x CP = 1800 - CP
10 CP = 100(1800 - CP)
Open the bracket
10 CP=180000 - 100CP
Divide both sides by 10
CP = 180000 - 100CP/10
CP = 18000 - 10CP
Combine like terms
CP + 10CP = 18000
11CP = 18000
Divide both sides by 11
CP = 18000/11
CP = $1, 636.36
write 16% as a decimal and reduced fraction
i need help
Answers
16% = 0.16 = [tex]\frac{4}{25}[/tex]
Step-by-step explanation:
Given,
16%
We need to find out the decimal and reduced fraction.
Decimal Fraction
16% = [tex]\frac{16}{100}[/tex] = 0.16
Reduced Fraction
16% = [tex]\frac{16}{100}[/tex] = [tex]\frac{4}{25}[/tex] [ Diving both by 4]
Answer:
0.16 as a decimal
4/25 as a reduced fraction
Step-by-step explanation:
16%
A percentage is an hundred. Hence, the percentage of any number is that number divided by 100.
16% will therefore be 16/100
To decimal form gives 0.16
To a reduced fraction, we have
16/100
Using 2 to reduce
8/50
Using 2 to reduce again
4/25
It can't be reduced with a common number again.
Classify a transformation as a rotation, a reflection, or a translation.
Answers
Answer:
a transformation could be a rotation, reflection, and/or a translation.
Step-by-step explanation:
In geometry, transformation refers to the movement of objects in the coordinate plane.
Therefore, a transformation could be a rotation, reflection, and/or a translation.
What is the value of the expression 3 ^ 3 - 2 ^ 3
Answers
Answer:
27 - 8 = 19
The answer is 19.
Step-by-step explanation:
The lengths of the three sides of a triangle are given. Classify each triangle as acute, right or
obtuse.
30, 40, 50
1)
Answers
Triangle with side lengths 30, 40, and 50 is a right triangle.
To classify the triangle based on the lengths of its sides, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For the given lengths of sides:
[tex]\(a = 30\)[/tex]
[tex]\(b = 40\)[/tex]
[tex]\(c = 50\)[/tex]
We can check if the triangle is a right triangle:
[tex]\[c^2 = a^2 + b^2\][/tex]
Substituting the values:
[tex]\[50^2 = 30^2 + 40^2\][/tex]
[tex]\[2500 = 900 + 1600\][/tex]
[tex]\[2500 = 2500\][/tex]
Since [tex]\(2500 = 2500\)[/tex], the Pythagorean theorem holds true, meaning this triangle is a right triangle.
So, the given triangle with side lengths 30, 40, and 50 is a right triangle.
What is the solution to the system of equations y=-3×-2 5×+2y=15
Answers
Answer: x = - 19
y = 55
Step-by-step explanation:
y = - 3x - 2 (1)
5x + 2y = 15 (2)
substitute y = - 3x - 2 into equation (2)
equation (2) becomes
5x + 2 (-3x - 2) = 15
5x + ( - 6x - 4) = 15
opening the bracket
5x - 6x - 4 = 15
collecting like terms
5x - 6x = 15 + 4
-x = 19
x = - 19
substituting x = - 19 into equation 1
y = - 3x - 2
y = - 3 (-19) - 2
y = 57- 2
y = 55
Answer:
x= 19/11
y=35/11
Step-by-step explanation:
If the circumference of a circle is 21.98cm, how much is the area?
Answers
Answer: 38.45
Step-by-step explanation:
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=21.98 \end{cases}\implies 21.98=2\pi r\implies \cfrac{21.98}{2\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi \left( \boxed{\cfrac{21.98}{2\pi }} \right)^2\implies A=\cfrac{21.98^2}{2^2\pi }\implies A\approx 38.445[/tex]
Use X= 5 to identify the value of each expression
.
Answers
Answer:
see explanation
Step-by-step explanation:
Using x = 5, then
x² = 5² = 5 × 5 = 25
[tex]1^{5}[/tex] = 1 × 1 × 1 × 1 × 1 = 1
[tex]5^{1}[/tex] = 5
Find the value of the expression. x2 + y for x = 5 and y = 6
Answers
Answer:
31
Step-by-step explanation:
[tex] {x}^{2} + y \\ = {5}^{2} + 6 \\ = 25 + 6 \\ = 31 [/tex]
Answer:
31
Step-by-step explanation:
25+6=31
Name the coordinates of the points on the graph.
F
G
H
M
P
Answers
Answer:
Is their a picture so we can see where to put it
Write an equation that represents the volume V as a function of the height h
Answers
Answer:
h=V/b
Step-by-step explanation:
The volume V can be represented as a function of height h by the equations V = lwh for a rectangular prism or V = πr²h for a cylinder. If other dimensions are constants, this can be simplified to V=k*h, where k represents the base area.
Explanation:To represent the volume V as a function of the height h, we typically consider the volume of a rectangular or cylindrical shape. The volume V of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. If we consider a cylinder, the volume is given by the equation V = πr²h, where r is the radius of the base circle and h is the height. However, if we simplify this formula assuming only the height can vary and all other dimensions are constants, the function could be simplified to V=k*h, where k represents the area of the base.
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two acute angles
two straight angles
two right angles
and two obtuse angles
Answers
Answer:
11.GBJ JBD 12.AD GE 13.GBC GBA 14.FCD JBE (is obtuse)
Step-by-step explanation:
Answer:
11.GBJ JBD 12.AD GE 13.GBC GBA 14.FCD JBE (is obtuse)
Step-by-step explanation:
Step-by-step explanation:
(a) Find the approximations T10, M10, and S10 for int 0- π (21 sin x) dx. 0 (Round your answers to six decimal places.) T10 = M10 = S10 = Find the corresponding errors ET, EM, and ES. (Round your answers to six decimal places.) ET = EM = ES = (b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error Bounds for Trapezoidal and Midpoint Rules and the Theorem about Error Bound for Simpson's Rule. (Round your answers to six decimal places.) |ET| ≤ |EM| ≤ |ES| ≤ (c) How large do we have to choose n so that the approximations Tn, Mn, and Sn to the integral in part (a) are accurate to within 0.00001? n = for Tn n = for Mn n = for Sn
Answers
The question refers to numerical approximation methods used for integration: the Trapezoidal, Midpoint, and Simpson's Rules. Answers for specific n-values and error calculations require a calculator or programming tool and are not provided here. The processes, however, involve application of respective formulae and comparison of approximations against the desired accuracy level.
Explanation:Solution:
The question is related to approximating the value of an integral using numerical methods, specifically using the Trapezoidal Rule (Tn), Midpoint Rule (Mn), and Simpson's Rule (Sn). Additionally, it asks about the corresponding estimation errors which are defined as differences between the true integral value and the approximations.
Part (a)
To find T10, M10, and S10 for ∫₀π (21 sin x) dx, we would use respective formulae. Unfortunately, without a calculator or computational tool, it's not practical to perform these calculations here in this answer.
Part (b)
The actual errors ET, EM, and ES compare to the theoretical error bounds given by the respective theorems for each rule. Again, without the approximated values from part (a), we cannot calculate these errors.
Part (c)
Choosing n so that the approximations are accurate to within 0.00001 is a trial and error process where you start with n and continue to increase it until the approximation is within the desired accuracy. This typically requires use of a computational tool or programming.
Please note, these answers can vary depending on the specific constants and functions used in the integration.
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The radius of the base of a right circular cone is 5 times greater than the radius of a second right circular cone. If the heights of both cones are the same, what is the volume of the larger cone divided by the volume of the smaller cone? A. 5 B. 10 C. 15 D. 25
Answers
The volume of the larger cone divided by the volume of the smaller cone is 25.
What is the ratio of the volumes?A cone is a three-dimensional object that is made up of a circular base and a vertex.
Volume of a cone = 1/3(πr²h)
Assumed dimensions of the smaller cone:
Height = 10 Radius = 3Volume = 1/3(π x 9 x 10) = 30π
Assumed dimensions of the larger cone:
Height = 10 Radius = 3 x5 = 15Volume = 1/3(π x 225 x 10) = 750π
Ratio of the volumes = 750π / 30π = 25
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Answer:
A, 25 is correct
Step-by-step explanation:
i got it right on edge 2023
Which graph COULD represent the table of values?
A) A
B) B
C) C
D) D
Answers
Answer:
This will be your answer. Good luck! :)
Step-by-step explanation:
'Desmos Graphing Calculator' is extremely helpful to anyone who needs help in math involving functions and solving equations. Take the time to learn how it works and it'll be your best friend. Free, reliable, and saves time!
LaTanya says that the growth factor of f(x) = 100(1.25) is 25%. What mistake did LaTanya make?
Answers
Answer:
The first error consists in the multiplication of f (x) = 100 * (1.25), the value she mentions is incorrect since it is 125.
It would be a 125% increase really.
In order for LaTanya's phrase to have no error she had to mention that it was a 25% increase over the original amount, in this way, the phrase would make sense and be valid.
Answer:
LaTanya confused growth factor with growth rate. The growth factor is 1.25. The growth rate is 25%.
Step-by-step explanation:
In the exponential growth model,
f(x)=a(1+r)x
a is the inital amount, r is the growth rate, and (1+r) is the growth factor. Hence, the growth factor of the given function is 1.25.