The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
In the given question, a five number summary is given as follows
2.9, 5.7, 10.0, 13.2, 21.1
We need to find the IQR
So, first we'll find the median of the given series
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0
Now to find the IQR the given formula will be used,
IQR = Q3 - Q1
Where Q3 is the last term in lower series and Q1 is the last term in upper series
Lower series - 2.9, 5.7
Upper series - 3.2, 21.1
Q3 = 5.7 , Q1 = 21.1
IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)
Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
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Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:
Given:
Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.
The total number of sample space is, N = 10.
Head for female kitten
T for male kitten.
The objective is to find the probability that at least three of the kittens will be male.
Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4
Now, the probability of at least three of the kittens will be male can be calculated by,
[tex]undefined[/tex]Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P,P, in terms of x,x, representing Madeline's total pay on a day on which she sells xx computers.
I need equation
The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.
Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We can model the equation for Madeline's total pay as follows -
P = base pay + (number of sold computer) × (cost of 1 computer)
P = 80 + 20x
Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x
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An inspector found 18 defective radios during an inspection. If this is 0.024% of the total number of radios inspected, how many radios were inspected?
Total number of defected radios is 18
Let the total number of defective radios be taken as y
If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y
[tex]\frac{0.024}{100}y=18[/tex]Solve for y, by cross multiplying
[tex]\begin{gathered} \frac{0.024}{100}y=18 \\ 0.024y=18\times100 \\ \text{Divide both sides by 0.024} \\ \frac{0.024y}{0.024}=\frac{1800}{0.024} \\ y=75000 \end{gathered}[/tex]Hence, the number of radios inspected, y, is 75000
using first principles to find derivatives grade 12 calculus help image attached much appreciated
Given: The function below
[tex]y=\frac{x^2}{x-1}[/tex]To Determine: If the function as a aximum or a minimum using the first principle
Solution
Let us determine the first derivative of the given function using the first principle
[tex]\begin{gathered} let \\ y=f(x) \end{gathered}[/tex]So,
[tex]f(x)=\frac{x^2}{x-1}[/tex][tex]\lim_{h\to0}f^{\prime}(x)=\frac{f(x+h)-f(x)}{h}[/tex][tex]\begin{gathered} f(x+h)=\frac{(x+h)^2}{x+h-1} \\ f(x+h)=\frac{x^2+2xh+h^2}{x+h-1} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^2+2xh+h^2}{x+h-1}-\frac{x^2}{x-1} \\ Lcm=(x+h-1)(x-1) \\ f(x+h)-f(x)=\frac{(x-1)(x^2+2xh+h^2)-x^2(x+h-1)}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^3+2x^2h+xh^2-x^2-2xh-h^2-x^3-x^2h+x^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^3-x^3+2x^2h-x^2h-x^2+x^2+xh^2-2xh-h^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{x^{2}h+xh^{2}-2xh+h^{2}}{(x+h-1)(x-1)}\div h \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(x^2+xh^-2x+h^)}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2+xh-2x+h}{(x+h-1)(x-1)} \end{gathered}[/tex]So
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\frac{x^2-2x}{(x-1)(x-1)}=\frac{x(x-2)}{(x-1)^2}[/tex]Therefore,
[tex]f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2}[/tex]Please note that at critical point the first derivative is equal to zero
Therefore
[tex]\begin{gathered} f^{\prime}(x)=0 \\ \frac{x(x-2)}{(x-1)^2}=0 \\ x(x-2)=0 \\ x=0 \\ OR \\ x-2=0 \\ x=2 \end{gathered}[/tex]At critical point the range of value of x is 0 and 2
Let us test the points around critical points
[tex]\begin{gathered} f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2} \\ f^{\prime}(0)=\frac{0(0-2)}{(0-1)^2} \\ f^{\prime}(0)=\frac{0(-2)}{(-1)^2}=\frac{0}{1}=0 \\ f^{\prime}(2)=\frac{2(2-2)}{(2-1)^2}=\frac{2(0)}{1^2}=\frac{0}{1}=0 \end{gathered}[/tex][tex]\begin{gathered} f(0)=\frac{x^2}{x-1}=\frac{0^2}{0-1}=\frac{0}{-1}=0 \\ f(2)=\frac{2^2}{2-1}=\frac{4}{1}=4 \end{gathered}[/tex]The function given has both maximum and minimum point
Hence, the maximum point is (0,0)
And the minimum point is (2, 4)
If f(x)=x squared + 3x - 10 then over which of the following intervals is f(x)<0 ?
Given data:
The given function is f(x)= x^2 +3x-10.
The given inequality is,
[tex]\begin{gathered} f(x)<0 \\ x^2+3x-10<0 \\ x^2+5x-2x-10<0 \\ x(x+5)-2(x+5)<0 \\ (x+5)(x-2)<0 \\ -5Thus, the value of x is -5For what values of b will F(x) = logb x be a decreasing function?A.0 < b < 1B.0 > b > -1C.b > 0D.b < 0
Given:
There is a function given as below
[tex]F(x)=\log_bx[/tex]Required:
For what value of b the given function in decreasing
Explanation:
The given function is logarithm function
also written as
[tex]F(x)=\frac{log\text{ x}}{log\text{ b}}[/tex]The base b is determines that if the function is increasing or decreasing
here
for
[tex]0the given function is decreasingfor
[tex]b>1[/tex]the given function is increasing
Final answer:
[tex]0
4) Using the number line to help you, decide which fraction is larger or if they are equal: one/twos or three/fifths. Label each fraction on the number line.
Explanation:
The number line is between 0 to 1. There are 10 smaller lines in between
Each of the small lines represent 1/10 or 0.1
one/twos is the same as 1/2 = 0.5
three/fifths is the same as 3/5 = 0.6
From the above, 0.6 is greater than 0.5
Showing both numbers on the number line:
which of these is closest to the unit distance between points M and M' ?
the coordinate of M is (-3, -5)
it is given that M is translated 6 unit right , and 5 unit up.
so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)
so, the distance between M and M' is,
[tex]d=\sqrt[]{(3-(-3))^2+(0-(-5))^2}[/tex][tex]\begin{gathered} d=\sqrt[]{6^2+5^2} \\ d=\sqrt[]{36+25} \\ d=\sqrt[]{61} \end{gathered}[/tex]d = 7.81
so, the closest to the unit distance is 8
thus, the answer is option D
A Snack company can pack 15 granola bars in a box how many boxes are needed for 600 granola bars ?
Answer:40
Step-by-step explanation: 15 bars to a box.
600 bars in total.
600/15= 40
40 boxes of granola bars
The ratio of the lengths of corresponding sides of two similar triangles is 5:8. The smaller triangle has an area of 87.5cm^2. What is the area of the larger triangle
Question:
Solution:
Remember the following theorem: the ratio of the areas of two
similar triangles is equal to the ratio of the squares of their corresponding sides. Then, here A1 and A2 are areas of two similar triangles, and S1 and S2 are their corresponding sides respectively :
S1 : S2 = 5 : 8
then
[tex]\frac{S1}{S2}=\frac{5}{8}[/tex]now, A1 = 87.5. Thus, according to the theorem, we get the following equation:
[tex](\frac{5}{8})^2=\frac{87.5}{A2}[/tex]this is equivalent to:
[tex]\frac{25}{64}=\text{ }\frac{87.5}{A2}[/tex]by cross-multiplication, this is equivalent to:
[tex](A2)(25)\text{ = (64)(87.5)}[/tex]solving for A2, we get:
[tex]A2\text{ =}\frac{(64)(87.5)}{25}=224[/tex]so that, we can conclude that the correct answer is:
The area of the larger triangle is
[tex]224cm^2[/tex]
Help please I’ll give 10 points
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
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.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredtheA = 50°. B = 45,a=3
Given:
The angels and sides of the triangle are
A = 50°. B = 45°, and a=3
Aim:
We need to find the angle C and sides c and b.
Explanation:
Use sine law.
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex][tex]\text{ Consider }\frac{\sin A}{a}=\frac{\sin B}{b}\text{ to find side b.}[/tex]Substitute A = 50°. B = 45°, and a=3 in the equation.
[tex]\frac{\sin 50^o}{3}=\frac{\sin 45^o}{b}[/tex][tex]b=\frac{\sin 45^o}{\sin 50^o}\times3[/tex][tex]b=2.77[/tex]Use the triangle sum property to find the angle C.
[tex]A+B+C=180^o[/tex]Substitute A = 50°. and B = 45° in the equation.
[tex]50^o+45^o+C=180^o[/tex][tex]95^o+C=180^o[/tex][tex]C=180^o-95^o[/tex][tex]C=85^o[/tex][tex]\text{ Consider }\frac{\sin A}{a}=\frac{\sin C}{c}\text{ to find side c.}[/tex]Substitute A = 50°. C= 85°, and a=3 in the equation.
[tex]\frac{\sin50^o}{3}=\frac{\sin 85^o}{c}[/tex][tex]c=\frac{\sin 85^o}{\sin 50^o}\times3[/tex][tex]c=3.90[/tex]Final answer:
[tex]C=85^o[/tex][tex]b=2.77[/tex][tex]c=3.90[/tex]Could you solve the table
The relation is decreasing by a factor of 2 each time, so:
[tex]\begin{gathered} y-9=-2(x-0) \\ y=-2x+9 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(100)=-2(100)+9 \\ y(100)=-200+9 \\ y(100)=-191 \end{gathered}[/tex]Answer:
-191
A shoe salesman earns a commission of 30%
of all shoe sales made.
Yesterday he sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80
each. How much did he earn in commission yesterday?
Answer: $111 is earn by shoe salesman as commission .
Step-by-step explanation:
As given the statement in the question be as follow.
Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.
Total cost of the pair of shoes = 3 × 70 + 2 × 80
= 210 + 160
= $ 370
As given
shoe salesman earns a commission of 30% of all shoe sales made.
30% is written is decimal form
= 0.30
Commission earns = 0.30 × Total cost of the pair of shoes .
= 0.30 × 370
= $ 111
Therefore $111 is earn by shoe salesman as commission .
Sarkis OganesyanCombine Like Terms (Basic, Decimals)May 20, 11:02:29 AMA triangle has side lengths of (1.1p + 9.59) centimeters, (4.5p - 5.2r)centimeters, and (5.3r + 5.4q) centimeters. Which expression represents theperimeter, in centimeters, of the triangle?14.89 + 5.6p + 0.2rO 0.1r + 5.6p + 14.99Submit Answer-0.7pr + 10.7qr + 10.6pq9.7qr + 10.9pr
The sides of the triagle have lengths:
1.1 p + 9.5 q
4.5 p - 5.2 r
5.3 r + 5.4 q
Or:
1.1 p + 0 r + 9.5 q
4.5 p - 5.2 r + 0 q
0 p + 5.3 r + 5.4 q
If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:
(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q
= 5.6 p + 0.1 r + 14.9 q
What is the value of the expression shown? 5 – a(3² + (ab + 2)² – 7) when a = 2 and b = –3
The expression has a value of -31 when a = 2 and b = –3
How to evaluate the expression?From the question, the expression is given as
5 – a(3² + (ab + 2)² – 7)
Also, we have the values of the variables to be
a = 2 and b = –3
Substitute a = 2 and b = –3 in the expression 5 – a(3² + (ab + 2)² – 7)
So, we have the following equation
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (2 * -3 + 2)² – 7)
Evaluate the expressions in the bracket
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (-4)² – 7)
Evaluate the exponents
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (9 + 16 – 7)
So, we have
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * 18
This gives
5 – a(3² + (ab + 2)² – 7) = 5 – 36
Evaluate the difference
5 – a(3² + (ab + 2)² – 7) = -31
Hence, the value of the expression is -31
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Dee, Sarah, Brett, and Betsy are splitting their dinner bill. After the tip, the total is $30.08. How muchdoes each owe if they split the bill four ways?
The four individuals Dee, Sarah, Brett and Betsy split their dinner bill four ways, which means its divided into four parts. Hence, after splitting, each person owes;
[tex]\begin{gathered} \text{Per person=}\frac{Total}{4} \\ \text{Per person=}\frac{30.08}{4} \\ \text{Per person=7.52} \end{gathered}[/tex]This shows that when paying the bill, each of the four individuals will have to pay $7.52
Please help with the question below (please try to answer in maximum 10/15 minutes).
Solution:
Given the dimensions of the composite figure below
[tex]\begin{gathered} For\text{ the cuboid:} \\ l=12\text{cm} \\ w=4\text{ cm} \\ h=3cm \\ For\text{ the triangular prism:} \\ a=3\text{ cm} \\ b=4\text{ cm} \\ c=13\text{ cm} \\ h=5\text{ cm} \end{gathered}[/tex]To find the surface area, SA, of the composite figure, the formula
[tex]SA=2(lh)+2(wh)+(lw)+2(\frac{1}{2}lh)+(bc)+(ah)[/tex]
Substitute the values of the variables into the formula above
[tex]\begin{gathered} SA=2\left(12\cdot3\right)+2\left(3\cdot4\right)+\left(12\cdot4\right)+2\left(\frac{1}{2}\left(12\cdot5\right)\right)+\left(13\cdot4\right)+\left(4\cdot5\right) \\ SA=2(36)+2(12)+(48)+(60)+(52)+20 \\ SA=72+24+48+60+52+20 \\ SA=276\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area, SA, is
[tex]276\text{ cm}^2[/tex]It’s supposed to answer in simplest formIf I die is rolled one time find the probability of
A die can have 6 possible outcomes.
The probability of an event is calculated using the formula:
[tex]P=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }total\text{ }outcomes}[/tex]Therefore, the probability of rolling a 1 is gotten to be:
[tex]P=\frac{1}{6}[/tex]The probability is 1/6.
A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }\times\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}[/tex]The function for the cost price becomes:
[tex]61000+1.5x[/tex]STEP 2: Get the function for the selling price
The function for the selling price becomes:
[tex]\text{ \$}15x[/tex]STEP 3: Calculate the number of books required to break even
To get the breakeven, the cost price will be equal to selling price. Therefore,
[tex]\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ \frac{61000}{13.5}=\frac{13.5x}{13.5} \\ 4518.518519=x \\ x\approx4519 \end{gathered}[/tex]Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519
hello can you help me with this trigonometry question and this a homework assignment
You have:
sin 2A = -√7/4
In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:
sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin
2A = -41.41° divide by 2 both sides
A = -41.41°/2
A = -20.705°
however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.
To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:
20.705 + 180° = 200.705°
Next, use calculator to calculate sinA:
sin(200.705°) = -0.3535
A sample of 7 students was taken to see how many pencils they were carrying.2, 3, 2, 5, 7, 1, 41. Calculate the sample mean.2. Calculate the standard deviation.
Sample mean = 3.43
sample standard deviation = 2.07
Explanation:
Given: 2, 3, 2, 5, 7, 1, 4
Total numbers = 7
1) Sample mean is calculated by finding the average of the data set
[tex]\begin{gathered} \text{Sample mean = }\frac{su\text{ m of data set}}{number\text{ of data set}} \\ \text{sample mean = }\frac{2+3+2+5+7+1+4}{7} \\ \text{sample mean = 24/7 } \\ \text{sample mean = }3.43 \end{gathered}[/tex]2) We have sample standard deviation and population standard deviation.
SInce the question asked for sample mean, we will be calculating sample standard deviation.
Standard deviation is calculated as:
[tex]\begin{gathered} s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum^{}_{}(x_1-mean)^2}{N-1}} \\ \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum ^{}_{}(2-3.43)^2+(3-3.43)^2+(2-3.43)^2+(5-3.43)^2+(7-3.43)^2+(1-3.43)^2+\mleft(4-3.43\mright)^2}{7-1}} \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{25.7143}{6}}\text{ = }\sqrt[]{4.2857} \\ s\tan dard\text{ deviation = }2.07 \end{gathered}[/tex]
Sharel spent the day at the mall. First, she bought five phones for $35each. Later, she found two five dollar bills. Write the total change to
if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175
And when she found two $5 bills, it is like she received 2 times 5 = $10
Normally, expenses are negative numbers and earning are positive numbers, in this case
-$175 + $10 = - $165
Sothe answer is -165
Pedro can't decide which size pizza to order. The 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza, the total price will be divided among 3people. If he chooses the 12-inch pizza, then the total price will be divided among 4 people. Which is the better buy? How much will each person pay? (Use 3.14 for r.)A. 10-inch pizza; $1.50B. 12-inch pizza; $1.50C. 10-inch pizza; $1.66 D. 12-inch pizza; $1.66
Answer: The better buy is the the 12-inch deluxe for $5.99.
B. 12-inch pizza; $1.50
Explanation:
From the information given, the 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza. We would calculate the area of both pizzas by applying the formula for calculating the area of a circle which is expressed as
Area = πr^2
where
π = 3.14
r is the radius of the circle
For the 10-inch cheese and sausage pizza,
diameter = 10
r = 10/2 = 5
Area = 3.14 x 5^2 = 78.5
If it is divided among 3 people,
each person gets 78.5/3 = 26.2 in^2
Amount that each person pays = 4.99/3 = $1.66
This means that each person pays $1.66 for 26.2 in^2
For the 12-inch cheese and sausage pizza,
diameter = 12
r = 12/2 = 6
Area = 3.14 x 6^2 = 113.04
If it is divided among 4 people,
each person gets 113.04/4 = 28.26 in^2
Amount that each person pays = 5.99/4 = $1.5
This means that each person pays $1.5 for 28.26 in^2
Thus, the better buy is the the 12-inch deluxe for $5.99.
The amount that each person pays is
B. 12-inch pizza; $1.50
wich choice shows the correct solution to 2544÷8?
ANSWER:
318
STEP-BY-STEP EXPLANATION:
We have the following operation:
[tex]2544÷8[/tex]So the answer is 318
give the coordinates of the image of each point under a reflection across to given line.(0,8); y=x
Answer:
(8, 0)
Explanation:
Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:
[tex](x,y)\to(y,x)[/tex]That is, the x-coordinate and y-coordinate change places.
Therefore, the image of the point (0,8) when reflected across the line y=x is:
[tex](8,0)[/tex]The correct answer is (8,0).
Please help me with my Calc hw, it is not outside scope of brainly tutor. I am following along diligently, thanks!
ANSWER
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]EXPLANATION
To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,
[tex]du=-\sin (x)dx[/tex]Thus, dx is,
[tex]dx=\frac{du}{-\sin (x)}[/tex]Replace the function and the differential in the integral,
[tex]\int \frac{\sin(x)}{\sqrt[]{1+\cos(x)}}dx=\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin (x)}[/tex]The sin(x) cancels out,
[tex]\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin(x)}=-\int \frac{1}{\sqrt[]{u}}du[/tex]We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,
[tex]\frac{d}{du}(\sqrt[]{u})=\frac{1}{2\sqrt[]{u}}[/tex]Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,
[tex]-\int \frac{1}{\sqrt[]{u}}du=-2\sqrt[]{u}+C[/tex]Finally, we have to replace u with the function we substituted before,
[tex]-2\sqrt[]{u}+C=-2\sqrt[]{1+\cos (x)}+C[/tex]Hence, the result of the integral is,
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]What is the mean for the data shown in the dot plot?
We will determine the mean as follows:
[tex]x=\frac{1(4)+4(5)+3(6)+2(7)+1(10)}{11}\Rightarrow x=6[/tex]So, the mean will be 6.
Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.
Problem
Last month, Ebony had 110 dollars in a
checking account. The current balance is
146 dollars. What is the percent change in
the account balance from last month to this
month? Round your answer to the nearest whole percent.
Solutiion
For this case we can use the following formula:
[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]And replacing we got:
[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]And then the answer wounded to the nearest percent would be:
33%