So we need to solve the following equation:
[tex]\log (5x)+\log (2x)=1[/tex]There are a few properties of logarithmic functions that we should remember. First, the logarithm of a negative number doesn't exist which means that x must be a positive number. Second, the addition of logarithms meets the following property:
[tex]\log (a)+\log (b)=\log (a\cdot b)[/tex]If we apply this to our equation we get:
[tex]\log (5x)+\log (2x)=\log (5x\cdot2x)=\log (10x^2)=1[/tex]Now we can pass the logarithm to the right side of the equation:
[tex]\begin{gathered} \log (10x^2)=1 \\ 10x^2=10^1=10 \\ 10x^2=10 \\ x^2=1 \end{gathered}[/tex]There are two possible solutions for x^2=1. These are x=1 and x=-1, however as I stated before x can't be a negative number which means that the solution of the equation is:
[tex]x=1[/tex]Then option C is the correct one.
I purchased a subscription to Brainly, but I can't figure out how to use it. I've snapped pictures of the questions, I snapped pictures of the problems. neither works. I get no answers. I can't type in a problem with numerous exponents. I don't know what to do. Can you help?
Given the functions:
[tex]\begin{gathered} f(x)=3x^{\frac{1}{2}} \\ \\ g(x)=2x^{-\frac{1}{4}} \\ \\ h(x)=6x^{\frac{1}{4}}^{} \end{gathered}[/tex]Let's solve for h[f(g(x))].
To solve this function operation, let's solve in parts.
First step is to find f(g(x)).
We have:
[tex]undefined[/tex]Krystals a Jewelry business. At a craft market, she boys and sell the bracelets she makes each week The graph below shows her weekly profit from bracelet sales 20 What is the amount of profit, per bracelet?
To find the amount of profit per bracelet we need to find the slope of the line. The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To find this slope we need two points on the line (whichever points we like). From the graph we select the points
Find the slope of the line in simplest form
Answer:
[tex]\boxed{\sf \sf Slope(m)=-\cfrac{5}{4}}[/tex]
Step-by-step explanation:
To find the slope between two points we'll use the slope formula:-
[tex]\boxed{\bf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]
Given points:-
(-3, 1)(1, -4)[tex]\sf \left(x_1,\:y_1\right)=\left(-3,\:1\right)[/tex]
[tex]\sf \left(x_2,\:y_2\right)=\left(1,\:-4\right)[/tex]
[tex]\sf m=\cfrac{-4-1}{1-\left(-3\right)}[/tex]
[tex]\sf m=-\cfrac{5}{4}[/tex]
Therefore, the slope of the line is -5/4!
____________________
Hope this helps!
Have a great day!
find the missing side. triangle trig
Answer:
see below; round to the correct number of digits (I couldn't see this part)
Step-by-step explanation:
cos(28°) = x / 14
x = 14cos(28°) ⇒ calculator
x ≈ 12.3612663
Answer:
x ≈ 12.36
Step-by-step explanation:
using the cosine ratio in the right triangle
cos28° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )
14 × cos28° = x , that is
x≈ 12.36 ( to 2 dec. places )
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The measure of ∠B AND ∠H is ∠B = 58° and ∠H = 122°
What is parallel lines?
Parallel lines are coplanar, straight lines in geometry that don't cross at any point. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.
If parallel lines are cut by a transversal , then corresponding angles are equal in measure.
∴ ∠B≅∠F
∠A≅∠E
∠C≅∠G
∠D≅∠H
If parallel lines are cut by a transversal , then interior angles on the same side are supplementary.
∠C+∠E=180°
∠D+∠F=180°
If one of the angles ( let it be ∠E) formed measures 122°, then m∠C=180°-122°=58°.
m∠B=m∠C=m∠F=m∠G=58°;
m∠A=m∠D=m∠E=m∠H=122°.
To learn more about parallel lines from the given link
https://brainly.com/question/11848535
#SPJ1
Answer:
if angle a measures122 degrees than angle b measures 58 degrees and angle h measures 122 degrees.
Q: what are parallel lines and their angles?
Answer:
Two lines that are stretched into infinity and still never intersect are called coplanar lines and are said to be parallel lines. The symbol for "parallel to" is //.
There are 4 types of angles formed between parallel lines i.e Corresponding angles, alternate angles , Interior angles, adjacent angle
the project is #Spj4
Step-by-step explanation:
Can you help me answer a, b and c please?
Answer
a)
[tex]B=B_{0}(1+\frac{a}{12})^{t}[/tex]b)
[tex]B=B_{0}(1+\frac{25}{3}a)^{t}[/tex]c)
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]Explanation
We're given the function:
[tex]B=B_0(1+r)^t[/tex]To represent the equation with the data given in the problem, we need to solve the three parts of this problem.
The part a ask us to write the expression in terms of annual percentage rate (APR) in decimal. If we call "a" the APR in decimal, then the monthly rate is the APR divided in 12:
[tex]r=\frac{a}{12}[/tex]Now we can rewrite the balance equation in terms of the initial investment, the number of months and the APR:
[tex]B=B_0(1+\frac{a}{12})^t[/tex]In part b, we need to write the balance equation using the APR as percentage. The APR as decimal is equal to the APR in percentage divided by 100. If we call A the APR in percentage:
[tex]a=\frac{A}{100}[/tex]Now we replace this value in the balance equation we got in part a:
[tex]B=B_0(1+\frac{100a}{12})^t[/tex]Then simplify:
[tex]B=B_0(1+\frac{25}{3}a)^t[/tex]That's the answer to b.
In part c, we need to write the balance equation with the time in years. Since 1 year has 12 months, if we call the number of months t, and the number of years y:
[tex]t=12y[/tex]Then:
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]And this is the answer to c.
consider a parabola that intersects the x axis at points (-1,0) and (3,0)
Given that we only have two points known in the parabola, the best way to determine the equation (having the options already) is to substitute the points on each equation to see which one is true for both points:
[tex]\begin{gathered} y=x^2+3x+2 \\ \text{for (-1,0)}\colon \\ 0=(-1)^2+3(-1)+2 \\ \Rightarrow0=1-3+2=3-3=0 \\ \text{for (3,0)}\colon \\ \Rightarrow0=(3)^2+3(3)+2=9+9+2=20 \end{gathered}[/tex]As we can see on the previous example, when we substitute the point (3,0), we get a contradiction, since 0=20 can never happen. Working this way we find that the equation y=x^2-2x-3 yields the desired results:
[tex]\begin{gathered} y=x^2-2x-3 \\ on\text{ (-1,0):} \\ 0=(-1)^2-2(-1)+3=1+2-3=0 \\ on\text{ (3,0):} \\ 0=(3)^2-2(3)-3=9-6-3=9-9=0 \end{gathered}[/tex]Therefore, the equation of the parabola is y=x^2-2x-3
#32 At 10am, a green car leaves a house at a rate of 60 mph. At the same time, a blue carleaves the same house at a rate of 50 mph in the opposite direction. At what time will the carsbe 330 miles apart?#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?
Charlotte has $6,367 in a savings account. The interest rate is 14%, compounded annually.To the nearest cent, how much will she have in 4 years?
Solution
Given the savings account, and solve for the interest:
Principal = $6,367
Interest rate = 14%
time = 4years
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]First, convert R as a percent to r as a decimal
r = R/100
r = 14/100
r = 0.14 rate per year,
Then solve the equation for A
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=6367(1+\frac{0.14}{1})^{(1)(4)} \\ A=6367(1+0.14)^4 \\ A=10753.61 \end{gathered}[/tex]A = $10,753.61
Therefore the correct answer is $10,753.61 (nearest cent)
write a part to part and a part to whole ratio for each problem situation of the 31 students surveyed 19 prefer white bread and the remaining students prefer wheat bread
Total number of students = 31
19 prefer white bread
31 - 19 prefer wheat bread ==> 31- 19 = 12 prefer wheat bread
Relations:
Part to part:
Relation between the number of students that prefer wheat bread to the number of students that prefer white bread:
Ratio: 12/19
Part to part:
Relation between the number of students that prefer white bread to the number of students that prefer white bread:
Ratio: 19/12
Part to whole:
Relation between the number of students that prefer wheat bread to the total number of students:
Ratio: 12/31
Part to whole:
Relation between the number of students that prefer white bread to the total number of students:
Ratio: 19/31
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)f(x) = 4x3 − 19x2 + 29x − 14; x − 1
Given:
The polynomial and one factor
[tex]f(x)=4x^3-19x^2+29x-14[/tex]Required:
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor.
Explanation:
We have one factor, we will us that
[tex]\begin{gathered} =\frac{4x^3-19x^2+29x-14}{x-1} \\ \text{ It can be written as } \\ =(x-1)(4x^2-15x+14) \\ \text{ So, roots are} \\ =1,2,\frac{7}{4} \end{gathered}[/tex]Answer:
answered the question.
To get around a small pond, a local electrical utility must lay two sections of underground cable that are 371 m and 440 m long. The two sections meet at an angle of 145°. How much extra cable is needed due to going around the pond?
If the cable could went through the pond there would be only one straight section conecting the two points. If we draw this new section in the picture we'll form a triangle:
In order to find how much extra cable is needed because of the pond we must find the length of the imaginary cable that connects the points through the dot, for this length we are going to use x.
The cosine rule will help as find it. Let's assume that we have a triangle with an angle A which has an opposite side with a length a and the lengths of the other two sides are b and c. Then the cosine rule states the following:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]We can apply this to our triangle. The 145° angle that we know is A, its opposite side a is x and the remaining sides b and c are the two cable sections of 371 m and 440 m. Then we get:
[tex]\begin{gathered} x^2=371^2+440^2-2\cdot371\cdot440\cdot\cos145^{\circ} \\ x^2=598677.7594 \end{gathered}[/tex]Then we apply a square root to both sides of this equation:
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{598677.7594} \\ x=773.74 \end{gathered}[/tex]So without the pond the length of the cable would have been of 773.74 m. In order to find the amount of extra cable needed we must take the total length of both sections and substract 773.74 m from it. Then we get:
[tex]371+440-773.74=37.26[/tex]AnswerThen the answer is 37.26m.
Find the degree of the polynomial f(x) = x6 + x2 + 5x.A.5B.6C.-5D.-6
To find the degree of a polynomial identify the greater exponent, that is the degree of the polynomial.
In the given polynomial the greater exponent is 6, then it is degree 6Answer: 6What linear equation represents the graph of a horizontal line, parallel to the Z-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed.
Problem
What linear equation represents the graph of a horizontal line, parallel to the Z-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed.
Solution
for this case the general equation of a plane is given by:
A(x-xo) + B(y-yo) + C(z-zo)=0
C=0 for this case
A(x-xo) + B(y-yo) =0
And for this case one possible answer would be:
y=4
Which of these expressions represents the product of an irrational number and a rational number being irrational?
ANSWER
Option B
EXPLANATION
We want to find which of the expressions is in the form:
Irrational number * Rational number = Irrational Number
An irrational number is a number that cannot be expressed as a ratio or fraction of two integers, such as pi or roots.
Options A and C cannot be correct because they each have two irrational numbers multiplying one another.
Simplifying Option D, we have:
[tex]\begin{gathered} 3\cdot\text{ }\sqrt[]{9} \\ \Rightarrow\text{ 3 }\cdot\text{ 3} \\ =\text{ 9 } \end{gathered}[/tex]The correct option is B, because:
[tex]\begin{gathered} \frac{1}{4}\cdot\text{ }\sqrt[]{44} \\ \frac{1}{4}\cdot\text{ }\sqrt[]{4\cdot\text{ 11}} \\ \frac{1}{4}\cdot\text{ 2 }\cdot\text{ }\sqrt[]{11} \\ \frac{1}{2}\sqrt[]{11} \end{gathered}[/tex]That is an irrational number that is a product of a rational number and an irrational number.
Therefore, the answer is Option B.
-4x - 3 = -11x + 16
We want to find which value must have x, so this equation is true:
-4x - 3 = -11x + 16
In order to solve the equation for x, we want to "leave it alone" on one side of the equation.
In order to do that we just have to remember one simple rule:
Finding xStep 1- taking all the terms with x to one side
We are going to take all the terms with x to the left side:
-4x - 3 = -11x + 16
↓ adding 11x both sides
11 x - 4x - 3 = 11x -11x + 16
↓ since 11x - 4x = 7x (left) and 11x - 11x = 0 (right)
7x - 3 = 0 + 16
7x - 3 = 16
Step 2- taking all the numbers to the other side
7x - 3 =16
↓ adding 3 both sides
7x - 3 + 3 = 16 + 3
↓ since -3 + 3 = 0 (left) and 16 + 3 = 19 (right)
7x + 0 = 19
7x = 19
Step 3- leaving x alone on the left side
7x = 19
↓ dividing 7 both sides
7x/7 = 19/7
↓ since 7x/7 = x (left) and 19/7 ≅ 2.7
x ≅ 2.7
Answer: x = 19/7 ≅ 2.7
For which of the following displays of data is it not possible to find the mean?histogramfrequency tablestem-and-leaf plotdot plot
Simplify: which of the following displays of data is it not possible to find the mean?
(a) histogram
(b) frequency table
(c) stem-and-leaf plot
(d) dot plot
Explanation: (a) histogram is correct answer because by using histogram it is not possible to find exact mean and median value.
Final answer: (a) histogram data is it not possible to find the mean.
Hi can someone please help me out on this drag and drop assignment? I’ll appreciate the help :)
Answer:
Step-by-step explanation:
1.
circumference of circular fence = 2πr
π = 3.14
r = radius
radius of circular fence, r= 10 feet
putting the values in the formula,
circumference = 2× 3.14 × 10
= 62.8 feet
therefore the fencing brad need will be 62.8 feet
2.
Area of the circular hot tub = πr²
π= 3.14
r = radius
as given in the question,
diameter = 80 inches
we know diameter is equal to half radius so r = 40 inches
putting the values in the formula,
area = 3.14 × 40× 40
= 5,024 inches
hence the area of the hot tub is equal to 5,025 inches
3.
Area of the circular wall clock = πr²
π= 3.14
r = radius
as per the question ,
area of 5 inches wall clock = 3.14× 5×5 = 78.5 inches
and area of 6 inches wall clock = 3.14 ×6×6 = 113.04 inches
To find the how much wall space will 6 inches wall clock takes we have to subtract both areas,
area of 6 inches wall clock - area of 5 inches wall clock = 113.04 - 78.5
= 34.54 inches
6 inches wall clock will take 34.54 inches of area more.
4.
In one rotation tire will cover whole area so to find the diameter we have to put area of circle equals to area of tire
Area of the circle = πr²
π= 3.14
r = radius
as per the question ,
area of the tire =116.18 inches
πr² = 116.18
r=6.08 inches
diameter = 2 × r= 12.16 inches
read more about circle:
https://brainly.com/question/2870743
Professional athletes are some of the highest paid people in the world. The average major league baseball player's salary has climbed from $1,998,000 in 2000 to $2,866,500 in 2006
Answer:
[tex]L(y)=144750y+1998000[/tex]
The slope means that each year the average professional baseball player's salary increased by $144,750 for every year after 2000.
The y-intercept means that in year 0 (2000) the average professional baseball player's salary was $1,998,000
The predicted average salary in 2007 is $3,011,250
(b)
[tex]E(y)=1998000\cdot1.062^y[/tex]The initial value represents the average professional baseball player's salary in year 0 (2000), which was $1,998,000.
The growth factor means that the rate of change increases each year by 1.062 times the previous year's increase.
The predicted average salary in 2007 is $3,044,233.94
Explanation:
The problem gives us two pieces of information:
In year 2000, we call t = 0, the average salary was $1,998,000
In year 2006, we call t = 6, the average salary was $2,866,500
If we want to make a function of the average salary variation over the years, we have two points that must lie in the equation of that function:
(0, 1998000) and (6, 2866500)
For (a) we need to assume that is linear growth. The equation of a line is:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept. In this case, since we established the year 2000 as t = 0, b = 1998000
Given two points P and Q, we can find the slope by the formula:
[tex]\begin{gathered} \begin{cases}P=(x_P,y_P){} \\ Q=(x_Q,y_Q)\end{cases} \\ . \\ m=\frac{y_Q-y_P}{x_Q-x_P} \end{gathered}[/tex]Then, if we call:
P = (0, 1998000)
Q = (6, 2866500)
[tex]m=\frac{2866500-1998000}{6-0}=\frac{868500}{6}=144750[/tex]Thus, the equation of the linear growth model is:
[tex]L(t)=144750t+1998000[/tex]Now, we can use this to find a prediction for 2007. 2007 is 7 years since 2000; thus t = 7
[tex]L(7)=144750\cdot7+1998000=1013250+1998000=3011250[/tex]In (b) we assume an exponential growth. The formula for the exponential growth is:
[tex]y=a(1+r)^t[/tex]Where:
a is the initial value. In this case, the average salary in 2000, $1,998,000
r is the ratio of growth. We need to find this value
t is the time in years
Then, we can use the point (6, 2866500), and the fact that a = 1998000:
[tex]2866500=1998000(1+r)^6[/tex]And solve:
[tex]\begin{gathered} \frac{2866500}{199800}=(1+r)^6 \\ . \\ \sqrt[6]{\frac{637}{444}}=1+r \\ . \\ 1.062=1+r \end{gathered}[/tex]We call the term "1 + r" growth factor.
Now, we can write the formula:
[tex]E(t)=1998000\cdot1.062^t[/tex]To find a prediction of the average salary in 2007, we use the function and t = 7:
[tex]E(7)=1998000\cdot1.062^7=1998000\cdot1.5236=3044233.937[/tex]
a cylindrical container with an 8 in. diameter and an 2 in. height is completely filled with water. all of its contents are poured into another cylindrical container that is 32 in. tall. if the water completely fills the second container, the second container's diameter is ___ in.
Volume of a cylinder: π r^2 h
Where:
r = radius
h= height
Calculate the volume of the first cylindrical container:
radius = diameter/2
Volume = π (8/2)^2 (2) = 100.5 in3
Second container
Volume = 100.5
heigth = 32 in
100.5 = π r^2 32
Solve for r
100.5/ (π 32 ) = r^2
1 = r^2
√1 = r
r=1
Diameter = 2 r = 2 (1) = 2 in
an object is thrown down from the top of a building. A height function for the object is given by the equation h=16(8+ t ) (5 - t) where T is the number of seconds elapsed since the object was thrown and H is the height of the object above the ground ( in feet). explain how to reason about the structure of the equation to determine when the object will hit the ground
The height is a function of the time, given by the following equation:
h(t) = 16(8+t)(5-t)
The object hits the ground when h(t) = 0. So
16(8 + t)(5 - t) = 0
This means that:
8 + t = 0 or 5 - t = 0
8 + t = 0
t = -8
We cannot have negative values for t.
5 - t = 0
-t = -5 *(-1)
t = 5
The object hits the ground when t = 5, which was easy to find since the equation was already factored by it's roots.
What is the missing exponent?w^3 x w^? = w^-6
Let the missing exponent be a,
[tex]w^3\times w^a=w^{-6}[/tex]From the law of indices stated below which satisfies the above equation,
[tex]\begin{gathered} x^a\times x^b=x^{a+b} \\ \text{relating the equation to the formula,} \\ w^3\times w^a=w^{-6} \\ w^{3+a}_{}=w^{-6} \\ \text{solving the exponents,} \\ 3+a=-6 \\ \text{Collect like terms} \\ a=-6-3 \\ a=-9 \end{gathered}[/tex]Hence, the missing exponent a is -9.
which of these choices show a pair of equivalent expressions? Check all that apply. A. 5^2/3 and (sq rt. 5)^3 B. (4 sq rt. 81)^7 C. 7^ 5/7 and (sq rt. 7)^5 D. 6 ^7/2 and (sq rt. 6)^7
SOLUTIONS
Which of these expression shows a pair of equivalent expressions:
Option A is wrong:
[tex]\begin{gathered} 5^{\frac{2}{3}}=(\sqrt{5})^3 \\ \sqrt[3]{\sqrt{5})^2}=(\sqrt{5})^3 \end{gathered}[/tex][tex]\begin{gathered} \sqrt[4]{81)^7}=81^{\frac{7}{4}} \\ \sqrt[4]{81^7}=\sqrt[4]{81^7} \end{gathered}[/tex]Option B is correct
Option C is wrong
[tex][/tex]Natalie bought a tank for her pet fish. She is measuring how much water will fill the tank.Which measurement will best help Natalie determine how much water will fill the tank?O Natalie should measure the area of the fish tank in square units.O Natalie should measure the area of the fish tank in cubic units.O Natalie should measure the volume of the fish tank in square units.O Natalie should measure the volume of the fish tank in cubic units.
Answer:
Natalie should measure the volume of the fish tank in cubic units.
Explanation:
The measure of the area is in square units and the measure of the volume is in cubic units.
The area gives you the measure of a plane surface and the volume gives you how much space a solid occupies
So, the measurement that will best help Natalie is the volume of the fish tank in cubic units.
What is the slope of the linear function given the following table?
х у-3. 6 -2. 51/3-1. 42/30. 43. 2Help please !
Let's use two points of the table:
[tex]\begin{gathered} (x1,y1)=(-1,3) \\ (x2,y2)=(0,1) \end{gathered}[/tex]Let's find the slope using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=-2(x+1) \\ y-3=-2x-2 \\ y=-2x+1 \end{gathered}[/tex]-------------------------------------------------
For the 2nd table:
[tex]\begin{gathered} (x1,y1)=(-3,6) \\ (x2,y2)=(0,4) \end{gathered}[/tex]Let's find the slope:
[tex]m=\frac{4-6}{0-(-3)}=-\frac{2}{3}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-6=-\frac{2}{3}(x+3) \\ y-6=-\frac{2}{3}x-2 \\ y=-\frac{2}{3}x+4 \end{gathered}[/tex]-47 > 1 - 8x ≥ -63????
Answer:
6<x<8
Step-by-step explanation:
−47>−8x+1>−63 (Simplify all parts of the inequality)
−47+−1>−8x+1+−1>−63+−1 (Add -1 to all parts)
−48>−8x>−64
−48/−8 > −8x/−8 > −64/−8 (Divide all parts by -8)
and the answer would be: 6<x<8
What is the area of this trapezoid? 13 ft Enter your answer in the box. 16 ft ft2 31 ft
The area of a trapezoid is given as
[tex]A=\frac{1}{2}(a+b)h[/tex]From the given trapezoid
[tex]a=13ft,b=31ft,h=16ft[/tex]Substitute the values of a, b, and h into the equation
This gives
[tex]A=\frac{1}{2}(13+31)\times16[/tex]Calculate the value of A
[tex]\begin{gathered} A=\frac{1}{2}(44)\times16 \\ A=44\times8 \\ A=352 \end{gathered}[/tex]Therefore the area of the trapezoid is
[tex]352ft^2[/tex]Answer:
Your answer would be 352ft²
Step-by-step explanation:
I took the test and got 100%
Draw the image of the figure under thegiven transformation.5. 180° rotation6.reflection across the x-axis7. (X,y) - (x - 4, y + 1)8. reflection across the y-axis
To obtain the 180° rotation, obtain the (-x,-y) coordinates of the given (x,y) coordinates.
The given coordinates of the points are as follows.
[tex]A(3,0),B(1,4),C(5,3)[/tex]Thus, the new coordinates will be as follows.
[tex]A^{\prime}(-3,0),B^{\prime}(-1,-4),C^{\prime}(-5,-3)[/tex]Plot the coordinates in a Cartesian coordinate system and then connect the points.
A high school has 52 players on the football team. The summary of the players weight is given in the box plot approximately what is the percentage of players weighing less than or equal to 194 pounds
Explanation
We are given the box plot below:
We are required to determine the percentage of players weighing less than or equal to 194 pounds.
We know that a box plot interprets as follows:
Therefore, we have:
[tex]Q_1=194[/tex]Also, we know that:
[tex]Q_1=\frac{1}{4}\text{ }of\text{ }100\%=25\%[/tex]Hence, the percentage of players weighing less than or equal to 194 pounds is:
[tex]\begin{equation*} 25\% \end{equation*}[/tex]3The number of hours that the employees at the local Fry's grocery store worked last week is normallydistributed with a mean of 28 hours and a standard deviation of 4. What percentage of employees workedbetween 24 and 36 hours?Answer:
We can solve this question by using the fact that a normal distribution is symmetric and using the empirical rules. The empirical rules are
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
In our problem, the mean is 28 and the standard deviation is equal to 4. Our interval is 24(one standard deviation below the mean) and 36(2 standard deviations above the mean)
[tex](24,36)=(28-4,28+8)=(28-\sigma,28+2\sigma)[/tex]Our area is the area that falls within one standard deviation of the mean plus the area between one standard deviation and two on the positive side. The first area is 68% of the data, and the second area we can calculate using the fact that a bell curve is symmetric. Since 68% of data falls within one standard deviation and 95% of the data falls within two standard deviations of the mean, the difference between them represents the data that falls between one standard deviation and two standard deviation.
[tex]95-68=27[/tex]Since the distribution is symmetric, the data that falls between one standard deviation and two standard deviation on the positive side is half of this value.
[tex]\frac{27}{2}=13.5[/tex]Now, we just add this value to 68% and we're going to have our answer.
[tex]68+13.5=81.5[/tex]The percentage of employees worked between 24 and 36 hours is 81.5%.