If we want to calculate the inverse, we have to solve for x the following equation
[tex]\begin{gathered} y=4x \\ x=\frac{y}{4} \end{gathered}[/tex]Therefore the inverse function is
[tex]h(x)=\frac{1}{4}x[/tex]Reason
A library has 144 books. A long
shelf can fit 100 books. A short shelf can fit 10 books.
The books that are left over can be put in a bin.
Draw two ways to sort books on a shelf.
100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
Given, a library has 144 books. A long shelf can fit 100 books. A short shelf can fit 10 books.
The books that are left over can be put in a bin.
Now, we have to find the way to sort the books on a shelf.
So, we can put the books in this fashion,
100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
Hence, 100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
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According to a pencil company's advertising campaign, 2 out of 3 students prefer the company's pencils to their competitor's pencils. A representative of the company went to a high school with 1479 students for alq & A session, and one of the students asked, "If this is true, in this high school, how many more students are there who prefer your pencils than students who prefer your competitor's pencils?" Help the company's representative come up with an answer. Assume that the company's claim is true.Part 1: How many of the students in the high school prefer the company's pencils? Part II: Out of 3 students, how many prefer the pencils of the company's competitor?Part III: How many of the students in the high school prefer the pencils of the company's competitor? Part IV: In the high school, how many more students are there who prefer the company's pencils than students who prefer their competitor's pencils?
Data:
2 of 3 students prefer the company's pencils to their competitor's pencils
high school with 1479 students
Part 1:You have 1479 students in total and know that 2 of 3 students prefer the company's pencils, then you multiply the toatl number of students by the factor 2/3
[tex]1479\cdot\frac{2}{3}=\frac{2958}{3}=986[/tex]Then, 986 students in the high school prefer the company's pencilsPart 2:Of 3 students 1 prefer the pencils of the company's competitorPart 3:Substract the number of students that prefer the company's pencils from the total of students:
[tex]1479-986=493[/tex]Then, 493 students in the high school prefer the pencils of the company's competitorPart 4:Substract the number of students who prefer the competitor's pencils fom the students that prefer the company's pencils:
[tex]986-493=493[/tex]Then, in the high school there are 493 students more that prefer the company's pencils than students who prefer their competitor's pencilsjust need help and a simple way to solve this
ANSWER
The length of the third leg is
STEP-BY-STEP EXPLANATION:
The figure given is a right-angled triangle.
To find the third length of the triangle, we need to apply Pythagora's theorem
It states that
[tex]\begin{gathered} (Hypotenuse)^2=(opposite)^2+(adjacent)^2 \\ \end{gathered}[/tex]The third length of the triangle is the hypotenuse because it is the longest
[tex]\begin{gathered} (Hypotenuse)^2=4^2+2^2 \\ (Hypotenuse)^2\text{ = 16 + 4} \\ (Hypotenuse)^2\text{ = 20} \\ \text{ Take the squareroots of both sides} \\ \text{ }\sqrt[]{(Hypotenuse)^2\text{ }}\text{ = }\sqrt[]{20} \\ \text{Hypotenuse = }4.472 \\ \text{Hypotenuse }\approx\text{ 4.5} \end{gathered}[/tex]Hence, the length of the third leg is 4.5
Weekly wages at a certain factory arenormally distributed with a mean of$400 and a standard deviation of $50.Find the probability that a workerselected at random makes between$500 and $550.
The Solution:
Step 1:
We shall state the formula for calculating Z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ \text{Where X}=5\text{00 ( for lower limit) and X=550 for upper limit.} \\ \mu=400 \\ \sigma=50 \end{gathered}[/tex]Step 2:
We shall substitute the above values in the formula.
[tex]\begin{gathered} \frac{500-400}{50}\leq P(Z)\leq\frac{550-400}{50} \\ \\ \frac{100}{50}\leq P(Z)\leq\frac{150}{50} \\ \\ 2\leq P(Z)\leq3 \end{gathered}[/tex]Step 3:
We shall read the respective probabilities from the Z score distribution tables.
From the Z-score tables,
P(3) = 99.9 %
P(2) = 97.7 %
Step 4:
The Conclusion:
The probability that a worker selected makes between $500 and $550 is obtained as below:
[tex]\text{Prob}(500\leq Z\leq550)=99.9-97.7\text{ = 2.2 \%}[/tex]Therefore, the required probability is 2.2 %
Triangles ABE, ADE, and CBE are shown on the coordinate grid, and all the vertices have coordinates that are integers. Which statement is true?
To check if Triangles ABE, ADE, and CBE are congruent, let us compute for the distance of each line using the Distance Formula,
[tex]\text{ }d\text{ = }\sqrt[]{(x_2-x_1)^2\text{ + (}y_2-y_1)^2}[/tex]Where,
d = Distance
(x1, y1) = Coordinates of the first point
(x2, y2) = Coordinates of the second point
Let's compute the distance of the following lines:
Triangle ABE: Lines AB, AE, and BE
Triangle ADE: Lines AD, AE, and ED
Triangle CBE: Lines CE, CB, and BE
For Triangle ABE,
[tex]\text{ d}_{AB}\text{ = }\sqrt[]{(-1-(-4))^2+(3-(-1))^2}\text{ = }\sqrt[]{(-1+4)^2+(3+1)^2}[/tex][tex]\text{ d}_{AB}\text{ = }\sqrt[]{(3)^2+(4)^2}\text{ = }\sqrt[]{9+\text{ 16}}\text{ = }\sqrt[]{25}[/tex][tex]\text{ d}_{AB}\text{ = 5}[/tex][tex]\text{ d}_{AE}\text{ =}\sqrt[]{(1-\text{ }(-1))^2+(0\text{ - }(-4))^2}\text{ = }\sqrt[]{(1+1)^2+(0+4)^2}[/tex][tex]\text{ d}_{AE}\text{ = }\sqrt[]{(2)^2+(4)^2}\text{ = }\sqrt[]{4\text{ + 16}}[/tex][tex]\text{ d}_{AE}\text{ =}\sqrt[]{20}[/tex][tex]\text{ d}_{BE}\text{ = }\sqrt[]{(1\text{ - (}3))^2+(0\text{ - (-1)})^2}\text{ = }\sqrt[]{(1-3)^2+(0+1)^2}[/tex][tex]\text{ d}_{BE}=\text{ }\sqrt[]{(-2)^2+(1)^2}\text{ = }\sqrt[]{4\text{ + 1}}[/tex][tex]\text{ d}_{BE}\text{ = }\sqrt[]{5}[/tex]For Triangle ADE, let's compute for the distance of line AD and ED since we already got the distance of line AE.
[tex]\text{ d}_{AD}\text{ = }\sqrt[]{(-1-(-1))^2+\text{ (}1\text{ - }(-4))^2}\text{ = }\sqrt[]{(-1+1)^2+(1+4)^2}[/tex][tex]\text{ d}_{AD}\text{ = }\sqrt[]{(0)^2+(5)^2}\text{ = }\sqrt[]{25}[/tex][tex]\text{ d}_{AD}\text{ = 5}[/tex][tex]\text{ d}_{ED}=\text{ }\sqrt[]{(-1\text{ - (}1))^2+(1-0)^2}\text{ = }\sqrt[]{(-1-1)^2+(1)^2}[/tex][tex]\text{ d}_{ED}\text{ = }\sqrt[]{(-2)^2_{}+(1)^2}\text{ = }\sqrt[]{4\text{ + 1}}[/tex][tex]\text{ d}_{ED}\text{ = }\sqrt[]{5}[/tex]For Triangle CBE, let's compute for the distance of line CE and CB since we already got the distance of line BE.
[tex]\text{ d}_{CE}\text{ = }\sqrt[]{(3-\text{ }1)^2+(4-0)^2}\text{ = }\sqrt[]{(2)^2+(4)^2}[/tex][tex]\text{ d}_{CE}\text{ = }\sqrt[]{4+16}\text{ = }\sqrt[]{20}[/tex][tex]\text{ d}_{CE}\text{ = }\sqrt[]{20}[/tex][tex]\text{ d}_{CB}\text{ = }\sqrt[]{(3-3)^2+(4\text{ - (}-1))^2}\text{ =}\sqrt[]{(0)^2+(4+1)^2}[/tex][tex]\text{ d}_{CB}\text{ =}\sqrt[]{(5)^2}\text{ = }\sqrt[]{25}[/tex][tex]\text{ d}_{CB}\text{ = 5}[/tex]In summary,
Triangle ABE:
[tex]AB=\text{ 5, AE = }\sqrt[]{20}\text{ and BE = }\sqrt[]{5}[/tex]Triangle ADE:
[tex]\text{ AD = 5, AE = }\sqrt[]{20}\text{ and ED = }\sqrt[]{5}[/tex]Triangle CBE: CE, CB, and BE
[tex]\text{ CB = 5, CE = }\sqrt[]{20}\text{ and BE = }\sqrt[]{5}[/tex]The sides of the three triangles shown in the grid are congruent based on the SSS Rule of Triangle.
Thus, the statement that meets our evaluation is:
D. Triangle ABE, ADE and CBE are all congruent.
Sue, who is 5 feet tall, is standing at Point D in the drawing. The tip of her head is a point E. a tree in the yard is at point B with the top of the tree at point C. Sue stand so her shadow meets at the end of the trees shadow at point a Which triangles similar?How do you know?Find the height of the tree (This distance from B to C).
Which triangles are similar?
The triangle AED and the triangle ABC is similar.
How do you know?
Because all the angles are equal, the triangle AED and ABC have the same angle values, then they're similar.
Find the height of the tree (This distance from B to C)
We can use the relation of the similar triangle to find BC, we can write the equation
[tex]\frac{AB}{AD}=\frac{BC}{ED}[/tex]The only unknown value here is BC, then
[tex]\frac{24+8}{8}=\frac{\text{BC}}{5}[/tex]Now we solve it for BC!
[tex]\begin{gathered} \frac{32}{8}=\frac{BC}{5} \\ \\ 4=\frac{BC}{5} \\ \\ BC=4\cdot5 \\ \\ BC=20\text{ ft} \end{gathered}[/tex]Hence, the height of the tree is 20 ft
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
I don't know the answer but I want to say something ...you can't just go around writing HELP!!! ILL GIVE 100 POINTS when your question only gives 5!!! it's just deceptive, if you want someone's help at least be honest! thank you for your time
8 with a exponent of 3 divided by 2
8³ ÷ 3
First we find the value of 8³;
8³ = 512
Then divide by 3
512/3 = 170.6
In Mr. Johnson’s third and fourth period classes, 30% of the students scored a 95% or higher on a quiz.Let be the total number of students in Mr. Johnson’s classes. Answer the following questions, and showyour work to support your answer.If 15 students scored a 95% or higher, write an equation involving that relates the number ofstudents who scored a 95% or higher to the total number of students in Mr. Johnson’s third andfourth period classes. Of the students who scored below 95% 40% of them are girls. How many boys scored below 95%?
Total number of students = scored below 95% + scored above 95% (I)
______________________________
Students scored below 95%
Scored below 95%* 0.40 = girls
Boys = total scored below 95% (100% - 40%)
Boys = total scored below 95% (60%)
Boys = total scored below 95% (0.6) (II)
__________________________________________
Can you see the updates?
_______________________________
30% of the students scored a 95% or higher on a quiz and 15 students scored a 95% or higher
Total number of students* 30 = 15
30%*n = 15
n= 15/ 0.3
n= 50
_____________________________
Replacing in (I)
Total number of students = scored below 95% + scored above 95%
50 = 15 + 35
Replacing in (II)
Boys = 15 (0.60) = 9
__________________________________________
Answer
9 of the students who scored below 95% are boys
The perimeter of a triangle ABC is 100 cm.The length of AB is 45 cm and the length of BC is 32 cm.What is the length ofCA?
Recall that the perimeter of the triangle ABC is given by the following formula:
[tex]Perimeter=AB+BC+CA\text{.}[/tex]Substituting the given data we get:
[tex]100\operatorname{cm}=45\operatorname{cm}+32\operatorname{cm}+CA\text{.}[/tex]Solving the above equation for CA we get:
[tex]\begin{gathered} CA=100\operatorname{cm}-45\operatorname{cm}-32\operatorname{cm} \\ =23\operatorname{cm}\text{.} \end{gathered}[/tex]Answer: The length of CA is 23cm.
Same took out a loan for 6200 that charges an annual rate of 8.6% compounded quarterly. Answer each part. Sent picture
Given:
Sam took out a loan for 6200 that charges an annual rate of 8.6% compounded quarterly.
Required:
Find effective annual interest rate.
Explanation:
a).
We know compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Now,
[tex]undefined[/tex]b).
We know the effective annual interest rate
[tex]EAR=(1+\frac{i}{m})^m-1[/tex]EAR = Effective annual interest
i = Annual nominal rate of interest
m = No. of compounding periods in a year.
[tex]\begin{gathered} EAR=(1+\frac{0.086}{4})^4-1 \\ EAR=0.088813 \\ \text{ To find percentage multiply by 100 } \\ =0.088813\times100 \\ =8.8813\% \end{gathered}[/tex]Answer:
answered the question.
What are the zeroes of f(x) = x^2 + 5x + 6? (4 points)A) x = -2, -3B) x = 2,3C) x= -2,3D) x = 2, -3
You have the following function:
[tex]f(x)=x^2+5x+6[/tex]in order to find the zeros of the previous function, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial. In this case:
a = 1
b = 5
c = 6
replace the previous values of the parameters into the formula for x:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(1)(6)}}{2(1)} \\ x=\frac{-5\pm\sqrt[]{25-24}}{2}=\frac{-5\pm1}{2} \end{gathered}[/tex]hence the solution for x are:
x = (-5-1)/2 = -6/2 = -3
x = (-5+1)/2 = -4/2 = -2
A) x = -2 , -3
The function g(x) approaches positive infinity as x approaches positive infinity. The zeros of the function are -1,2 and 4. Which graph best represents g(x)?
Explanation
We are asked to select the correct option for which g(x) approaches positive infinity as x approaches positive infinity.
Also, the zeros of the function are -1,2 and 4.
The correct option will be
Which is the closest to the area of the triangle in square centimeters?
Option c ) 40 is the closest to the area of the triangle in square centimeters .
Formula for Area of a right-angled triangle :
Area of a right-angled triangle = [ ( 1 / 2 ) * base * height ]
According to question ,
base = 10.1 cm
height = 8.2 cm
So , Area of triangle = [ ( 1 / 2 ) * 10.1 * 8.2 ]
= 41.41 [tex]cm^{2}[/tex]
This is closest to option c ) 40 .
Hence , option c ) 40 is the closest to the area of the triangle in square centimeters .
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A student has 5 pairs of plants, 2 shirts and 7 necklaces. He chooses one shirt, one pair of pants, and one necklace. How many different outfits could he make?
Answer:
70
Explanation:
By the rule of multiplication, we can calculate the number of different outfits as
5 x 2 x 7 = 70
pants shirts necklaces
Therefore, there are 70 different outfits
The figure below shows the graph of f’ , the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangentlines at x = 2 and x = 4.
Solution
- The points of inflection of f(x) in a graph of f'(x) is gotten by just finding the points where the graph moves from increasing to decreasing, and also from decreasing to increasing.
- Thus, we have
- The points where the graph changes from increasing to decreasing is at point (2, 0) and the point where the graph moves from decreasing to increasing is (4, -2.5)
- Thus, the inflection points of the graph of f are at (2, 0), and (4, -2.5)
pls help I've had a bad day and I've been trying to figure this out forever
the given expression is
4Ix-2I - 3
The volume of a sphere is a function of it's radius, V=4/3* πr^3. evaluate the function for the volume of a volleyball with radius of 11.3 cm.Round to the nearest tenth.
Volume of sphere = 6040.9cm³
Explanation:
Volume of sphere = 4/3* πr³
radius = r = 11.3cm
if π = 3.14
[tex]\begin{gathered} \text{volume = }\frac{4}{3}\times3.14\times11.3^3 \\ \end{gathered}[/tex][tex]\begin{gathered} V\text{ = }\frac{4}{3\text{ }}\times3.14\times1442.897 \\ V=6040.929cm^3 \end{gathered}[/tex]Rounding to the nearest tenth:
Volume of sphere = 6040.9cm³
Find the surface area of a cylinder with a base radius of 6 ft and a height of 9 ft.Use the value 3.14 for n, and do not do any rounding.Be sure to include the correct unit.
The surface area of the cylinder can be found below
[tex]\text{surface area=}2\pi r(r+h)[/tex]h = 9 ft
r = 6 ft
Therefore,
[tex]\begin{gathered} \text{surface area=2}\times3.14\times6(6+9) \\ \text{surface area=}37.68(15) \\ \text{surface area=}565.2ft^2 \end{gathered}[/tex]Solve the equation for X. Round the answer to three decimal places. 4^x = 6
Answer:
c. x =1.293
Explanation:
To solve the expression, we will apply the properties of the logarithms, so
[tex]\begin{gathered} 4^x=6 \\ \log 4^x=\log 6 \\ x\log 4=\log 6 \\ x=\frac{\log 6}{\log 4} \\ x=1.293 \end{gathered}[/tex]Therefore, the value for x is
c. x =1.293
Hello, how are you? I would like you to help me solve this exercise, please!
Given
Formula for the length of an arc
[tex]\begin{gathered} Measureof\text{Arc of a circle=}\frac{\theta}{360}\times2\pi r \\ \\ \end{gathered}[/tex]Parameters;
[tex]\begin{gathered} \theta=?\text{ , r=1m} \\ \text{measure of arc =}\frac{\pi}{9} \end{gathered}[/tex]We can substitute into the formula
[tex]\begin{gathered} \frac{\pi}{9}=\frac{\theta}{360}\times2\times\pi\times1 \\ \\ \frac{\pi}{9}=\frac{2\theta\pi}{360} \\ \text{cross multiply} \\ 18\theta\pi=360\pi \\ divide\text{ both sides by 18}\pi \\ \frac{18\theta\pi}{18\pi}=\frac{360\pi}{18\pi} \\ \theta=20^0 \end{gathered}[/tex]Now, change to radian
[tex]\frac{\pi}{180}\times20^0=\frac{20^0\pi}{180^0}=\frac{\pi}{9}[/tex]The final answer
[tex]\frac{\pi}{9}[/tex]the beginning of the question is "if the slope of..." please help
we know that
If two lines are parallel, then their slopes are equal
In this problem
mAB=mCD
substitute the given values
3/4=(x-2)/12
solve for x
multiply by 12 both sides
(x-2)=12(3/4)
x-2=9
x=9=9+2
x=11state the solution for the quadratic equation depicted in the graph.
For this problem, we were provided with the graph of a quadratic equation, and we need to determine the solutions for this graph.
The solutions of a quadratic equation are the values of "x" that make the expression equal to "0". Therefore, we need to look at the graph for the values at which the graph crosses "y=0".
We have two points for this problem. The first one is approximately -5, and the second is 6.
CJ loves Girl Scout cookies. He eats 3 cookies per hour. After 5 hours, there are 24 cookies left in the box. Write an equation in slope intercept form. Determine how many hours it will take CJ to eat the entire box of cookies.
To solve this problem: y will represent the number of cookies, and x the number of hours.
To find the number of cookies that CJ eats per hour, we multiply 3 (since he eats 3 per hour) by x (the number of hours)
Since there we only 24 cookies left in the box, we will need to substract 3 by the number of hours that have passed, from 24 to find the number of cookies "y":
[tex]y=24-3(x-5)[/tex]This equation represents that the number of cookies "y" is equal to the 24 cookies that where left after 5 hours, and to that we substract 3 (which is the number of cookies per hour) by total number of hours that have passed since those 5 hours (x-5) because 5 hours that have already passed we substract them from x.
We need to simplify that equation to represent in slope-intercept form:
[tex]\begin{gathered} y=24-3x+15 \\ y=-3x+39 \end{gathered}[/tex]Now we need to determine the number of hours it would take to finish the cookies. So we are looking for the value of x, that makes y=0:
[tex]0=-3x+39[/tex]solving for the number of hours x:
[tex]\begin{gathered} -3x=-39 \\ x=-\frac{39}{(-3)} \\ x=13 \end{gathered}[/tex]It would take 13 hours for CJ to eat the entire box of cookies.
The center of a circle and a point on the circle are given. Writecenter: (3,2), point on the circle: (4,3)
Given:
The center of the circle is the point ( 3, 2 )
And the point on the circle is ( 4, 3 )
To write the equation of the circle, we need to find the radius
The radius = the distance between the center and the point on the circle
so, the radius is the distance between ( 3, 2) and ( 4, 3)
So,
[tex]\begin{gathered} r=d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ r=\sqrt[]{(4-3)^2+(3-2)^2^{}}=\sqrt[]{1+1}=\sqrt[]{2} \end{gathered}[/tex]The general equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) is the coordinates of the center of the circle, r is the radius
So,
[tex]\begin{gathered} (h,k)=(3,2) \\ r=\sqrt[]{2} \end{gathered}[/tex]so, the equation of the circle will be:
[tex](x-3)^2+(y-2)^2=2[/tex]State if the triangles in each pair are similar. If so, state how you know they are similar andcomplete the similarity statement.1) 2)
Triangles Similarity
For two shapes to be similar, two conditions must be satisfied:
* They must have the same angles.
* The side lengths must be in proportion
Let's focus on the image provided in problem 1.
We must try to find if the length sides of ABU and VWU are in proportion.
To do it, we find the ratio of the sides. If we find the same ratio of two pairs of sides, then the second condition is met.
Alex surveyed 60 student about their Vera zoo animals and made the circle graph of the results shown below
we can use the cross multiplication
we know that the full angle of a circle is 360° so the total angle corresponds to 60 students
so, what is 72 degrees?
[tex]\begin{gathered} 360\longrightarrow60 \\ 72\longrightarrow x \end{gathered}[/tex]where x is the number of students than said giraffes
[tex]\begin{gathered} x=\frac{72\times60}{360} \\ \\ x=12 \end{gathered}[/tex]the students than said giraffes are 12
Use the GCF to factor this expression.40x + 24y - 56
The given expression is,
[tex]40x+24y-56[/tex]The factors of 40, 24 and 56 are,
[tex]\begin{gathered} 40\colon2,4,5,8,10 \\ 24\colon2,4,3,8 \\ 56\colon2,4,7,8 \end{gathered}[/tex]The greatest common factor is therefore, 8.
Therefore, the given expression can be written as,
[tex](8\times5)x+(8\times3)y-(8\times7)[/tex]Taking 8 as common, we have,
[tex]8(5x+3y-7)[/tex]Can you help me with this assignment
Those are vertical angles, therefore:
[tex]\begin{gathered} m\angle ONB=m\angle MNK \\ so\colon \\ m\angle ONB=85 \end{gathered}[/tex]maurice read a research 10 pages that is 50 percent of the paper lenght what i the paper lenght
we know that
10 pages -------> represent 50%
so
Multiply by 2 both sides
20 pages --------> 100%
therefore
the paper length is 20 pagesApply proportionRemember that the paper length represent the 100%
10/50=x/100
solve for x
x=10*100/50
x-20 pages100/50x-20 pages