Okay, here we have this:
Considering the provided information we obtain the following:
7 singles P(1)=7/26
12 fives P(5)=12/26
5 twenties P(20)=5/26
2 hundreds P(100)=2/26
E(X)=1*7/26+5*12/26+20*5/26+100*2/26
E(X)≈14.115
Finally we obtain that the approximately fair price is $14.115.
a man is standing 20m from a large tree. he can see the top of the tree with an angle of elevation of 25 degrees. if the man's eyes are at a height of 2m, what is the height of the tree
Given:
The distance from the tree to the man = 20m.
The angle of elevation is 25 degrees.
The man's eyes are at a height of 2m.
Required:
We need to find the height of the tree.
Explanation:
Let h be the height of the tree.
[tex]h=2+x[/tex]Since 2m is the distance from the ground to the man's eye.
Consider the triangle ABC.
Here Opposite side =BC=x, Adjacent sides = AB=20m,
Use tan formula.
[tex]tan\theta=\frac{Opposite\text{ side}}{Adjacent\text{ side}}[/tex][tex]\text{ Substitute }\theta=25^o\text{ , Opposite side =x, and Adjacent sides = AB=20m in the formula.}[/tex][tex]tan25^o=\frac{x}{20}[/tex][tex]x=20\times tan25^o[/tex][tex]x=9.3261[/tex]Substitute x =9.3161 in h=2+x .
[tex]h=2+9.3261[/tex][tex]h=11.3261[/tex]Final answer:
The height of the tree is 11.33 m.
How many gallons is 454 ounces?
Answer:
3.546875gallons
Explanation:
Using the conversion factor;
1 fluid ounces = 0.0078125 gallons
454 ounces = x
Cross multiply
1 * x = 454 * 0.0078125
x = 3.546875gallons
Hence 454 ounces to gallons is 3.546875gallons
Riley and Rhoda plan to buy 2 bags of dog food and a dog collar (x). Each bag of dog food costs $7 and the dog collar costs $4.50. They have $30.Write an inequality and solve :Explain what your solution means for riley and rhoda:
EXPLANATION
Let's see the facts:
-Riley and Rhoda bags= 2 ---> x
- Bag cost = $7
-Collar cost = $4.5
They can spend $30.
7x + 4.5 ≤ 30
Now, we need to solve the inequality as shown as follows:
Adding -4.5 to both sides,
7x ≤ 30 - 4.5
Simplifying:
7x ≤ 25.5
Dividing both sides by 7:
x ≤ 25.5/7
Simplifying:
x ≤ 3.64 approx 3.64 bags, therefore 3 bags of dog food
Answer: Since the bags are available in full units, with their $30, Riley and Rhoda will buy 0, 1, 2, or 3 bags and 0 or 1 dog tag.
What is the diameter of XA.12cmB.4cmC.8cmD.2cm
What is the diameter of X
A.12cm
B.4cm
C.8cm
D.2cm
Remember that
The diameter of a circle is two times the radius
so
in this problem
r=4 cm
that means
D=2*4=8 cm
answer is option Con232428 29 30 312725 2632 33Y is inversely proportional to the square root of x. True or False: If Y=6 when x = 81, then Y= 9, when x is 36.
Solution
Step 1
Y is inversely proportional to the square root of x.
[tex]y\text{ = }\frac{k}{\sqrt{x}}[/tex]Step 2
Find the value of k if Y=6 when x = 81.
[tex]\begin{gathered} 6\text{ = }\frac{k}{\sqrt{81}} \\ \\ 6=\text{ }\frac{k}{9} \\ \\ k\text{ = 6}\times9 \\ \\ k\text{ = 54} \end{gathered}[/tex]Step 3
Let find y when x = 36
[tex]\begin{gathered} y\text{ = }\frac{k}{\sqrt{x}} \\ \\ y\text{ = }\frac{54}{\sqrt{36}} \\ \\ y\text{ = }\frac{54}{6} \\ \\ y\text{ = 9} \end{gathered}[/tex]Final answer
True
in 25 minutes li can run 10 laps around the track. determine the number of laps she can run per minute find the constant of proportionality in this situation.
The number of laps run by Li in a minute is 0.4 laps.
The constant of proportionality is found as 2/5.
What is referred as the term Unitary method?The unitary method would be a technique for solving problems that involves first determining the value of a given unit and then multiplying that value by the required value.To represent the relationship, create an equation.
Let L represent the number of laps and m represent the number of minutes.
Laps per minute is also simply division... laps/minute
Laps per minute;
L/m = 10/25
L/m = 2/5 or 0.4 laps per minute
Thus, the number of laps run by Li in a minute is 0.4 laps.
Now, if number of laps she can run is directly proportional to time 't'.
Then,
L ∝ t
L = k t
k is the constant of proportionality.
k = L/m
k = 2/5
Thus, the constant of proportionality is found as 2/5.
To know more about the Unitary method, here
https://brainly.com/question/24587372
#SPJ1
25. Write the equation for lines 'a' and 'b'Line 'a':Line 'b'
As you can see, line a intersects the y axis at point ( 0, 1 ) and the x axis at point ( -2, 0).
Basically, the slope (m) is rise over run, that is, m = (y2 - y1) / (x2 - x1) = 0-1 / -2-0 = 1/2. And our y=intercept, b is 1 (since the line intersects that y axis at 1). Using the point slope form , y = mx +b, the equation of line a is:
[tex]\begin{gathered} y=\frac{1}{2}x+1 \\ 2y=x+2 \\ x-2y+2=0 \end{gathered}[/tex]As you can see, line b intersects the y axis at point ( 0, -2 ) and the x axis at point ( -1, 0).
Basically, the slope (m) is rise over run, that is, m = (y2 - y1) / (x2 - x1) = 0-(-2) / -1-0 = 2 / -1 = -2. And our y=intercept, b is -2 (since the line intersects that y axis at -2). Using the point slope form , y = mx +b, the equation of line a is:
[tex]\begin{gathered} y=(-2)x+(-2) \\ y=-2x-2 \\ 2x+y+2=0 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} a\colon x-2y+2=0 \\ b\colon2x+y+2=0 \end{gathered}[/tex]I don’t know how to do it with 3 only with 2 so can you answer it it’s geometry
Answer:
Notice that:
[tex]\begin{gathered} \frac{UV}{FG}=\frac{32}{22}=\frac{16}{11}, \\ \frac{VW}{GH}=\frac{33}{23}, \\ \frac{WU}{HF}=\frac{15}{9}=\frac{5}{3}\text{.} \end{gathered}[/tex]Since all the corresponding proportions are different, we get that triangles UVW and FGH are not similar.
the equation 2x^2+10x+1-=0 has two solutions A and B where A
Given the equation ;
[tex]2x^2+10x+1=0[/tex]The general solution of the equation is :
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the given equation ;
a = 2 , b = 10 , c = 1
so,
[tex]\begin{gathered} x=\frac{-10\pm\sqrt[]{10^2-4\cdot2\cdot1}}{2\cdot2}=\frac{-10\pm\sqrt[]{92}}{4} \\ So, \\ x=\frac{-10+\sqrt[]{92}}{4}=-0.102 \\ OR \\ x=\frac{-10-\sqrt[]{92}}{4}=-4.898 \end{gathered}[/tex]So, the solution is :
A = -4.898
B = -0.102
Given the triangle, find x to the nearest one hundredth.
The Solution:
Given:
Required:
Find the value of x.
Applying the Trigonometric Ratio:
[tex]\tan30=\frac{x}{12}[/tex]Cross multiply:
[tex]x=12\tan30=6.9282\approx6.93[/tex]Answer:
6.93
in 6th grade and does not under stand math at all
Well you better go and refer to a textbook and have guidance by teachers, parents, and/or siblings.
Mathematics is such a broad topic, that there is no way that it can be described here - it will take you forever to read (yet understand in your case).
The table and scatter plot show the time spent studying, x and the midterm score, y, for each of 10 students.The equation of the line of best fit is y = 3.5x + 16.18 .
Given
[tex]y=3.5x+16.18[/tex]Observe midterm score
Predicted midterm score
For 12
[tex]\begin{gathered} y=3.5(12)+16.18 \\ y=42+16.18 \\ y=58.18 \end{gathered}[/tex]for 18
[tex]\begin{gathered} y=3.5(18)+16.18 \\ y=63+16.18 \\ y=79.18 \end{gathered}[/tex]A residual is the difference between the observed value and the mean value that the model predicts for that observation
[tex]\begin{gathered} Residue\text{ =58.16-58.16=0} \\ residue\text{ =75-79.18=-4.18} \end{gathered}[/tex]The final answer
Identify whether the given situation represents one-to-one function. Justify your answer. 10.)The relation pairing a television to universal remote control.
hello! We have to analyze this sentence and justify the type of function.
The relation pairing a television to a universal remote control.
A universal remote control means that this control works for any television.
So, if we have three models of television, A, B, and C, this remote control would be able to work in all of the TVs, independent of the model.
In this case, we have a situation that represents one-to-many functions, and not a one-to-one function.
Using the same example, if the remote control just works for TV A, it would be a one-to-one function.
3. Suppose f(x) = x squared - 2x +3 and g(x) = x squared -3. Compute the composition f(g(x)) and simplify.
The given functions are
[tex]\begin{gathered} f(x)=x^2-2x+3 \\ g(x)=x^2-3 \end{gathered}[/tex]The composition f(g(x)) refers to substituting the x-variables of f(x) for the function g(x).
[tex]f(g(x))=(x^2-3)^2-2(x^2-3)+3[/tex]Then, we solve the power and product. We solve the squared binomial using the following
[tex](a-b)^2=a^2-2ab+b^2[/tex][tex]\begin{gathered} f(g(x))=x^4-2\cdot x^2_{}\cdot3+9-2x^2+6+3 \\ f(g(x))=x^4-6x^2-2x^2+18 \\ f(g(x))=x^4-8x^2+18 \end{gathered}[/tex]Therefore, the composition is[tex]f(g(x))=x^4-8x^2+18[/tex]Mia has at most $24 to spend on jewelry. She wants to spend $6 on a pair ofearrings and spend the rest of the money on necklaces. Each necklace costs $9.Which inequality could she use to find the number, x, of necklaces she can buy?A 6x + 9 = 24B9x 24a 6x24 + 9D 9x + 6 5 24
She has a budget of $24 to spend on jewelry, so we know that the spending has to be less or equal than 24.
There is a spending that is already decided, and is $6 on a pair of earrings.
The rest will be spend on necklaces, wich cost $9 each one. If x is the number of necklaces, the spending on necklaces is 9x.
Then, the total spending is 6+9x and it has to be less or equal than 24, so we can write the inequality as:
[tex]6+9x\le24[/tex]If you invest $2,000 what interest rate do you need for your money to become 10,000 in 20 years
The principal money is P=2000.
The time is t=20 years.
The value of amount is A=10,000.
Determine the intrest obtained on the principal amount.
[tex]\begin{gathered} A=I+P \\ 10000=I+2000 \\ I=10000-2000 \\ =8000 \end{gathered}[/tex]The formula for the intrest on the principal money is,
[tex]I=\frac{P\times R\times t}{100}[/tex]Substitute the values in the formula to obtain the rate percentage.
[tex]\begin{gathered} 8000=\frac{2000\times R\times20}{100} \\ R=\frac{8000}{400} \\ =20 \end{gathered}[/tex]The value of intrest rate is 20%.
Proving Lines Parallel PracticeIn each case, state the theorem that proves a || b.1.
Question 1
Given two parallel lines, cut across by a transversal as shown below
When two lines meet , angles are formed. Therefore as the transversal cut the two parallel lines, different angles are formed. To mention but few of these angles are
Corresponding angles
Alternate interior angles
Vertical angles
Alternate exterior angles and so on
From the image in the question, the angles indicated are formed on each of the parallel lines at the same position on the transversal. This angles are shown below
These two angles that form on each of the parallel lines at similar position on the transversal are called corresponding angles and are congruent
Hence, the theorem that proves a is parallel to b (a || b) is the corresponding angle theorem
te the following.a. Estimate the x-intercept(s).b. State whether the leading coefficient is positive or negative.c. Determine whether the polynomial function is cubic or quartic.
As you can see, the graph has three x-intercepts. These are located at:
x=-2 , x=2 , and x=6.
The x-intercept values are all the values above the x-axis where the function cuts
Now, remember that:
Based in this table, if we look at our graph, we notice that:
If
[tex]\begin{gathered} x\to-\infty,f(x)\to+\infty \\ x\to+\infty,f(x)\to-\infty \end{gathered}[/tex]This situation happens when the leading coefficient is negative and the degree of the polynomial is odd. So,
- The leading coefficient is negative.
- The polynomial function is cubic.
Solve.{2d+e=8 d−e=4Use the linear combination method. The solution is (4, 0).There are infinitely many solutions.There is no solution.The solution is (5, −2).
EXPLANATION
Given the system of equations:
2d + e
51 divided by 4539 answer
51/4539 = (51/3)/(4539/3) = 17/1513 = (17/17)/(1513/17) = 1/89 = 0.011
Use synthetic division and the remainder theorem to find P(a). P(x)=x^3+4x^2-3x+6; a=4 P(a)= _______(Simplify your answer.)
Given:
[tex]P(x)=x^3+4x^2-3x+6;\text{ a=4}[/tex]Let's use synthetic division and the remainder theorem to find P(a).
To use synthetic division, place the numbers which represents the divisor and the dividend in a long division like method.
We have:
Dividend = 1, 4, -3, 6
Divisor = 4
Now, bring down the first number (which is 1), multiply the number by the divisor, place the product under the second number, add both numbers then bring down the result.
Multiply the result by the divisor, place the result under the third number, add the numbers.
Continue with the method until you are done with the third number.
The terms under the boundary line are the results while the last number in the result is the remainder.
We have:
Therefore, the remainder is = 122
Hence, we have:
P(4) = 122
Also, using the remainder theorem, we have:
P(4).
To find P(4), substitute 4 for x in the function and evaluate:
[tex]\begin{gathered} P(4)=4^3+4(4)^2-3(4)+6 \\ \\ P(4)=64+64-12+6 \\ \\ P(4)=122 \end{gathered}[/tex]ANSWER:
P(a) = 122
find two consecutive odd integers whose sum is -36
-17,-19
1) Given that -36 is even and we can add two odd numbers to get an even one. Then:
-17 -19 = -36
Hence, the answer is -17,19 two consecutive odd numbers.
Translate the sentence into an equation Four more than the product of a number and 7 is 6 Use the variable w for the unknown number
unknown number = w
four more than the product of a number and 7 is 6
four more = +4
product = multiplication
product of a number and 7 = 7x
four more than the product = 7x+4
is 6 = 6
7x+4=6
use the long division method to find the result when 4x3 + x2 272 + 18 is divided by 4x - 3. If there is a remainder, express the result in the form q(x) + r(x)/b(x)
ANSWER:
[tex]x^{2}+x-6[/tex]STEP-BY-STEP EXPLANATION:
We have the following polynomial:
[tex]4x^3+x^2-27x+18[/tex]We must divide it by 4x - 3, using the long division method, therefore:
[tex]4x^3+x^2-27x+18\div \left(4x-3\right)[/tex]We solve it below:
[tex]\begin{gathered} \text{ We divide the leading term of the dividend by the leading term of the divisor:} \\ \\ \frac{4x^3}{4x}=x^2 \\ \\ \text{ We multiply it by the divisor} \\ \\ x^2\cdot(4x-3)=4x^3-3x^2 \\ \\ \text{ We subtract the dividend from the obtained result: } \\ \\ 4x^3+x^2-27x+18-4x^3+3x^2=4x^2-27x+18 \\ \\ \text{ Finally it would be:} \\ \\ x^2+\frac{4x^2-27x+18}{4x-3} \end{gathered}[/tex]Now, we repeat the same procedure:
[tex]\begin{gathered} \text{ We divide the leading term of the dividend by the leading term of the divisor:} \\ \\ \frac{4x^2}{4x}=x \\ \\ \text{ We multiply it by the divisor} \\ \\ x\cdot(4x-3)=4x^2-3x \\ \\ \text{ We subtract the dividend from the obtained result: } \\ \\ 4x^2-27x+18-4x^2-3x=-24x+18 \\ \\ \text{ Finally it would be:} \\ \\ x^2+x+\frac{-24+18}{4x-3} \end{gathered}[/tex]We do the division for the last time and we would have the following:
[tex]\begin{gathered} \text{ We divide the leading term of the dividend by the leading term of the divisor:} \\ \\ \frac{-24x}{4x}=-6 \\ \\ \text{ We multiply it by the divisor} \\ \\ -6\cdot(4x-3)=-24x+18 \\ \\ \text{ We subtract the dividend from the obtained result: } \\ \\ -24x+18-24x+18=0 \\ \\ \text{ Finally it would be:} \\ \\ x^2+x-6 \end{gathered}[/tex]So, the correct answer is:
[tex]4x^3+x^2-27x+18\div\left(4x-3\right)=x^2+x-6[/tex]factor trinomialsx^2+2x-80
We will factor as follows:
[tex]x^2+2x-80=(x+10)(x-8)[/tex]***
What we try to find in the values that are added [Or subtracted from x] is the following:
*When both numbers are multiplied between them and added together the solution musth be the value in the middle of the trinomial.
*W
While hanging Christmas lights for neighbors, Terrell counted the number of broken lights on each string Number of broken lights Number of strings 10 3 42 4 93 6 101 4 135 3 < is the number of broken lights that a randomly chosen string had. What is the expected value of X? Vrite your answer as a decimal.
The expected value is defined by
[tex]E=\Sigma x\cdot P(x)[/tex]This means we have to find the probability of each number of broken lights:
[tex]\begin{gathered} P_1=\frac{3}{20} \\ P_2=\frac{4}{20}=\frac{1}{5} \\ P_3=\frac{6}{20}=\frac{3}{10} \\ P_4=\frac{4}{20}=\frac{1}{5} \\ P_5=\frac{3}{20} \end{gathered}[/tex]Then, we multiply each probability by its x-value, and we add them to find the expected value:
[tex]\begin{gathered} E=10\cdot\frac{3}{20}+42\cdot\frac{1}{5}+93\cdot\frac{3}{10}+101\cdot\frac{1}{5}+135\cdot\frac{3}{20} \\ E=1.5+8.4+27.9+20.2+20.25 \\ E=78.25 \end{gathered}[/tex]Hence, the expected value is 78.25.17.If y varies inversely as x and x=5 when y=20, then what is the constant ofvariation, k?A10064121CBD
Given
If y varies inversely as x and x=5 when y=20.
To find: The constant of variation k.
Explanation:
It is given that, y varies inversely as x.
That implies,
[tex]y=\frac{k}{x}[/tex]Then for x=5 and y=20.
[tex]\begin{gathered} 20=\frac{k}{5} \\ \Rightarrow k=20\times5 \\ \Rightarrow k=100 \end{gathered}[/tex]Hence, the constant of variation k is 100.
Finding length of hypotenuse d is marked bc I jus needed to press an answer
Given:
The objective is to find the hypotenuse c of the right triangle.
Consider the right triangle as,
The length of the side c can be calculated using Pythagoras theorem.
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ c^2=36^2+15^2 \\ c^2=1296+225 \\ c^2=1518 \\ c=\sqrt[]{1518} \\ c=38.96 \\ c\approx39 \end{gathered}[/tex]Hence, option (B) is the correct answere.
help me with geometry homweork
For a parallelogram, 3y+8 = 2x-4 and 5y = x+8
This is because the parallel sides are equal
3y + 8 = 2x-4 ..........(1)
5y = x+8...............(2)
from equation 2, y =(x+8)/5 .......(3)
substituting for y in equation (1) we have
3(x+8)/5 + 8 = 2x -4
3x+24 +(5x8) =5(2x-4)
3x+24 + 40 = 10x - 20
10x -3x = 40 +24+20
7x = 84
x = 12
From (2) , substituting for x yields
5y = x+8
5y = 12 +8
5y =20
y = 4
48. Find the x– and y–intercepts of the line: 3x + 4y = –24.A. 3, 4B. 8, 6C. –8, –6D. –3, –4
Answer:
C. –8, –6
Explanation:
Given the equation:
[tex]3x+4y=-24[/tex](a)x-intercept
The x-intercept is the value of x at which y=0.
When y=0:
[tex]\begin{gathered} 3x+4y=-24 \\ 3x+4(0)=-24 \\ 3x=-24 \\ \text{Divide both sides y 3} \\ \implies x=-\frac{24}{3} \\ x=-8 \end{gathered}[/tex]b)y-intercept
The y-intercept is the value of y at which x=0.
When x=0:
[tex]\begin{gathered} 3x+4y=-24 \\ 3(0)+4y=-24 \\ 4y=-24 \\ \text{Divide both sides by 4} \\ \implies y=-\frac{24}{4} \\ y=-6 \end{gathered}[/tex]The x– and y–intercepts of the line: 3x + 4y = –24 are –8 and –6.
Option C is correct.