Answer:
longer = 28 meters
Total = 40 meters
Step-by-step explanation:
Let the smaller piece be s,
and the longer piece be b
s = ¼b + 5
s = 12
¼b + 5 = 12
¼b = 7
b = 28 m
Total length = 28+12 = 40 meters
Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x, y) point.
y= -x^2-10x-22
Answer:
vertex: (-5, 3)
Step-by-step explanation:
Besides providing the graph of the given quadratic equation, I will also demonstrate the algebraic method of solving for the vertex of a parabola.
Method 1: Algebraic SolutionGiven the quadratic equation, y = -x² - 10x - 22, where:
a = -1, b = -10, and c = -22.
Find the x-coordinate of the vertex:In order to find the vertex of the given equation, use the following formula to find the x-coordinate of the vertex: [tex]x = \frac{-b}{2a}[/tex].
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{-(-10)}{2(-1)}[/tex]
[tex]x = \frac{10}{-2}[/tex]
x = -5
The x-coordinate of the vertex is: x = 5.
Find the y-coordinate of the vertex:Next, substitute the value of the x-coordinate into the given quadratic equation to find its corresponding y-coordinate:
y = -x² - 10x - 22
y = -(-5)² - 10(-5) - 22
y = -25 + 50 - 22
y = 3
Therefore, the vertex of the given parabola is: (-5, 3), where it is the maximum point.
One of the attachments is the screenshot of the graphed quadratic equation (using Desmos), where it shows the vertex as the maximum point.
Method 2: Graphing CalculatorIf you have a graphing calculator (such as the Texas Instruments graphing calculator):
Press Y=Then, simply enter the given quadratic equation, -x² - 10x - 22.Next, press 2ND ⇒ Quit. Press the GRAPH button. Press 2ND ⇒ TRACE Select option 4: maximumIt will ask for the "Left Bound?": move the cursor as close to the maximum point as possiblePress ENTER. Next, it will ask for the "RightBound?" Repeat the same process as in step #7. Press ENTER.It will ask for "Guess?" ⇒ press ENTER, and it will provide the same coordinates for the vertex, (-5, 3).Please let me know if you have any questions or concerns regarding this post.
2. Suppose that you are looking for a student at your college who lives within five miles of you. You know that 55% of the 25,000 students do live within five miles of you. You randomly contact students from the college until one says he or she lives within five miles of you.
(a) What is the probability that you need to contact four people?
(b) How many students from the college you expect to contact until you find one lives within five miles of you?
(C) What is the standard deviation of the number of students to be contacted until one says who lives within five miles of you?
(d) Suppose you randomly ask 5 students at your college, what is the probability that 3 of them live within five miles of you?
(e) Suppose you randomly ask 5 students at your college, what is the expected number of students who live within five miles of you?
How to do this five questions ? thanks
Using the binomial distribution, it is found that:
a) There is a 0.0501 = 5.01% probability that you need to contact four people.
b) You expect to contact 1.82 students until you find one who lives within five miles of you.
c) The standard deviation is of 1.22 students.
d) There is a 0.3369 = 33.69% probability that 3 of them live within five miles of you.
e) It is expected that 2.75 students live within five miles of you.
For each student, there are only two possible outcomes. Either they live within 5 miles of you, or they do not. The probability of a student living within 5 miles of you is independent of any other student, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
55% of the students live within five miles of you, thus [tex]p = 0.55[/tex].Item a:
This probability is P(X = 0) when n = 3(none of the first three living within five miles of you) multiplied by 0.55(the fourth does live within five miles), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.55)^{0}.(0.45)^{3} = 0.091125[/tex]
[tex]p = 0.091125(0.55) = 0.0501[/tex]
0.0501 = 5.01% probability that you need to contact four people.
Item b:
The expected number of trials in the binomial distribution until q successes is given by:
[tex]E = \frac{q}{p}[/tex]
In this problem, [tex]p = 0.55[/tex], and 1 trial, thus [tex]q = 1[/tex], hence:
[tex]E = \frac{1}{0.55} = 1.82[/tex]
You expect to contact 1.82 students until you find one who lives within five miles of you.
Item c:
The standard deviation of the number of trials until q successes are found is given by:
[tex]S = \frac{\sqrt{q(1 - p)}}{p}[/tex]
Hence, since [tex]q = 1, p = 0.55[/tex]:
[tex]S = \frac{\sqrt{0.45}}{0.55} = 1.22[/tex]
The standard deviation is of 1.22 students.
Item d:
This probability is [tex]P(X = 3)[/tex] when [tex]n = 5[/tex], hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.55)^{3}.(0.45)^{2} = 0.3369[/tex]
There is a 0.3369 = 33.69% probability that 3 of them live within five miles of you.
Item e:
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
Hence, since [tex]n = 5, p = 0.55[/tex]:
[tex]E(X) = 5(0.55) = 2,75[/tex]
It is expected that 2.75 students live within five miles of you.
A similar problem is given at https://brainly.com/question/25343741
4 4/6 + 3 7/8 = ? ........................................
Answer:
[tex]8\frac{13}{24\\}[/tex]
Step-by-step explanation:
[tex]4\frac{4}{6}+3\frac{7}{8}[/tex]
[tex]\frac{28}{6}+\frac{31}{8}=\frac{205}{24}=8\frac{13}{24}[/tex]
Joe is a photographer . For every 15 rolls of film he shoots, 10 are black and white. If Joe uses 57 rolls of film, how many rolls are in black and white?
Answer:
38 black and white rolls.
Step-by-step explanation:
15 rolls = 10 black and white
57 rolls = 57 divided by 15 multiplied by 10
57 rolls = 3.8 x 10 Leaving 38 Therefore there will be a total of 38 black and white rolls.
3. Mr. Morris orders a bottle of lotion that contains (15)liters. He use 2/6 of a liter of
lotion a day. How many days can he use the bottle of lotion until it is empty?
Pls help and show me how to do it
Answer:
45
Step-by-step explanation:
If he uses 2/6 of a liter thats 3 days for 1 liter.
3 x 15 is 45. so 45 days
15 mm 4 mm 3 mm what is the surface area of the prism
Answer:
234 millimeters^2 is the answer
Step-by-step explanation:
What is the elapsed time from 11:34 A.M. to 12:06 P.M.?
Answer:
12hrs and 32 minutes
Step-by-step explanation:
because the same am time to pm time is exactly 12 hrs and 11:34am is 26 minutes away from 12am so you can 26 minutes to get to 12am then 12am is 12hrs away from 12pm so you add 12hrs and now you are at 12pm at 12pm you add 6 minutes to get to 12:06pm which is a total of 12hrs and 32 minutes
Please show how you solved the problem.
4a - 14 = 7a - 8
4a - 14 = 7a - 8
4a - 7a = 14 -8
-3a = 6
a = 2
ok done. Thank to me :>
Answer:
a= -2
Step-by-step explanation:
4a -14 = 7a -8
Subtract 7a from both sides
-3a -14= -8
Add 14 to both sides of equation
-3a = -8 +14
Add -8 and 14
-3a = 6
Divide each term by -3
a = -2
Help??? Lma.o sorry I need the answer asap
Answer:
f(5)=38
Step-by-step explanation:
f(5) means x=5, or in this case, a=5. We plug in 5 as A. f(5)=7(5+1)-4. f(5)=7(6)-4.
f(5)=42-4
f(5)=38
When Li Juan's auto yard is filled to capacity with only cars, it has 60 cars. When it is filled to capacity with only vans, it has 50 vans. Which linear equation models the number of cars, c, and vans, v, that could be in Li Juan's auto yard when it is filled to capacity? А c/60 + v/50 =1 B. 60c + 50v =1 C. c/50 + v/60 =1 D. 50c + 60v =1
The linear equation that could be used to model Li Juans auto yard is c/60 + v/50 = 1
A linear equation is in the form:
y = mx + b;
where m is the rate of change, b is the initial value of y and y, x are variables.
Let c represent the number of cars and v represent the number of vans.
Hence when it is filled to capacity:
c/60 + v/50 = 1
The linear equation that could be used to model Li Juans auto yard is c/60 + v/50 = 1
Find out more at: https://brainly.com/question/25718473
Function or not functional pls help
Answer:
It is a function.
Step-by-step explanation:
Each input goes to exactly one output. Therefore, this is a function.
A square is 3 inches by 3 inches. What is its area
Answer:
9
Step-by-step explanation:
Because area is multipication, you need to multiply legth and width. So 3x3=6. Hope it helps! :)
Please can some one help me please
Answer:
a)3
b)33
Step-by-step explanation:
a)10% is the same as 10/100 so 30/100=0.3 x 10= 3
b) 3+30 = 33
What’s the answer need in 20 minutes
Find the y intercept of the line -5x-2y=-14
Answer:
the y intercept is7
Step-by-step explanation:
at y-axis x=0, y=7
4/7 into decimal??? Then rounded to 3 decimal places??
Answer:
0.571
Step-by-step explanation:
:)
PLEASE HELP WITH THIS ONE QUESTION
Answer:
Left 3 down 4
Step-by-step explanation:
I'm not sure how to explain it, but I can give advice. A site that really helped me with this was Desmos Graphing Calculator.
What is the volume of an oblique square pyramid with base edges 25 ft and height 24ft?
A. 5,000 ft^3
B. 7,500 ft^3
C. 10,000 ft^3
D. 15,000 ft^3
Check the picture below.
Hi , what is sun helppp pls
Answer: sun are the main light source
Step-by-step explanation:
Answer:
What is sun ?
»The Sun is a star. It is a huge, spinning, glowing sphere of hot gas.Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories.
1. If she eats 2 servings of granola, how many calories does she eat?
calories
2. If she wants to eat 1050 calories of granola, how many servings should she eat
servings
3. Write an equation that will give us the number of calories (c) from the number of servings (s) eaten.
Answer:
1. 700 calories
2. 3 servings
3. c = 350s
Step-by-step explanation:
1. 5 servings = 1,750 calories
divide by 5 on both sides
1 serving = 350 calories
multiply both sides by 2
2 servings = 700 calories
2. 1 serving = 350 calories
1050 calories = 350 calories X 3
3 servings = 1,050 calories
3. 1 serving = 350 calories
# of calories = 350 per serving
c = 350s
be precise yesterday
Answer:
is this supposed to be a free point question? I'm confuzzled
59 oz = ____ lb ______oz
Explain yourselves
Answer:
3 lb 11 oz
Step-by-step explanation:
Divide 59 by 16
Answer:
3 pound and 11oz
Step-by-step explanation:
hop3 this helps
Cassidy places 40 stamps on each of 8 albums pages how many stamps dose she place
Answer:
Cassidy places 5 steps on each album page.
Cassidy places 320 stamps in total.
Step-by-step explanation:
40÷8=5 stamps on each album page
40×8=320 stamps in total
Can somebody answer this for me?
Given: passes though (6,3) and m=(5/3).
Ok so we know that y = mx + b is the equation of a line and we have m and we can find b via substitution.
y = mx + b
3 = (5/3)(6) + b
3 - (5/3)(6) = b
b = -7
Great now we know b so we can construct the rest of the linear function.
y = f(x) = (5/3)(x) - 7
You can always check the answer by plugging 6 into the x variable.
f(6) = (5/3)(6) - 7 = 3
(6,3) checks out.
Solve: m = 5 – (-10).
Answer:
m=15
Step-by-step explanation:
A refreshment stand makes 5 large servings of frozen yogurt from 8 pints. Graph the line and then write
its equation. Let the x-axis represent the number of pints and the y-axis represent the number of
servings. Use only fractional form, if necessary.
Answer:
x= (8/5)
Step-by-step explanation:
x= 8÷5
evaluate the equation/expression
x=1.6
then convert to a fraction x= BasePoly 1.6 → 16/10 →8/5
Answer:
Pls help me I think its 5/8
Step-by-step explanation:
what is the domain of the relation below?
Answer:
The domain of a relation is the set of all first coordinates (x-coordinates) of the ordered pairs. The range of a relation is the set of all second coordinates (y-coordinates) of the ordered pairs.Step-by-step explanation:
Answer:
A - {-1, 0, 1, 3}
Step-by-step explanation:
the domain is how far the relation stretches across the x axis. the points here are -1, 0, 1, and 3, so that is the domain
In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
If the spectator has an angle of 115° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
hole?
25.6°
39.4°
64.3°
65.0°
Using the law of sines, it is found that the angle that the golfer has between the spectator and the hole is of 25.6º.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lenghts and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, in this problem, we have that:
[tex]\frac{\sin{115^\circ}}{200} = \frac{sin{x}}{140}[/tex]
[tex]sin{x} = \frac{140\sin{115^\circ}}{200}[/tex]
[tex]x = \arcsin{0.6344}[/tex]
x = 39.4º.
Considering that the sum of the internal angles of the triangle is of 180º, the angle that the golfer has between the spectator and the hole is given by:
A = 180 - (115 + 39.4) = 25.6º.
More can be learned about the law of sines at https://brainly.com/question/27174058
#SPJ1
Answer:
25.6
Step-by-step explanation:
I got it right
If point A is located at (-7 , 5) on a coordinate plane, and point B is located at (4 , 5), what is the distance between the two points?
Answer:
[tex]11[/tex]
Step-by-step explanation:
[tex]\sf{Use\: the\: distance\: formula\: to\: determine\: the\: distance\: between\: two\: points.[/tex]
[tex]\sf{Distance=\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]\mathrm{Plug\:the\:points}[/tex]
[tex]\sqrt{\left(4-\left(-7\right)\right)^2+\left(5-5\right)^2}[/tex]
[tex](4+7)^2=11^2\\(5-5)^2=0[/tex]
[tex]\sqrt{11^2+0}[/tex]
[tex]11^2+0=11^2\\\sqrt{11^2}[/tex]
[tex]\mathrm{Apply\:radical\:rule:\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\:\mathrm{is\ greater\ than \:or\ equal\: to \:0}[/tex]
[tex]=11[/tex]
Work out the area of the parallelogram.
13 cm
790
21 cm
Answer:
Step-by-step explanation:
please try to provide a more accurate information 13cm of what? 790?
Answer:
The area of parallelogram can be found by product of its base and height. The calculations are shown below:
Step-by-step explanation:
We know that,
Area of parallelogram = base × height
assume base to be 21 cm.
Then,
sin 79° = [tex]\frac{height}{13}[/tex]
∴ height = 13 × 0.98 = 12.74
Area of parallelogram = 21 × 12.74
= 267.54 [tex]cm^{2}[/tex]
The area of parallelogram is calculated as 267.54 [tex]cm^{2}[/tex]