Answer:
A 16 inches diameter will reward you with the largest slice of pizza.
Step-by-step explanation:
Let r be the radius and [tex]\theta[/tex] be the angle of a circle.
According with the graph, the area of the sector is given by
[tex]A=\frac{1}{2}r^2\theta[/tex]
The arc length of a circle with radius r and angle [tex]\theta[/tex] is r [tex]\theta[/tex]
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
[tex]2r+r\theta=32 \:in[/tex]
We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]
[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]
Next, we substitute this equation into the area equation
[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]
The domain of the area is
[tex]0<r<12[/tex]
To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.
[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]
To check if r=8 is a maximum we use the Second Derivative test
if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.
The second derivative is
[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]
Because [tex]A''(r)=-2 <0[/tex] the largest slice is when r = 8 in.
The diameter of the pizza is given by
[tex]D=2r=2\cdot 8=16 \:in[/tex]
A 16 inches diameter will reward you with the largest slice of pizza.
Please answer this correctly
Answer: 1/4
Step-by-step explanation:
The cheesiest recipe would be 1 cup and the least cheesy recipe would be 3/4 cups
1 - 3/4 = 1/4
Answer:
[tex]\frac{1}{4}[/tex] cup of cheese
Step-by-step explanation:
The least cheesiest recipe uses [tex]\frac{3}{4}[/tex] cup of cheese while the most cheesiest uses 1 cup of cheese.
[tex]1-\frac{3}{4} =\\\\\frac{1}{4}[/tex]
The most cheesiest uses [tex]\frac{1}{4}[/tex] cup more cheese than the least cheesiest.
Insurance Underwriters have established that the probability of city experiencing disasters in the next five years is 0.3 for a Tornado, 0.4 for Hurricane, and 0.1 for both Tornado and Hurricane. A) What is the probability of city experiencing only a Tornado in the next five years?B) What is the probability of city experiencing neither a Tornado nor Hurricane in the next five years?
Answer:
a. 20%
b. 40%
Step-by-step explanation:
We have the following from the statement:
P (T) = 0.3
P (H) = 0.4
P (T n H) = 0.1
Thus:
a. Tornado-only probability would be the probability of a tornado minus the probability of both tornado and hucaran
P (only T) = P (T) - P (T n H)
replacing:
P (only T) = 0.3 - 0.1
P (only T) = 0.2
In other words, the probability that only one tornado will occur is 20%
b. The probability that there is neither of the two would be the complement of the union between both events, that is:
P (T U H) '= 1 - P (T U H)
and the union is equal to:
P (T U H) = P (T) + P (H) - P (T n H)
replacing:
P (T U H) = 0.3 + 0.4 - 0.1
P (T U H) = 0.6
now if replacing in P (T U H) ':
P (T U H) '= 1 - 0.6
P (T U H) '= 0.4
That is to say that the probability that neither of the two happens is 40%
Do all perpendicular lines have negative reciprocal slopes?
Not necessarily, the more correct definition is opposite reciprocal slopes.
The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.
In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.
1/2x+4=2/3x+1, solve for x
Answer:
x=18
Step-by-step explanation:
Step 1: Subtract 2/3x from both sides.
1/2x+4=2/3x+1
-2/3x -2/3x
= -1/6x+4=1
Step 2: Subtract 4 from both sides.
-1/6x+4=1
-4 -4
= -1/6x=-3
Step 3: Multiply both sides by 6/(-1).
-1/6x=-3
*6/(-1) * 6/(-1)
x=18
Which values for h and k are used to write the function f(x) = x2 + 12x + 6 in vertex form?
h=6, k=36
h=-6, k=-36
h=6, k=30
h=-6, k=-30
Answer: The answer is h=-6, k=-30
Step-by-step explanation:
d on edg
Find the area and the circumference of a circle with radius 7 cm.
Use the value 3.14 for me, and do not round your answers. Be sure to include the correct units in your answers.
cm
7 cm
Area: 0
Circumference: 0
Х
[tex]answers \\ area = 153.86 \: {cm}^{2} \\ circumference = 43.96 \: cm \\ \\ solution \\ radius = 7cm \\ area \: of \: circle = \pi {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: 3.14 \times {7}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 49 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 153.86 \: {cm}^{2} \\ circumference \: of \: circle = 2\pi \: r \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 3.14 \times 7 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 43.96 \: cm \\ hope \: it \: helps \\ good \: luck \: on \: you r \: assignment[/tex]
Answer:
[tex] Area \: of \: circle = 153.86 \: {cm}^{2} \\ \\ Perimeter \: of \: circle = 43.96 \: cm [/tex]
Given:
Radius of circle (r) = 7 cm
Step-by-step explanation:
[tex]Area \: of \: circle = \pi {r}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times ({7}^{2} ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times 49 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 49 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 153.86 \: {cm}^{2} [/tex]
[tex]Circumference \: of \: circle = 2\pi r \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \pi \times 7\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \times \pi\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \times 3.14\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 43.96 \: cm[/tex]
Which equation describes a relationship that is directly proportional?
(A) y = 9
(B) y = 1/5
(C) y = 3x
(D) y = x + 4
Answer:
(C) y = 3x
Step-by-step explanation:
Directly proportional relation is one in which the value of x and y gets increases or decreased in same proportion.
example of such relation can be y = kx
where k is the constant of proportionality which depicts by how much value of y will change in response to change of x.
_______________________________________________
now in the option
A and B
y= 9 , y =1/5
value of y is constant and does not depend on other variable. it value will remain same.
for y = x+4
value of y increases with x but it does not increase proportionally.
let see an example for x =1 , y = 1+4 = 5
x =2 , y = 2+4 = 6
(1,5) and (2,6) are not proportionally changing also this equation is not of form y = kx
thus, it is incorrect option.
_______________________________
(C) y = 3x
here equation is form y =kx . in place of k there is 3
let see an example for x =1 , y = 3*1 = 3
x =2 , y = 3*2 = 6
(1,3) and (2,6) are proportionally changing (1/3 = 2/6) also this equation is of form y = kx
thus, it is correct option.
An online furniture store sells chairs for $100 each and tables for $550 each. Every day, the store can ship at most 25 pieces of furniture and must sell no less than $7000 worth of chairs and tables. If 9 chairs were sold, determine all possible values for the number of tables that the store must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Answer:
(10, 11, 12, 13, 14, 15, 16)
Step-by-step explanation:
The minimum number of tables that the store has to sell in order to meet the requirements is given by:
[tex](25-t)*100+t*550=7,000\\(550-100)t=7,000-2,500\\t = 10\ tables[/tex]
The company must sell at least 10 tables.
Since the company already sold 9 chairs, and they can ship at most 25 items, they can sell at most 16 tables. Every integer number between the minimum and maximum is also possible:
(10, 11, 12, 13, 14, 15, 16).
Answer:
12,13,14,15,16
Step-by-step explanation:
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }t=
Let t=
\,\,\text{the number of tables sold}
the number of tables sold
\text{Let }c=
Let c=
\,\,\text{the number of chairs sold}
the number of chairs sold
\text{\textquotedblleft at most 25 pieces"}\rightarrow \text{25 or fewer pieces}
“at most 25 pieces"→25 or fewer pieces
Use a \le≤ symbol
Therefore the total number of furniture pieces sold, t+ct+c, must be less than or equal to 25:25:
t+c\le 25
t+c≤25
\text{\textquotedblleft no less than \$7000"}\rightarrow \text{\$7000 or more}
“no less than $7000"→$7000 or more
Use a \ge≥ symbol
The store makes $550 for each table sold, so for tt tables, the store will make 550t550t dollars. The store makes $100 for each chair sold, so for cc chairs, the store will make 100c100c dollars. Therefore, the total revenue 550t+100c550t+100c must be greater than or equal to \$7000:$7000:
550t+100c\ge 7000
550t+100c≥7000
\text{Plug in }9\text{ for }c\text{ and solve each inequality:}
Plug in 9 for c and solve each inequality:
The store sold 9 chairs
\begin{aligned}t+c\le 25\hspace{10px}\text{and}\hspace{10px}&550t+100c\ge 7000 \\ t+\color{green}{9}\le 25\hspace{10px}\text{and}\hspace{10px}&550t+100\left(\color{green}{9}\right)\ge 7000 \\ t\le 16\hspace{10px}\text{and}\hspace{10px}&550t+900\ge 7000 \\ \hspace{10px}&550t\ge 6100 \\ \hspace{10px}&t\ge 11.09 \\ \end{aligned}
t+c≤25and
t+9≤25and
t≤16and
550t+100c≥7000
550t+100(9)≥7000
550t+900≥7000
550t≥6100
t≥11.09
\text{The values of }t\text{ that make BOTH inequalities true are:}
The values of t that make BOTH inequalities true are:
\{12,\ 13,\ 14,\ 15,\ 16\}
{12, 13, 14, 15, 16}
\text{(the final answer is this entire list)}
(the final answer is this entire list)
A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, V2V3 might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day.
Required:
a List the sample points in this experiment of ordering paper on two successive days.
b Assume the vendors are selected at random each day and assign a probability to each sample point.
c Let A denote the event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P( A), P( B), P( A U B), and P( A ∩ B) by summing the probabilities of the sample points in these events.
Find the given attachments
If a man takes 30 minutes to drive at work and it is 44 miles into work what is the average speed?
Answer:
1.46666 miles / minutes
88 miles per hour
Step-by-step explanation:
The speed is distance over time
44 miles / 30 minutes
1.46666 miles / minutes
or if we want in miles per hour
44 miles / .5 hours
88 miles per hour
Answer:
1.467 mile/minute
Step-by-step explanation:
you should divide the distance on the time i.e. 44/30
Which statements are true?
If all angles of a quadrilateral are right angles, then the quadrilateral must be a square.
Two shapes are similar if and only if their corresponding angles are equal.
All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º.
if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
There are three vertices in a triangle, or there are four sides in a pentagon.
Any two triangles are either similar or congruent.
Answer:
Step-by-step explanation:
1) If all angles of a quadrilateral are right angles, then the quadrilateral must be a square. This is not true because the quadrilateral can also be a rectangle.
2) Two shapes are similar if and only if their corresponding angles are equal. This is true.
3) All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º. This is false because the sum of the angles is 360°
4) if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus. This is true.
5) There are three vertices in a triangle, or there are four sides in a pentagon. This is false because a Pentagon has 5 sides.
6) Any two triangles are either similar or congruent. This is not true. Congruent triangles are always similar
Therefore, the true statements are 2 and 4
Answer:
its B and D
Step-by-step explanation:
5 of 5
It is worked out that if 5 ladles full of soup are given to
each person,
140 people can be fed.
The customers have complained in the past that the
portions are too small.
The cook decides to give 7 ladles full of soup to each
person.
How many people can now be fed soup?
people
Answer:
Number of people that can be served 7 ladles = 100 people
Step-by-step explanation:
We are told that;
Initial number of ladles proposed per person = 5
Number of persons to be fed based on 5 ladles = 140 persons
Thus, amount of ladles based on that data is;
140 people x 5 ladle/1 person = 700 ladles full of soup
Now, since the cook decides to give 7 ladles full of soup to each person, the number of people that can be fed will now be;
700 ladles ÷ 7 ladles/person = 100 persons
PLEASE HELP ALGEBRA PROBLEM!!! 20 POINTS ANSWER A-D
Answer:
A. 1.5 seconds
B. 36 feet
C. 0 feet
D. After 3 seconds
Step-by-step explanation:
I graphed it on desmos.
Tricia has a birthday party. During the party, she opened 36 gifts, which was 60% of all her gifts. After the party, she opened the rest of the gifts and found that 25% of them were the same present, so she returned all but one of the duplicate gifts. How many gifts did she return?
Answer:
She returned 5 gifts.
Step-by-step explanation:
36 gifts is 60% = 0.6 of all the gifts that she received. How many presents are 100% = 1?
36 gifts - 0.6
x gifts - 1
0.6x = 36
x = 36/0.6
x = 60
She received 60 gifts.
She opened the rest of the gifts and found that 25% of them were the same present
The rest is 60 - 36 = 24 gifts.
25% is (1/4)*24 = 6 duplicate figts
She returned all but one of the duplicate gifts.
That is, she returned 6 - 1 = 5 gifts.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Volume of cylinder = πr²h
= (3.14)(4)(0.75)
= 9.4
Since she'll fill it half so
Amount of water to be filled = 4.7
rearrange the equation t = vf - vi /a
to make acceleration appear on the left hand side
Answer:
a= (vf - vi)/t
Step-by-step explanation:
t = vf - vi /a
a* t =(vf - vi /a)*a
at = vf - vi
at/t = (vf - vi)/t
a = (vf - vi)/t
Hope it works
How can I make the red segment less steep than the blue segment , and more steep than the green segment ?
(12 /`15) ÷ (25/ 16) =
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
[tex]\frac{12}{15} \div \frac{25}{16}[/tex]
[tex]\frac{12}{15} \times \frac{16}{25}[/tex]
[tex]\frac{12 \times 16}{15 \times 25}[/tex]
[tex]\frac{192}{375}[/tex]
[tex]\frac{64}{125}=0.512[/tex]
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
=> [tex]\frac{12}{15} / \frac{25}{16}[/tex]
Changing the division sign into multiplication and inverting the term after the sign.
=> [tex]\frac{12}{15} * \frac{16}{25}[/tex]
=> [tex]\frac{12*16}{15*25}[/tex]
=> [tex]\frac{192}{375}[/tex]
=> [tex]\frac{64}{125}[/tex]
This is the required form.
What expression is equivalent to 6•6•6•6•6
Answer:
6^5
Step-by-step explanation:
6 multiplied with itself 5 times is equal to 6^5
Can someone please help me
Answer:
6
Step-by-step explanation:
Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.
x = 8 *3/4 = 6
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. G(x) = |x| + 7
Step-by-step explanation:
→For the function G(x) to shift upwards, there needs to be a number being added to the whole function.
→The answer isn't "A," because the 1 is being subtracted, making it shift downwards 1 unit, not upwards.
→The answer isn't "B," because adding the 2 there would cause the function to shift to the left for 2 units, not upwards.
→The answer isn't "C," because 10 is being multiplied, which would cause the function to narrow, and not shift upwards.
This means the correct answer is "D," because the 7 is being added, making the function shift upwards 7 units.
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?
Answer:
4.6%.
Step-by-step explanation:
The probability that a can of paint contains contamination(C) is 3.23%
P(C)=3.23%
The probability of a mixing(M) error is 2.4%.
P(M)=2.4%
The probability of both is 1.03%.
[tex]P(C \cap M)=1.03\%[/tex]
We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]
In probability theory:
[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]
The probability that a randomly selected can has contamination or a mixing error is 4.6%.
The sum of two consecutive even integers is at most 400. The pair of integers with the greatest sum is 196 and 198.
Answer:
Step-by-step explanation: If the sum of two equal even numbers is 400, the numbers will be 200+200. Therefore the largest possible consecutive even numbers which have a sum of 400 or less are 198 and 200 which have a sum of 398.
i guss this would be helpful :]
Answer:
Step-by-step explanation:
Noah has a t-shirt collection. Three-eighths of the t-shirts are blue. Of the blue t-shirts,two-ninths of them have a pocket. What fraction represents the numbers of t-shirts that are blue and have a pocket?
Answer:
1/12
Step-by-step explanation:
blue = (3/8)collection
blue&pocket = (2/9)blue = (2/9)(3/8)collection
blue&pocket = (6/72)collection = (1/12)collection
1/12 of Noah's collection is blue and has a pocket.
what two numbers add to -7 and multiply to -60
Answer:
The answer would be 5 and -12
The following are daily outputs from shift A and shift B at a factory.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
Answer:
shift B
Step-by-step explanation:
shift a is 78.6 repeating
shift b is 79.3 repeating
mean is when you add them all then divide it by the numbers it has
Answer:
shift B
Step-by-step explanation:
To calculate the mean for a set of data, add all the numbers in that set, then divide by the number of data points in the set.
All of the following are examples of quantitative data EXCEPT ________.
a. the amount of sleep normally gotten by the students in a class
b. the number of siblings that students have
c. the cholesterol levels of the students in a class
d. the exam scores for the students in a class
d. the gender of the students in a class
Answer:
e. the gender of the students in a class
Step-by-step explanation:
Quantitative data is measured is numbers. For example 1, 2, 3.5,...
Qualitative data are labels, that is, tall, short, male, female, Brazilian, Colombian,...
In this question:
The only data that is not measured in numbers is the gender of the studens in class, which can be male or female, they do not assume any numeric value. So the answer is e.
The quantitive data example does not include option e. the gender of the students in a class.
Data:Quantitative data is measured in numbers. like 1, 2, 3.5,..While on the other hand, Qualitative data are labels i.e. tall, short, male, female, etc. Based on this, the last option is correct.learn more about the data here: https://brainly.com/question/20296761
4x+6y=-10 8x+10y=-26 solve the system of the linear equation
Now by using equation 1 in equation 2 we get,
[tex]4x + 5y = - 13 \\ \\ 4( \frac{ - 5 - 3y}{2} ) + 5y = - 13 \\ \\ \frac{ - 20 - 12y}{2} + 5y = - 13 \\ \\ \frac{ - 20 - 12y + 10y}{2} = - 13 \\ \\ - 20 - 2y = - 26 \\ \\ - 2y = - 26 + 20 \\ \\ - 2y = - 6 \\ \\ y = 3[/tex]Now upon using the value of y in equation 1, we get
[tex]x = \frac{ - 5 - 3y}{2} \\ \\ x = \frac{ - 5 - 3 \times 3}{2} \\ \\ x = \frac{ - 5 - 9}{2} \\ \\ x = \frac{ - 14}{2} = - 7[/tex]Which of the following terminating decimals is equivalent to -1 3/4
Answer:
-1.75
Step-by-step explanation:
