It is B. You will take 3 times 3 which is 9 then you would take 4 times 3 which is 12. so your ratio would be 9:12.
The expression that describes the ratio of teaspoons of sugar to salt you will use is 9: 12
If a cookie mixture requires 3 teaspoons of sugar for every 4 teaspoons of salt, the ratio of sugar to cookies to teaspoon will be expressed as
sugar: teaspoon = 3: 4
If the mixture is tripled, we will simply multiply the ratio by the scale factor which is 3 as shown:
New ratio of sugar to teaspoon = 3(3) : 3(4)
New ratio of sugar to teaspoon = 9: 12
Hence the expression that describes the ratio of teaspoons of sugar to salt you will use is 9: 12
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You survey 50 randomly chosen audience members at a theater about whether the theater should produce a new musical. The diagram shows the results. You conclude that 80% of the audience members support production of a new musical. Is your conclusion valid?
The conclusion will be valid if a value of 40 in the diagram is gotten since 80% of 50 is 40
What is Percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
In this scenario, they survey 50 randomly chosen audience members at a theater about whether the theater should produce a new musical
If 80% of the audience members support production of a new musical, the number will be:
= 80% × 50
= 0.8 × 50
= 40
Note that the information in the diagram should also correlate to 40 to be correct.
Note that the information is incomplete but was answered based on the information given.
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how to simplify a ratio with units
Answer:
1. Convert the larger unit to the smaller unit
2. Simplify the ratio as normal
Step-by-step explanation:
simplify 25mm : 5cm
convert the centimetres into millimeters by multiplying by 10.
5×10=505cm=50mm
simplify by dividing by 25
25:50÷25=1:2
Select the correct answer from each drop-down menu. Quadrilateral PQRS, with vertex P(-5, -3), undergoes a transformation to form quadrilateral P′Q′R′S′, with P′ at (5, 3). The type of transformation PQRS undergoes is a ( A. 180 rotation about the origins. B. Translation 2 units rights 7 units up. C. Reflection over the x - axis. D reflection over the y - axis. ) . If vertex Q is at (-4, -5), then vertex Q′ is at ( A. (-4,-5) B. ( -4,5) C. (4,5) D.(5, -4) .
Answer:
i) A. 180º rotation about the origin, ii) \(Q' = (4, 5)\).
Step-by-step explanation:
i) In this case, we understand that vertex \(P = (-5,-3)\) changed to \(P' = (5,3)\) after doing an operation. At first we must calculate the distance of each point regarding origin by Pythagorean Theorem:
Point P:
\(OP = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}\)
If we know that \(x_{P} = -5\), \(y_{P} = -3\), \(x_{O} = 0\) and \(y_{O} = 0\), the distance \(OP\) is:
\(OP = \sqrt{(-5-0)^{2}+(-3-0)^{2}}\)
\(OP \approx 5.831\)
Point P':
\(OP' = \sqrt{(x_{P'}-x_{O})^{2}+(y_{P'}-y_{O})^{2}}\)
If we know that \(x_{P'} = 5\), \(y_{P'} = 3\), \(x_{O} = 0\) and \(y_{O} = 0\), the distance \(OP'\) is:
\(OP' = \sqrt{(5-0)^{2}+(3-0)^{2}}\)
\(OP' \approx 5.831\)
As \(OP = OP'\), origin is the center of rotation.
Besides, \(P'\) is a multiple of \(P\), that is:
1) \((-5, -3)\) Given
2) \(((-1)\cdot 5, (-1)\cdot 3)\) \((-a)\cdot b = -a\cdot b\)
3) \((-1)\cdot (5, 3)\) Scalar multiplication of a vector/Result.
The value of the scalar proves that P experimented a 180º rotation about the origin. Hence, the correct answer is A.
ii) If \(Q = (-4, -5)\) and the same operation described in item i) is used, then, the location of \(Q'\) is:
\(Q' = (-1)\cdot Q\)
\(Q' = (-1) \cdot (-4,-5)\)
\(Q' = ((-1)\cdot (-4), (-1)\cdot (-5))\)
\(Q' = (4, 5)\)
Which corresponds to option C.
Answer:
1. A, 2. C
Step-by-step explanation:
What are the center and radius of the circle defined by the equation
x2 + y2 - 6x+8y +21= 0 ?
Answer:
the center is (3, -4) and the radius is = 2
Step-by-step explanation:
whats 78,563 divided by 98
Ty for whoever helps me <3
Answer:
801.66
Step-by-step explanation:
calculator
Answer:
801.6632653061
Step-by-step explanation:
.......
Find the value of x
Answer:
29
Step-by-step explanation:
[remember: angle sum property of a triangle is always 180]
2x-7+ 3x + 42 = 180(angle sum property of a triangle)
2x + 3x -7 + 42 = 180
5x + 35 = 180
5x = 180-35
5x = 145
x = 145/5
x = 29
hope it helps you!
Trigonometry please help!
Answer:
the first one
Step-by-step explanation:
Find the slope of the line
y = –3/8x − 6/5
Answer:
-3/8
Step-by-step explanation:
This equation is formatted as y=mx+b where m is the slope of the line, x is the x value, and b is the y-intercept. When finding the slope of such an equation, just find what the coefficient of x in the function is. So, this equation is y = -3/8x - 6/5 and m is -3/8, so your slope is -3/8. Hope that helps!
Matthew has 75 papers to sell he only sold 45 papers so far, what percentage of the total number has he sold? Explain your thinking
Answer:
60%
Step-by-step explanation:
To make it easier, I divided 75 by 100 (0.75), and did the following:
45 / 0.75 = 60
Answer:
60%
Step-by-step explanation:
75 would be represented as 100 percent.
One card is drawn from a standard deck of 52 cards. Find the probability of drawing the following. an eight or a diamond
The probability of a simple event to occur is this:
\(P(x)=\frac{\text{total number of favorable outcomes}}{\text{total }number\text{ of possible outcomes}}\)In the question given, the favorable outcomes are either 8 or diamond.
In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.
Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:
\(p(x)=\frac{16}{52}=\frac{4}{13}\approx0.3077\)The probability, in fraction, is 4/13.
In decimal form, it is 0.3077.
In percentage form, it is 30.77%
Find the value of each variable.
Answer:
EF = 18 in. & m∠F = 134 °
Step-by-step explanation:
Hi there,
In order to find the length of side EF, you should realize that this is an isosceles triangle. We know that two sides and two angles of this type of triangle are equal to each other. We also know that the lengths of the sides opposite of the congruent angles are equal to each other. Thus, we proved that length of side EF is equal to the length of side FG.
Therefore, EF is 18 inches because FG is 18 inches.
In order to find m∠F, you need to know that the sum of the angles in a triangle add up to 180°. You add all of the known angle values and subtract it by 180°.
m∠E + m∠G + m∠F = 180°
23° + 23° + m∠F = 180°
46° + m∠F = 180°
m∠F = 134°
Hope this explanation helps you understand this problem. Cheers.
Find the midpoint of the segment with the following endpoints.
(5,5) and (10,1)
Answer:
(7.5,3)
Step-by-step explanation:
Image for explanation
FILL IN THE BLANK a/an ____________________________ diagram can be used to show how the tables in a database are defined and related..
A/an database schema diagram can be used to show how the tables in a database are defined and related.
This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and their attributes, and the relationships between them.
The database schema diagram helps in the understanding the logical design of the database, including primary keys, for foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in designing, modifying, and querying the database effectively.
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What is 9/24 inches?
Answer:
i=√−1i=-1.
Step-by-step explanation:
so esa es la respuesta
please help asap!! answer AND explanation
To be greater than a negative number, negative values need to be smaller as they get closer to zero.
The answer would be B) -5, -4.5, -3
Answer:
B
Step-by-step explanation:
This is because you could have a number greater of equal to -5, since b is the only one that has that it makes it true.
does anyone know how to solve these
Answer:
e=49
f=131
d=90
Step-by-step explanation:
A (tiny) library has 5 history texts, 3 sociology texts, 6 anthropology texts and 4 psychology texts. Find the number of ways a student can choose:
Thus, there are 18 ways to choose one book, 153 ways to choose two books, and 360 ways to choose three books, one from each category.
To find the number of ways a student can choose from the given library, we need to use the formula for combinations.
The formula for combinations is:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to be chosen, and ! denotes factorial.
Let's consider the different ways a student can choose:
1. Choosing one book from any category:
Total number of books = 5+3+6+4 = 18
n = 18, r = 1
Number of ways = 18C1 = 18! / 1!(18-1)! = 18
2. Choosing two books from any category:
n = 18, r = 2
Number of ways = 18C2 = 18! / 2!(18-2)! = 153
3. Choosing three books, one from each category:
For this, we need to choose one book from each category, and the order of selection does not matter.
n1 = 5, r1 = 1 (for history)
n2 = 3, r2 = 1 (for sociology)
n3 = 6, r3 = 1 (for anthropology)
n4 = 4, r4 = 1 (for psychology)
Number of ways = (5C1 x 3C1 x 6C1 x 4C1) = (5 x 3 x 6 x 4) = 360
Therefore, there are 18 ways to choose one book, 153 ways to choose two books, and 360 ways to choose three books, one from each category.
In summary, a student can choose:
- 18 ways to choose one book
- 153 ways to choose two books
- 360 ways to choose three books, one from each category
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Waheed's father is twelve years older than his mother. The sum of their ages is 76 years old. How old is Weheed's father
Answer:
32
Step-by-step explanation:
Let, the age of father and mother be x and y respectively. then,
According to question,
x + y = 76.........(i)
x= y + 12...............(ii)
Now,
x + y = 76
or, ( y + 12) + y = 76
or, y + 12 + y = 76
or, 2y = 76 – 12
or, 2y = 64
or, y = 64/2
.
. . y = 32
hope it will help you.
Students arrive at the Administrative Services Office at an average of one every 12 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. Required: (a) What percentage of time is Judy idle? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) (b) How much time, on average, does a student spend waiting in line? (Round your answer to the nearest whole number.) (c) How long is the (waiting) line on average? (Round your answer to 2 decimal places.) (d) What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Round your answer to 3 decimal places.)
The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.
To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333
The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:
The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.
(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.
(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:
P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.
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What time is 5 1 4hours after 7:00 p.m.?
for the 514 hours after 7 p.m. the answer to that is 5 a.m.
Which of the points shown below are on the line given by the equation Y = X +3? Check all that apply. A). Point A : (-1, 2) B). Point B : (-1, -2) C). Point C : (2, 5) D). Point D : (-3, 0) Please No jokes I really need help :))
Answer:
Point APoint CPoint DStep-by-step explanation:
The points are in the format (x , y) so given x which is the first figure, you can find y by following the formula.
Y in the point needs to satisfy the criterion of X + 3.
Point A
x = -1
y = x + 3
= -1 + 3
y = 2
Point A satisfies the equation as y from the equation is y in the point given.
Point B
x = -1
y = x + 3
= -1 + 3
y = 2
Point B does not satisfy the equation and so is not on the line.
Point C
x = 2
y = 2 + 3
y = 5
Point C satisfies the equation as y from the equation is y in the point given.
Point D
x = -3
y = -3 + 3
y = 0
Point D satisfies the equation as y from the equation is y in the point given.
help me with my math please
(2 -1/2 * 7 1/3)^6
Answer:
21 316/729
Key rules to solve:
\(\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\)\(\frac{1}{\frac{b}{c}}=\frac{c}{b}\)Convert mixed numbers to improper fractionsStep-by-step explanation:
\(\left(\frac{2-1}{2\cdot \:7\frac{1}{3}}\right)^6\)
\(=\left(\frac{2-1}{2\cdot \frac{22}{3}}\right)^6\)
\(=\frac{\left(2-1\right)^6}{\left(2\cdot \frac{22}{3}\right)^6}\)
\(=\frac{1}{\left(2\cdot \frac{22}{3}\right)^6}\)
\(=\frac{1}{\frac{7256313856}{729}}\)
\(\rightarrow 21 \frac{316}{729}\)
GP 3: Haley is making admission tickets to the middle school dance. So far she has made 112 tickets, and her planis to make 320 tickets.What percent of the admission tickets has Haley produced so far?VerbalPractionDecimal
The 100% of tickets are 320 tickets (this is Haley's goal), she made 112 tickets. To determine what percentage of 320 does 112 represent you can use cross multiplication:
320 ____ 100%
112 _____ x%
Both relations are at the same ratio so that
\(\begin{gathered} \frac{100}{320}=\frac{x}{112} \\ x=112(\frac{100}{320}) \\ x=35 \end{gathered}\)112 tickets represent 35% of 320, which means that she made 35% of the admission tickets so far.
animal scientists studied foraging behavior of the scrub lizard, found in central florida. foraging is the process of searching for food. to study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. a 95 percent confidence interval constructed from the sample is given as
The statement is valid in light of the fact that the stretch can oblige three head developments every moment.
How does probability work?The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.
At the point when this happens, we broadcast that there is plausible that the occasion will happen. In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.
By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.
As a result, the claim is true because the time allows for three head movements per minute.
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.
A mouse has made holes in opposite corners of a rectangular kitchen. Starting from its hole
in the northwest corner, the mouse scurries 20 feet along the length of the kitchen to reach a
piece of cheese in the southwest corner. Then the mouse scurries 15 feet along the width of
the kitchen to its other hole in the southeast corner. Finally the mouse scurries back to the
first hole. What is the total distance the mouse scurries?
Answer:
60 ft
Step-by-step explanation:
a² + b² = c²
20² + 15² = c²
c = √625
c = 25
total distance = 20 ft + 15 ft + 25 ft = 60 ft
which angle corresponds to ∠8 ?
The angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.
What are parallel lines ?
parallel lines can be defined as the lines which are equi distant from each other and these lines never interest to each other.
Given ,
from the figure
the parallel lines are l and m.
the angles ∠1,∠2,∠3,∠4,∠5,∠6,∠7,∠8.
∠1,∠2,∠3,∠4. are in one plane
and ∠5,∠6,∠7,∠8. are in another plane.
so the angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.
Hence , the angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.
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please evaluate the equation
Step-by-step explanation:
\( = \sum \limits_{n = 1}^{7} ( - 2. {6}^{n - 1} )\)
\( = \sum \limits_ {n = 1}^{n_{ \text{max}}} (a_1. {r}^{n - 1} )\)
\( \: \)
\(a_1 = - 2\)
\(n = 7\)
\(r = 6 \to r >1\)
\( \: \)
• Find S7.
\(s_n = a_1.( \frac{ {r}^{n} - 1}{r - n} )\)
\(s_7 = - 2.( \frac{ {6}^{7} - 1 }{6 - 1} )\)
\(s_7 = - 2.( \frac{279.936 - 1}{5} )\)
\(s_7 = - 2.( \frac{279.935}{5} )\)
\(s_7 = - 2 \: . \: 55.987\)
\(s_7 = - 111.974\)
The answer is B.
Now move points C, D, and E on the circle, and note the interior angle measurements for the quadrilateral in the table below. Notice that m∠B is predetermined, so set that angle measure first.
Answer:
Explanation:
Plato
PLEASE I REALLY NEED HELP
Answer:
BA ≅ DA
Step-by-step explanation:
∠BAC = ∠DAC Given
AC = AC Reflexive
At this point you have a side and an angle
if BA ≅DA then SAS
Jones invests only a part of his wealth into a risky asset that has a positive return of 10% with probability π and has a negative return of −4% with probability 1−π. The risk-free rate is 1%. Jones' utility function is u=ln(w), where w is his wealth. Which of the following is true about π ?
a. 0.2857≤π≤0.358
b. 0.388≤π≤1
c. 0.357≤π≤0.389
d. None of the above
Option a is correct. we are given that Jones invests only a part of his wealth into a risky asset that has a positive return of 10% with probability π and has a negative return of −4% with probability 1−π.
The risk-free rate is 1%. Jones' utility function is u=ln(w), where w is his wealth.
Let us solve the problem: Let x be the fraction of Jones’ wealth that he invests in the risky asset. Thus, (1 - x) is the fraction he invests in the risk-free asset.:
\(U = x * ln(1 + 10%) + (1 - x) * ln(1 + 1%) = x * ln(1.1) + (1 - x) * ln(1.01)\)
Let EV be the expected value of his investment. Thus, we have:
\(E(V) = x * 10% + (1 - x) * 1% = 9% * x + 1%\)
Let us assume that Jones invests enough of his wealth in the risky asset so as to make it the optimal portfolio. This means that the expected utility from the investment in the risky asset equals the expected utility from the risk-free asset. Mathematically,
\(x * ln(1.1) + (1 - x) * ln(1.01) = ln(w)\)
On solving this equation, we get x =\((ln(w) - ln(1.01)) / (ln(1.1) - ln(1.01)) = ln(w) - ln(1.01) / ln(1.1) - ln(1.01)\)
Let us assume that Jones invests at least part of his wealth in the risky asset. Thus,\(0 ≤ x ≤ 1\). This means that \(0 ≤ π ≤ 1\).
The correct option is a.\(0.2857 ≤ π ≤ 0.358\).
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