Mrs. Moore made the tray of cupcakes for a party.

The adults at the party ate 1/3 of the tray of cupcakes. The children at the party ate 5/12 of the tray of cupcakes. What fraction more of the tray of cupcakes was eaten by the children than by the adults at the party?


a. 9/12

b. 1/12

c. 6/12

d. 8/12

Answer and  explanation:

(a) Classify a call as long, lasts more than three minutes. What is P [L)?

Given probability of event a call lasts more than three minutes, M the probability and B is denoted as the event that a call is billed minutes.

P (L) = 1 – P (3 or less than three minutes)

        =1 – P (Bm) – P (Bm) –P (Bm)                                for m=1,2,3

         =1 – P(B1) – P(B2) – P(B3)                                                       as P (Bm) = a (1-a) m-1

        =1 –  a(1 –a)1-1 – a (1-a)2-1– a (1-a)3-1                          

        = (1-a) 3

        = 0.57

(b)

Probability of billed for nine minutes or less= P (nine minutes or less)

                                                                            = ∑i=19 a (1-a)i-1

                                                                      = 1 – (0.57)3

Given:

P (L) = 1 – P (3 or less than three minutes)

       =1 – P (Bm) – P (Bm) –P (Bm)    for m=1,2,3

        =1 – P(B1) – P(B2) – P(B3)                                                      

P (Bm) = a (1-a) m-1

           =1 –  a(1 –a)1-1 – a (1-a)2-1– a (1-a)3-1                          

           = (1-a) 3

           = 0.57

The probability that a call will be billed for nine minutes or less :

Probability of billed for nine minutes or less= P (nine minutes or less)

                                                                           = ∑i=19 a (1-a)i-1

                                                                           = 1 – (0.57)3

                                                                           =0.814

The probability that a call will be billed for nine minutes is less .

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Answer:

11.94

Step-by-step explanation:

$1.99 multiplied by 6 is 11.94

Answer:

8

Step-by-step explanation:

Number of Riders on the Train

Week 1

Day

Monday

Tuesday

Wednesday

Thursd

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Part A: Grocery Store: unit price = $1.65 (Tomatoes)

Farmer's Market: unit price  = $1.75

Part B: Grocery Store offers a better deal because the unit price is less.

Unit price is defined as the price for one of something. For example, if 10 oranges cost $50, the unit price will be $50/10 = $5 i.e.  $5 for one orange.

PART A:

Let's choose tomatoes

Grocery Store

8 tomatoes for $13.20

Unit price = $13.20/8 = $1.65

10 tomatoes for $17.50

Unit price = $17.50/10 = $1.75

Part B:

The location that offers a better deal is Grocery Store. This is because the unit price is less.

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Because of this, we can infer from the given figure that x is 17, mat is 38°, and tah is 52°. Mah is 90° right angle.

(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]

(B) (2x+4)+(3x+1) = 90

5x+5 = 90

x= 17

(C) 2x+4 = 2×17 + 4 = 38°

(D) 3X + 1 = 3 × 17 + 1 = 52°

A graph is a graphic representation or diagram that groups facts or values in mathematics. The links among two or more objects are commonly shown by the points on a graph.

In discrete mathematics, a graph is made up of vertices, which are collections of points, and edges, which are the connections between them. In addition to linked and unconnected graphs, balanced graphs, bipartite graphs, directed and unguided graphs, and simple graphs, there are many other forms of graphs.

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The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.

Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"

Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:

diagοnaI² = height² + width²

Since the height is 9 ft and οne side οf the square is 12 ft, we can write:

diagοnaI² = 9² + 12²

diagοnaI² = 81 + 144

diagοnaI² = 225

Taking the square rοοt οf bοth sides, we get:

diagοnaI = √(225)

diagοnaI = 15 ft

Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

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In the figure, the length of any line segment in the image is longer the length of the corresponding line segment in the preimage. The scale factor of the dilation is 2

The scale factor of dilation is defined as the change in size of a figure. Thus, a scale factor that is greater than 1 is referred to as an enlargement while a scale factor that is greater than 0 but less than 1 is referred to as a reduction.

Now, we are told that ΔABC has been dilated from center D to form ΔRST, This means that the lengths in ΔRST are longer than the lengths in ΔABC.

Secondly, by close inspection we can see that it was dilated by a scale factor of 2.

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Answer:

4/9

Hope it helps!!! :)

Hi, there!

 ______

\(\begin{tabular}{c|1} \boldsymbol{Things \ to \ Consider} \\\cline{1-3} \end{tabular}\)

(1)

 - The slopes of parallel lines are identical.

{The line \(\sf{y=7x-1}\) has a slope of 7}

Thus,

{The slope of the line that is parallel to the aforementioned line (whatever its equation happens to be) is \(\sf{7}\).}

(2)

 - The slopes of perpendicular lines are negative inverses of each other.

The negative inverse of 7 is

\(-\dfrac{1}{7}\).

Therefore,

\(\textsc{Answers:\begin{cases} \bf{7} \\ \bf{-\dfrac{1}{7}} \end{cases}}\)

Hope the answer - and explanation - made sense,

happy studying!!                                                                 \(\tiny\boldsymbol{Frozen \ melody}\)

If a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel

A jet engine close up produces sound at 152 decibels

The the relative intensity of one jet engine = \(126^{152}\)

The relative intensity of a pair of jet engines = 2× \(126^{152}\)

The reading of a pair of nearby jet engine in decibel = 10log(The relative intensity of a pair of jet engines)

Substitute the values in equation

The reading of a pair of nearby jet engine in decibel = 10×log(2× \(126^{152}\))

= 168.62 decibel

Hence, if a jet engine close up produces sound at 152 decibels then the decibel reading of a pair of nearby jet engines is 168.62 decibel

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145 is the median :)

Answer:

145

Step-by-step explanation:

130 + 150 + 120 + 170 + 130 + 120 + 160 + 160 + 190 + 140 = 1470

1470 ÷ 10 = 145

Answer:

a). 85 people

b). 4362 people

Step-by-step explanation:

The given bar graph shows how many people per 100 spelled each word correctly.

a. From the graph given extreme end of the bar for the word "weird" is between 80 - 90.

Therefore, approximate number of the persons who spelled weird correctly will be 85 (rounded to the nearest 5).

b. The number of people who can correctly spelled word "weird" = 85

The number of people who can correctly spelled word "inoculate" = 35

In 100 people, number of people who can correctly spell "weird" more than "inoculate"

= 85 - 35

= 50

in a group of 8724 randomly selected people, number of people who can spell the word "weird" correctly more than "inoculate"

= \(\frac{50}{100}\times 8724\)

= 4362 people

Random selection means each individual has equal chance of being selected.

Given graph has the following information:

Total number of people under survey=100

a. To estimate the number of people per 100 who spelled weird correctly

From the graph it is around 84 and rounding it to nearest 5 will results in 85.

b. From the graph,

Number of people can correctly spell inoculate= 35

Number of people can correctly spell weird than inoculate=85-35

=50 out of 100

Using unitary method as follows:

100-------->50

1------------>1/2

8724------>1/2x8724

=4362

Thus, out of  8724 randomly selected​ people, 4362 people can correctly spell weird than inoculate.

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The set of 3 lengths that make a right triangle is {8, 15, 17}

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

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When P and Q are combined, they will be completely contained in the plane if P and Q are already inside the plane. PQ would therefore be totally in the aircraft.

A plane may contain a number of points. A plane is carrying P and Q. A two-dimensional figure that never ends, the plane. It implies that there is no end. It has a level surface. If we draw a line to join the two points P and Q, the line will also be in the same plane. since the plane never comes to an end.

Collinear points are a group of points that all lie on the same line.The right response to this question is that a segment is a finite portion of a line connecting two locations, including its two ends.Coplanar points are groups of at least four points that all lie on the same plane. Keep in mind that given any two points, they are always coplanar, as are given any three points.

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Answer:

Volume ≈ 153.93804 cm^3

Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.

Step-by-step explanation:

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

ASC, AIC, APL

Step-by-step explanation:

Tangents make right angles with the center of the circle, so any point angle starting a the center leading to the tangent will be a right angle

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that, SL , PL and IC are tangents . Tangents are lines which touch the circle at only one point. Also , there is a Theorem, which is ,

Theorem:-

From this , we can say that the angles,

\( \angle ASC \) , \( \angle AIC \) and \( \angle APL \) are right angles .

My recommendation to Carlos and Clarita would be to prepare for 3 cats and 3 dogs. This combination offers the highest profit potential based on the given prices and costs.

In order to maximize their profit, Carlos and Clarita should choose the combination of cats and dogs that yields the highest total profit.

In order to make a reasonable recommendation, we can create a profit table based on different values of x and y:

x y Total Profit

0 0 0

1 0 6

0 1 15

1 1 21

2 1 27

1 2 30

2 2 36

3 2 42

2 3 45

3 3 51

From the table, we can see that the highest total profit is achieved when they accommodate 3 cats and 3 dogs. This combination would result in a daily profit of $51.

Therefore, my recommendation to Carlos and Clarita would be to prepare for 3 cats and 3 dogs.

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The value of angle x in the triangle is 15°

Given: the triangle ABC with equal sides of 9 units.

Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).

Thus, <A = <B = < C =  4x°

Since the sum of angles in a triangle is 180°. We have:

<A + <B + < C = 180°

4x + 4x + 4x = 180°

12x = 180

x = 180/12

x = 15°

Therefore, the value of x is 15°

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Answer:

x<-2

Step-by-step explanation:

Answer:

5,400 ÷ 90 = 60

Step-by-step explanation:

hope it helps!

Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

To determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.

If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.

Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.

However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.

Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

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1. The percentage of maize flour is given as 16.7 %

2. The common ratio of the GP is r = 1.5.

1. We have to set up equation

60x + 90(1 - x) = 85

60x + 90 - 90x = 85

now we have to solve for the value of x

-30x = -5

x = 5 / 30

x = 0.167

Hence percentage of maize flour is given as 16.7 %

2. a + ar = 20 (1)

ar + ar^2 = 30 (2)

We can rearrange equation (1) to get an expression for a:

a = 20 / (1 + r)

Now, we can substitute a into equation (2) to get an equation only in terms of r:

\(20r / (1 + r) + 20r^2 / (1 + r) = 30\\20r + 20r^2 = 30(1 + r)\\20r + 20r^2 = 30 + 30r\\20r^2 - 10r - 30 = 0\\2r^2 - r - 3 = 0\)

Solving this quadratic equation, we get:

We have two solutions, r = 1.5 and r = -1. But since the GP is increasing, we discard the negative solution. Therefore, the common ratio of the GP is r = 1.5.

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Step-by-step explanation:

5x 234 = 1170 pounds

hope this is right, the number was hard to read.

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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