To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained.
132 students ate breakfast.
183 students ate lunch.
273 students ate dinner.
69 students ate breakfast and lunch.
113 students ate breakfast and dinner.
95 students ate lunch and dinner.
55 students ate all three meals.
How many students ate
(a) At least one meal in the cafeteria?
students

(b) Exactly one meal in the cafeteria?
students

(c) Only dinner in the cafeteria?
students

(d) Exactly two meals in the cafeteria?
students

The notation to write the rule that maps each preimage to its image will be rotation about the origin.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

If the geometry is rotated, then there is no change in angles.

Preimage           Image

A(-4,4)                A'(4,4)

B(-1,2)                B' (2, 1)

C(-4,1)                C’(1,4)

From the diagram, we can conclude that the notation to write the rule that maps each preimage to its image will be rotation about the origin.

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The ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

If two solids that are similar to each other, have volumes A and B respectively, and have a scale factor of a:b, thus, the ratio of their volumes would be expressed as:

Volume of solid A/Volume of solid B = a³/b³

or

Volume of solid A : Volume of solid B = a³ : b³

Thus, the given similar solids have a scale factor of 5:3, therefore, the ratio of their volumes would be expressed as shown below:

5³ : 3³

125 : 27

Thus, the ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

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Answer:

126.5 cm^2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

253\(cm^{2}\)

Step-by-step explanation:

11 times 23 =253\(cm^{2}\)

Answer:

5

Step-by-step explanation:

Margo bought 7 pens for $23.

Some pens are $3 and some $4.

We need to find how many $3 pens she bought.

Let the number of $3 pens be represented by p and let the number of $3 pens be represented by r. So:

p = $3  and r = $4

Now we know 7 pens were purchased so is we add the number of $3 pens purchased to the number of $4 pens purchased, we will get 7.

p + r = 7

We know that the total cost of the pens is $23 so that equation would be found by takign the $3 pen multiplied by the number of $3 pens purchsed added to the $4 pen multiplied by the number of $4 pens purchsed, which equals $23.

$3p + $4r = $23

Now we have 2 equations and 2 unknowns.

p + r = 7

$3p + $4r = $23

Let's solve for r in the first equation.

p + r = 7     Subtract p from both sides.

p - p + r = 7 - p   The p on the left cancels.

r = 7 - p

Now that we know r, we can substitute it into the second equation and solve for p.

$3p + $4r = $23

3p + 4( 7 - p) = 23       Multiply it out.

3p + 4*7 - 4*p = $23

3p + 28 - 4p = 23      Combine like terms.

3p  - 4p + 28 = 23

- 1p + 28 = 23       Subtract 28 from both sides.

- p + 28 - 28 = 23 - 28  

- p = - 5   Divide each side by -1

- p/- 1 = - 5/ - 1       The negative cancels on each side.

p = 5

We can see Margo bought 5 $3 pens.

For fun, let's solve for how many $4 pens she bought. We know p, so we plug it in the first equation and solve for r.

p + r = 7

5 + r = 7  Subtract 5 from each side

5 - 5 + r = 7 - 5

r = 7 - 5

r = 2

So Margo bought 5 $3 pens and 2 $4 pens!

The answer would be

A. True

Answer:

300.05 miles

Step-by-step explanation:

initial fee= $39.99

final bill = $ 100

cost =$ 0.20 per mile

remaining amount = $ 60.01

solution,

she drive = remaining amount / cost

=60.01/0.20

=300.05 miles

Answer:

500 miles

Step-by-step explanation:

Let us use cross multiplication to find the unknown amount.

Given:

1) Cost for 1 mile=$0.20

2)Cost for x miles=$100

Solution:

No of miles                             Cost

1) 1                                             $0.20

2)x                                             $100

By cross multiplying,

100 x 1= 0.20x

x=100/0.20

x=500 miles

Thank you!

The best estimate of the solution to the system of linear equations is the point are (x,y) will be (0.76, 4.30).

A linear equation in two variables is one that is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Given:

as x,y are variables,

-3x + y = 2 ..............(1)

- 4x + 7y = 1 ...........(2)

We know that,

The solution of the system of linear equations is the intersection point of both graphs

Multiply equation (1) by 7 on both sides and then subtract it from eq (2)

- 4x + 7y = 1 ...........(2)

-21x + 7y = 14 ..............(1)

⇒- 17 x = -13

⇒ 17 x = 13

⇒ x =\(\frac{13}{17}\)

⇒ x = 0.76

Now on putting value of x  = 0.76 in eq (1) we get

- 3x + y = 2 ............ (1)

⇒- 3(0.76) + y = 2

⇒y = 4.30

The best estimate of the solution to the system of linear equations is the point (x,y) will be (0.76, 4.30).

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Answer:

Step-by-step explanation:

Let the distance from the tie in point to the point at the level of Tutu's neck be x.

Then the length of the rope is the hypotenuse of the right triangle formed by this line and height of the tree at which rope is tied in.

We can find x as:

Required distance is:

Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

Answer:

\(\dfrac{25}{216}\)

Step-by-step explanation:

From the given information:

The probability (p) of winning a bottle cap = \(\dfrac{1}{6}\)

The probability of not winning a bottle cap will be (q) = 1 - p

\(= 1- \dfrac{1}{6}\)

\(= \dfrac{5}{6}\)

Since we are told that the winning is placed once on every sixth bottle

Then the required probability = P( of not winning the first purchase) × P( of not winning the second purchase) × P( of winning the third purchase)

\(= \dfrac{5}{6} \times \dfrac{5}{6} \times \dfrac{1}{6}\)

\(= \dfrac{25}{216}\)

The domain of the equation include the following: D. all real numbers.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞}

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Answer: x > 1

Step-by-step explanation: check image

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

$98

Step-by-step explanation:

For this we will set the equations equal and cross multiply.

(4 / 28) = (14 / x)

4x = 392

x = 98

Answer:

same

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

13x2=26

14x3=42

Greatest common Factor of 26 and 42 is 2

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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According to the problem, and using the central angle theorem, we know that the central angle is 135°.

Then, we use the following formula

Answer:

K+T=20

$9K + $6T = $168

K is the Kentucky blue grass in pounds

T is the Tall fescue in pounds

Step-by-step explanation:

You can start with the first equation. We don't know the exact amounts of each but we know that there was a total of 20 pounds, and there were 2 types of grass seeds, so we can get that the amount of pounds of Kentucky blue grass(K) and the pounds of Tal Fescue(T) has a sum of 20.

K + T = 20

For the second equation we know that there is a sum of $168 so we'll start with that. Then, we know he paid $9 per pound of K so $9* the value of K is the amount paid for Kentucky blue grass total. This can be represented as 9K. We do the same for T, 6T. Since the sum of the cost of $9T and $6K must be $168 we can write this as:

$9K + $6T = $168

Answer:

I think x = 1 and y = 1/2. For the second: x = -1 4/13 or -1.307692, y = 4 1/4 or 4.25

Step-by-step explanation:

After conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.

So, pounds of Almonds Lisa purchased:

Now, calculate the pounds of almonds Lisa purchased as follows:

(Refer to the image attached below for calculation)

Therefore, after conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.

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The correct question is given below:

Lisa purchased almonds for $3.50 per pound. She spent a total of $24.50. How many pounds of almonds did she purchase?

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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Answer:

the first mixed number is 1 8/10 which is reduced to 1 and 4/5 and the seconde is 2 and 3/5 added equals 4 and 2/5

Step-by-step explanation:

1 plus 2 equals 3

and 3/5 plus 4/5 equals 7/5

turn it into a mixed number which equals 1 and 2/5 the add 3 and u get 4 and 2/5

The lines are neither parallel nor perpendicular to line p

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

y = -3x + 10

As a general rule

Using the above as a guide, we have the following:

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Answer:

a

  \(P(shipment\ accepted) =0.6337 \)\

b

   \(P(shipment\ not\ accepted)= 0.3663 \)  

Step-by-step explanation:

from the question we are told that

   The number of boxes N  =  100

     The  number of keyboard in each box is  k =  20  

     The sample size is  n =  5

Generally the number of ways of selecting 1 keyboard from the 5 selected keyboard is mathematically represented as

     \(G  =  \ ^{5}C_1\)

Here  C stands for  combination (Hence in the question we will be making use of the combination functionality in our calculator )

Generally the number of ways of selecting 0 keyboard from the 5 selected keyboard is mathematically represented as

       \(H  =  \ ^{5}C_0\)

Generally the number of ways of selecting 5 keyboard from the 20 keyboards is mathematically represented as

          \(F  =  \ ^{20}C_5\)

Generally the number of ways of selecting 5 keyboard from the  15 keyboards is mathematically represented as

        \(W  =  \ ^{15}C_5\)

Generally the number of ways of selecting 5 keyboard from the  15 keyboards is mathematically represented as

        \(V  =  \ ^{15}C_4 \)

Generally the probability that a shipment will be accepted is mathematically represented as

 Probability of  0 defect out of  5 + Probability of  1 defect out of 5

Now  

  Probability of  0 defect out of  5 is mathematically represented  as

        \(P(A_1) =  \frac{H*W }{ F}\)

=>      \(P(A_1) =  \frac{1 *3003 }{ 15504}\)

=>      \(P(A_1) =  0.1937\)

And  Probability of  1 defect out of 5 is mathematically represented as

     \(P(A_2) =  \frac{ G * V}{ F}\)

 => \(P(A_2) =  \frac{ 5 * 1365}{15504}\)  

 =>   \(P(A_2) =  0.440\)  

Generally the probability that a shipment will be accepted is mathematically represented as

     \(P(shipment\ accepted) =0.1937 +  0.440\)

=>    \(P(shipment\ accepted) =0.6337 \)

Generally the probability that this shipment will not be accepted is mathematically represented as

    \(P(shipment\ not\ accepted)= 1 -P(shipment \ accepted)\)

     \(P(shipment\ not\ accepted)= 1 - 0.6337 \)  

     \(P(shipment\ not\ accepted)= 0.3663 \)