Emmett's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion.
Pick all the expressions that represent the total cost of the field trip.

Amy needs 9 lengths of skirting board.

Amy wants new skirting boards in her living room and skirting boards come in lengths of 2.4 m.

Hence, we need to find the number of lengths of skirting board Amy needs.

Amy has this sketch of her living room:

From the given sketch, we can see that the total length of the skirting board required for the living room is:

(4.5 + 6.5 + 4.5 + 6.5) m = 22 m

But skirting boards should not go across the doorway and the fireplace, as shown in the given diagram. Hence, we need to deduct the length of the skirting boards which are not required.

The length of the skirting board required for the living room can be calculated as follows:

Length of skirting board required = Total length of the room - length of skirting board not required

= 22 m - length of skirting board across doorway - length of skirting board across fireplace

= 22 m - 0.9 m - 1.2 m

= 20.9 m ≈ 21 m

Therefore, the number of lengths of skirting board Amy needs = (Total length required) / (Length of each skirting board)

= 21 / 2.4

= 8.75 ≈ 9 lengths of skirting board are required.

Note: While solving the problem, care should be taken to measure the length accurately.

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Answer:

log 4 ( 4096 )  = 6

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base  ( 4 )  of the right side  ( 4096 )  equals the exponent  ( 6 )

Answer:

Option C : 173.8 km² is the correct answer.

Step-by-step explanation:

Given that:

Side length = 6 kilometers

A shape with 8 sides is called an octagon, therefore, the given figure is an octagon.

Area of octagon is given by;

Area = \(2(1+\sqrt{2})a^2\)

Putting a=6

Area = \(2(1+\sqrt{2})(6)^2\)

Area = \((2+2\sqrt{2})(36)\)

Area = 173.82

Rounding off to one decimal place

Area = 173.8 km²

Hence,

Option C : 173.8 km² is the correct answer.

A cumulative relative frequency distribution shows option (A) the proportion of data items with values less than the upper limit of each class

A cumulative relative frequency distribution shows the proportion of data items with values less than or equal to the upper limit of each class. It provides a cumulative summary of the data distribution by adding up the frequencies or proportions of all preceding classes.

To construct a cumulative relative frequency distribution, you start with the lowest class and calculate the relative frequency (proportion) of data items in that class. Then, for each subsequent class, you add the relative frequency of that class to the cumulative relative frequency from the previous class. This cumulative value represents the proportion of data items with values less than or equal to the upper limit of the current class.

In essence, a cumulative relative frequency distribution allows you to track the accumulation of data values as you move through the classes, giving insights into the overall distribution and the proportion of data items falling below specific values.

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Answer:

Let 3x and 2x are divided into 250.

Step-by-step explanation:

3x + 2x = 250

⇒ 5x = 250

⇒ x =  = 50

∴ 3x = 3 × 50 = 150 and

2x = 2 × 50 = 100

Thus, the required numbers are 150 and 100.

Answer:

d=3

Step-by-step explanation:

so yu do 18+18 and yu get 36 and then you do 43+3 vause that is how muvk the lockers cost

Answer:

$2

Step-by-step explanation:

Fees = $18

Locker fee =$d

Total cost for 2 people,including locker for 2 people

=$40

2($18 + d) = $40

$36 +2d = $40

2d = $4

d = $2

if you want to check

Fees for one people =$18

Two people =$18 × 2 = $36

Total cost for 2 people - locker for 2 people = $40 - $ 2($2) = $40 - $4 = $36

Answer:

1684.8 cubic units

Step-by-step explanation:

In oblique cylinder the height (altitude) is measured from the opposite base to the base of the cylinder, but it lies outside. We can find the height using Pythagoras theorem.

       h + 7² = 13²

              h²= 169 - 49

              h² = 120

               h = √120

                h = 10.95 units

radius = r = 7 units

\(\boxed{\text{\bf Volume of oblique cylinder = $\bf\pi r^2h$} }\)

                                                    = 3.14 * 7 * 7 * 10.95

                                                    = 1684.8 cubic units

Answer:

\(\sqrt{45}\)

Step-by-step explanation:

Hi there,

In order to solve this problem, you have to know the Pythagorean Theorem:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

We can see from the graph that line segment ML and LN are 6 and 3 units respectively. Since we know the lengths of two sides of the triangle, we can use the theorem above to find the hypotenuse (MN).

⇒ \(6^{2}\) + \(3^{2}\) = \(c^{2}\)

⇒ 45 = \(c^{2}\)

⇒ c = \(\sqrt{45}\)

Hope this explanation helps. Cheers.

Answer:

Slope= 1/2

Step-by-step explanation:

The slope of the given line is 0.5.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The points on the table lie on a line, as follows;

x: (-2), 0, 2, 4

y: 3,4,5,6

To determine the slope of a line, you can use the formula:

(change in y)/(change in x)

As per the points in the table,

the change in x is (4-(-2)) = 6, and the change in y is (6-3) = 3.

Slope =  (3)/(6)

Slope = 1/2

Apply the division operation, and we get

Slope = 0.5

Therefore, the slope of the line is 0.5.

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When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

carnival game:

spinner: 1 to 8

Step 02:

simple probability:

p = favorable outcomes / total outcomes

1. probability of an event:

a. p (odds):

p (odds) = 4 / 8 = 1 / 2

b. p (evens):

p (evens) = 4 / 8 = 1 / 2

c. p (3):

p (3) = 1 / 8

d. p (4 or 6):

p (4 or 6) = 2 / 8 = 1 / 4

e. p (7'):

p (7') = 7 / 8

f. p (1):

p (1) = 1 / 8

That is the full solution.

Answer:

1.89 inch²

Explanation:

\(\sf \boxed{\sf \dfrac{pq}{2} } \ \ \ where \ p \ and \ q \ are \ the \ diagonals \ of \ the \ kite\)

Here given:

Find the Area:

\(\rightarrow \sf \dfrac{2.7 \ x \ 1.4}{2} \ = \ 1.89 \ in^2\)

Answer:

?

Step-by-step explanation:

The cars must have had the same Average Speed

Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time. Even with varying speed, the values of total time and the total distance covered can be used, and with the help of the formula for average speed, we can find a single value to represent the entire motion.

The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:

\(\frac{Total distance covered by the object}{Total time taken}\)

Given :-  

Substituting the given values in the formula for A and B respectively we get

Average Speed of A = \(\frac{30}{5}\) m/s = 6 m/s

Average Speed of B = \(\frac{42}{7}\) m/s = 6m/s

Thus the cars must have had the same Average Speed.

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Answer:

\({ \tt{ = 28a - {4a}^{2} }} \\ = 4a(7 - a)\)

Answer:

2 with the sqaure root of 12 is = 6.9     simp =  6.9

4 with the sqaure root of 10 is = 12.6    simp= 12.6

sum = 19.5

I hoped this helped! :)

(i) The number of different divisions possible when 15 children divide themselves into teams of 5 each (Team A, B, and C) is 756.

(ii) If the teams are not distinguishable, the number of different divisions possible is 756 divided by 3!, which equals 126.

(i) To determine the number of different divisions when 15 children divide themselves into three teams of 5 each, we can calculate the number of combinations.

Since the order of the teams does not matter, we use the combination formula.

The formula is nCr = n! / (r! * (n - r)!), where n is the total number of children and r is the number of children per team.

Plugging in the values, we have 15C5 * 10C5 = (15! / (5! * 10!)) * (10! / (5! * 5!)) = 756.

(ii) If the teams are not distinguishable, we need to account for the fact that the order of the teams doesn't matter.

Each division would be counted multiple times if we considered the teams distinguishable. Since there are 3! (3 factorial) ways to arrange the teams, we divide the previous result by 3!, which gives us 756 / 3! = 126.

This accounts for the different arrangements of the same teams and gives us the number of distinct divisions.

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I have no : idea

Step-by-step explanation: WHat grade is this for I might be able to help you.

Answer:

Step-by-step explanation:

Remember that

c^2=a^2+b^2

therefore

Is always true

c>a and c>b

The volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of \(\(r\)\), is \(\(18\pi - 4\pi r^2\) cm^3\) .

To find the volume of material in the wall of the open cylinder, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder. The outer cylinder has a radius of \(\(r + 2\)\)cm, while the inner cylinder has a radius of \(r\) cm. The length of both cylinders is \(9r\) cm.

The volume of the outer cylinder can be calculated using the formula: \(\(V_{\text{outer}} = \pi \cdot (r + 2)^2 \cdot 9r\) cm^3\).

The volume of the inner cylinder can be calculated using the formula: \(\(V_{\text{inner}} = \pi \cdot r^2 \cdot 9r\) cm^3\).

To find the volume of material in the wall, we subtract the volume of the inner cylinder from the volume of the outer cylinder:

\(\[V_{\text{wall}} = V_{\text{outer}} - V_{\text{inner}} = \pi \cdot (r + 2)^2 \cdot 9r - \pi \cdot r^2 \cdot 9r= 9\pi r(r + 2)^2 - 9\pi r^3= 9\pi r[(r + 2)^2 - r^2]= 9\pi r[4r + 4].\]\)

Simplifying further:

\(\[V_{\text{wall}} = 36\pi r^2 + 36\pi r \text{ cm}³ = 36\pi(r^2 + r).\]\)

Therefore, the volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of \(r\), is \(\(18\pi - 4\pi r^2\) cm^3\) .

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Points C and D are elements of the same direct variation as Points A and B. When we say that Point A is an element of a direct variation, it means that there is a relationship between Point A and another point.

Let's call it Point B, such that when one value changes, the other changes in a specific way. Specifically, in a direct variation, when one value increases, the other value increases proportionally.

To select two other points that are also elements of this direct variation, we need to find two other points that have this same proportional relationship. One way to do this is to find points that have the same ratio of their values as Point A and Point B. For example, if Point A has values (2,4) and Point B has values (4,8), we can find two other points that have the same ratio of y-values to x-values.

Let's say we choose Point C to have x-value 3. Then its y-value would be 6, since 6/3 = 2/1 (the same ratio as Point A and Point B). Similarly, if we choose Point D to have x-value 5, then its y-value would be 10, since 10/5 = 2/1. Thus, Points C and D are elements of the same direct variation as Points A and B.

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Answer:

\(y=-1(x-2)^2+1\)

Step-by-step explanation:

The parabola has the vertex (2, 1) and goes through the point (4, -3).

We will use the vertex form, given by:

\(f(x)=a(x-h)^2+k\)

Where (h, k) is the vertex and a is the leading coefficient.

Line 1)

So, by substitution:

\(\text{Vertex}=(h,k)=(2,1)\Rightarrow y=a(x-2)^2+1\)

Lines 2-4)

Since (4, -3) is a point, y = -3 when x = 4:

\(-3=a(4-2)^2+1\)

\(-3=a(2)^2+1\)

\(-4=4a\Rightarrow a = -1\)

Line 5)

By substitution, we acquire our equation*:

\(y=-1(x-2)^2+1\)

The term  4^-3 x 4 can be rewritten using a single positive exponent as 1/4^2.

The positive exponent serves as the exponents that contain a positive number, it should be noted that the exponent is the degree at the top[ of the given number which is a negative exponents and the question expect us to turn it to a positive exponents after simplification of the given terms which will be simplified below to the simplest expression.

To rewrite the given term so that it can have a positive exponents then it can be expressed as :

=4^-3 x 4

= 4^-2

1/4^2

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Answer:

1.5:1

Step-by-step explanation:

the original answer is 12:8, so you have to simplify it down. you can get it down to 3:2 with whole numbers, but to get it down to a ratio with one, you'll have to divide each number by 2 because the bottom number is 2, so the final answer would be 1.5:1

The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees

angle b is equal to angle c the reason id that they form alternate internal angles

A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.

Linear pair is special cases of supplementary angles involving only two angles that are adjacent

How to solve for angle b

b + 120 = 180

b = 180 -120

b = 60

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