A theatre has the capacity to seat people across two levels, the Circle and
the Stalls.
The ratio of the number of seats in the Circle to the number of seats in
the Stalls is 2:5
Last Friday, the audience occupied all the 528 seats in the Circle and
the seats in the Stalls.
Work out the percentage of occupancy of the theatre last Friday.​

Answer:

5460

Step-by-step explanation:

The number of different four-letter secret codes can be formed if the first letters must be an S or a T is; 35,152

How to solve permutation and combination?

If the first letters of a four-letter secret code must be an S or a T, there are 26 possible choices for the remaining two letters. This is because there are 26 letters in the alphabet, and each letter can be one of the remaining 26 letters after the first two are used.

To calculate the total number of possible combinations, you can use the following formula:

26×26×26×2.

This formula represents the number of possible combinations for each of the remaining letters. Multiplying these values together gives you the total number of possible four-letter secret codes:

26×26×26×2=35,152

So, there are 35,152 different four-letter secret codes that can be formed if the first letters must be an S or a T

There are 48 green ribbons

Given that the ratio of red ribbons to green ribbons is 4 to 6

Which can be written in following way:-

[tex]\frac{\text {Red} r i b b o n}{\text {Green ribbon}}=\frac{4}{6}[/tex]

There are total number of 32 red ribbons

We have to determine the number of green ribbon

Let the number of green ribbon be ‘6a’

And number of red ribbons be "4a"

Given number of red ribbons = 32

4a = 32

a = 8

number of green ribbon = 6a = 6(8) = 48

Therefore number of green ribbons is 48

Final answer:

To find the number of green ribbons, the ratio of red to green is scaled to match the actual count of red ribbons. With 32 red ribbons and a ratio of 4:6, there are 48 green ribbons.

Explanation:

To solve the problem, we need to find out how many green ribbons there are when we know that the ratio of red ribbons to green ribbons is 4 to 6 and there are 32 red ribbons in total.

First, let's use the given ratio. Ratios can be scaled up by the same factor on both sides to represent actual quantities. So, if we have 4x red ribbons and 6x green ribbons, and we know 4x = 32, we can solve for x: x = 32 / 4 = 8. This means for every 8 red ribbons, there are 12 green ribbons since 6x = 6 × 8 = 48.

Therefore, if there are 32 red ribbons, there are (32 / 8) × 12 = 4 × 12 = 48 green ribbons.

Answer:

5 cm

Step-by-step explanation:

What you have there is an equilateral triangle. An equilateral triangle is a triangle that has sides with equal lengths and interior angles are equal as well. So if all angles are equal in a triangle, then that means that this is an equilateral triangle. So we can say that if one side of this triangle is 5cm

then the n would also be equal to 5cm.

See in the explanation:

Here we have the following system of linear equations in two variables:

[tex](1) \ 2x+7y=-8 \\ \\ (2) \ 2x-5y=-1[/tex]

So if you graph these two equations you will get two lines with different slopes. The question is:

What is the result of subtracting the second equation from the first?

So this can be written mathematically as:

[tex]2x+7y-(2x-5y)=-8-(-1) \\ \\ Breaking \ parentheses: \\ \\ 2x+7y-2x+5y=-8+1 \\ \\ \\ Combining 'like 'terms: \\ \\ 2x-2x+7y+5y=-7 \\ \\ 12y=-7 \\ \\ y=-\frac{7}{12}[/tex]

So the result of subtracting the second equation from the first is:

[tex]12y=-7[/tex]

and from this we can calculate y.

Methods for solving System of Linear Equations:

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Answer:

P(student plays both soccer or basketball)= 40/300

Simplify : 2/15

In a group of 300 students, 18 students play basketball, 11 students play football. 10 students play both sports.

Now, A student is chosen randomly from this group.

What is the probability that the student plays both soccer or basketball?

Probability of any event=no. of favorable outcomes/total no. of outcomes

 Here, no. of favorable outcomes

=no. of students who plays both soccer or basketball

=  32+18-10

= 40

and, total no. of outcomes= 300

If a student is selected at random, the probability that a student plays soccer or basketball is  [tex]\frac{2}{15}[/tex]

To start, we list the variables given

32 ----- Soccer

18 ---- Basketball

10 ----- Basketball + Soccer

If you look at the question, it was stated that 10 people plays basketball and soccer. The keyword being "and". While we are asked to find the probability that a student plays basketball or soccer. This then means that we add the number of people playing basketball together with those playing soccer.

32 + 18 = 40.

Probability of a student playing soccer or basketball is then 40/300 = 2/15

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Answer:

$100

Step-by-step explanation:

6 1/4=25/4

25/4%=0.0625

0.0625*1600=100

---------------------------

Answer:

20%

Step-by-step explanation:

% of error is given by the following formula:

% Error = [tex]\frac{|\textrm {Approx Value  - Exact Value}|}{\textrm {Exact Value}} \times 100[/tex]

Now, Jessie estimated the weight of his cat to be 12 pounds i.e. Approximate value is 12 pounds.

Again, The actual weight of the cat is 15 pounds i.e. the exact value is 15 pounds.

Therefore, the % error = [tex]\frac{|12 - 15|}{15} \times 100 = \frac{3}{15} \times 100 = 20[/tex]% (Answer)

Answer:

20%

Step-by-step explanation:

Jessie thinks to greatly of his cat

and I took the test

Answer:

E=5

Step-by-step explanation:

Given,

[tex]32= 2^E[/tex]

We know [tex]32[/tex] can be written as [tex]2^5[/tex]

Substituting [tex]2^5[/tex] in place of [tex]32[/tex]

We get,

[tex]2^5 = 2^E[/tex]

Since the base is equal, now comparing the exponent.

Therefore [tex]E=5[/tex] is the missing exponent.

Answer:

E = 5 and [tex]32 = 2^5[/tex]

Step-by-step explanation:

Given:

[tex]32 = 2^E[/tex]

Now we know that E is denoted as an exponent term,

Exponent term indicates the value which can be to the power of a number.

Now 32 can be written as,

[tex]32 = 2\times 2\times2\times 2\times2[/tex]

Hence from above we can say that 2 can be multiplied 5 times to get the value as 32.

hence we can say that,

[tex]32 = 2^5[/tex]

Hence E=5

Answer:

step 1: addition property of equality

step 2: additive inverses

step 3: additive identity

step 4: multiplication property of equality

Step-by-step explanation:

edg 2020

Answer:

step 1: addition property of equality

step 2: additive inverses

step 3: additive identity

step 4: multiplication property of equality

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

=20/25  x 100

= 4/5 x 100

=4 x 20

= 80%

Answer:

[tex]\$84[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ years\\ P=\$80\\ A=\$?\\r=5\%=5/100=0.05[/tex]

substitute in the formula

[tex]A=80(1+0.05*1)[/tex]

[tex]A=80(1.05)[/tex]

[tex]A=\$84[/tex]

Answer:

5 part symmetry

Step-by-step explanation:

I did the test

Answer:

5 part symmetry.

Step-by-step explanation:

I took the test and got it right.

Answer:

A

Step-by-step explanation:

When we read your example. we can see that we have not diagram, but we have text and we can conclude what is that tell.

This construction demonstrates that the set of points equidistant from the endpoints of a line segment

is the perpendicular

of the segment.- this text tells us that it is bisector

Answer:

a

Step-by-step explanation:

Answer:

Mean = 3.25°C

Step-by-step explanation:

The mean (or average) is given by the formula:

Mean = Sum/Number of Numbers

For first 7 days, the mean was 3, so we can say:

Mean = Sum/Number of Numbers

3 = Sum/7

Sum = 3 * 7 = 21

Then on 8th day, the temperature was 5, so the new sum would be (for 8 numbers):

New Sum = 21 + 5 = 26

Now we calculate the mean for 8 numbers:

Mean = 26/8

Mean = 3.25°C

Answer:

The value of x = 13.5.

Step-by-step explanation:

In this question x is missing.

So, the question would be:

tan 34° = x/20.

Now, to find the value of [tex]x[/tex]:

[tex]tan 34 = \frac{x}{20}[/tex]

[tex]\frac{x}{20} = tan 34[/tex]

Multiplying both sides by 20 we get:

[tex]x=tan 34\times 20[/tex]

On simplifying both sides we get:

[tex]x=13.49[/tex]

So, to get the value of [tex]x=13.49[/tex] to nearest tenth is 13.5. As we see in hundredth place it is 9 and 4 in tenth place, so after rounding to tenth place 4 will change to 5 so the value is 13.5.

Therefore, the value of x = 13.5.

Answer:13.5

Step-by-step explanation:

Answer:

7.5% < 7.49 <  [tex]7\frac{49}{50}[/tex]

Step-by-step explanation:

To make this easier to look at, first you change them into the same form. Let us make them all into fractions and compare:

7.49 as a fraction is [tex]7\dfrac{49}{100}[/tex]

[tex]7\dfrac{49}{50}[/tex] is already a fraction so let's leave it first.

7.5% in fraction form is [tex]\dfrac{75}{1000}[/tex]

Now knowing this, we can already say that 7.5% is already the least comparing it to the others.

Now we compare the two:

[tex]7\dfrac{49}{100} < 7\dfrac{49}{50}[/tex]

If we make them into similar fractions:

[tex]7\dfrac{49}{50} = 7\dfrac{98}{100}\\\\Then\\\\7\dfrac{49}{100}<7\dfrac{98}{100}[/tex]

The number of flour tortilla packages could be 9 or any number that results from subtracting 7 (corn tortilla packages) from a multiple of 16 (total packages). It's necessary to keep the ratio between corn tortillas and total packages at 7:16.

The subject of this question refers to the mathematical concept of ratios. Given the ratio of corn tortillas to the total number of packages is 7:16, this means that out of every 16 packages, 7 are corn tortillas. Therefore, the remaining packages must be flour tortillas.

To figure out the possible number of packages of flour tortillas, you would subtract the number of corn tortilla packages (7) from the total (16). So, there could be 9 packages of flour tortillas on the shelf.

Please note that this ratio can apply to any multiple of 16. As long as the number of packages is divisible by 16, you can use the ratio to find the number of flour tortilla packets. For example, if the total number of packages was 32, you could have 18 packages of flour tortillas (since 32-14=18) and so on.

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Answer:

8 tomatoes are required to balance 1 cabbage

Step-by-step explanation:

Given :

Two lemons and seven tomatoes are required  to balance one cabbage:

2 Lemons + 7 tomatoes = 1 cabbage                 (equation 1)

two lemons balance one tomato

2 lemons = 1 tomato

put in equation 1:

1 tomato + 7 tomatoes = 1 cabbage

8 tomatoes = 1 cabbage

8 tomatoes required to balance one cabbage

Answer:

The correct answer is that the annual sales for 2018 is US$ 819,813 (Rounding to the whole nearest dollar)

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Annual sales for a restaurant in 2006 = US$ 575,000

Duration of the sales analysis = 12 years

Annual sales increase rate = 3%

2. Let's find the annual sales turnover after 12 years in 2018, using the following formula:

Sales 2018 = Sales 2006 * (1 + r) ⁿ

Sales 2006 = US$ 575,000

number of periods (n) = 12

rate (r) = 3% = 0.03

Replacing with the real values, we have:

Sales 2018 = 575,000 * (1 + 0.03) ¹²

Sales 2018 = 575,000 * 1.42576089

Sales 2018 = US$ 819,813 (Rounding to the whole nearest dollar)

Answer:

$819,812.50

Step-by-step explanation:

Shouldn't round in this case because they're asking for the numerical value of money which the .50 in cents is vital to the problem.

Answer:

Reasoning and Proof Unit Test

Step-by-step explanation:

1. 67

2. counterexample

3. If you join the gym, then it is free for the first three months.

Hypothesis: you join the gym

Conclusion: it is free for the first three months

4. Yes; two lines intersect at right angles if (and only if) they are perpendicular

5. An angle is obtuse if and only if its measure is greater than 180

6. Symmetric Property

7. 12

8. RT-ST

9. x=8, y=9

10. 7

11. Symmetric Property

12. invalid

13. A. is Substitution Property of Equality, B. is Supplementary Angles, C. is Subtraction Property of Equality

14. (A) 180, (B) 180, (C) transitive property, (D) 3, (E) 3

15. The value of x is 3.

a) Addition of line segments

b) Substitution rule

c) Simplification by addition of like terms

d) Collecting lie terms

e) Dividing both sides by 8

AB = 2x

BC = 6x + 8

AC = 32

AB + BC = AC (Addition rule)

Addition of the component segments of a line

2x + 6x + 8 = 32 (Substitution rule)

Substituting for AB, BC, and AC in the equation AB + BC = AC

8x + 8 = 32 (Simplification)

Simplifying 2x + 6x + 8 = 32 by adding like terms

8x = 24 (Collecting like terms)

8x = 32 - 8

8x = 24

x = 3 (Divide both sides by 8)

8x / 8 = 24/8

x = 3

16. If it is square it is a Quadrilateral.

17. 7y = 8x - 14

7(6) = 8x - 14

Collect like terms.

42 = 8x - 14.

8x = 42 + 14

8x = 56

x = 56/8

x = 7

These are all the correct answers as of 2022

Answer:

Distance = |b - c|

Step-by-step explanation:

Suppose a, b, and c are all negative numbers.

We have to describe the way to find the distance between points (a,b) and (a.c).

Since the x-coordinates of the two points are the same and are a, therefore, the distance between the y-coordinates of the two points will give the distance between the two points.

Mathematically the distance d will be given by d = |b - c|, where |x| is the absolute value function of x. (Answer)

Answer:

BC=25

Step-by-step explanation:

The provided data in the figure is different from the written text. We'll use the set of conditions in the figure

We know the triangle is isosceles, so the sides AC and AB are equal, i.e.

4x+4=6x-14

Operating

4+14=6x-4x

x=18/2=9

Knowing that x=9, then

BC=2x+7=18+7=25

Note: If we used the data provided in the text, the answers would be

x=11, BC=25

Answer:25

Step-by-step explanation:

i did the test lol

Answer:

b

Step-by-step explanation:

The equation:

3

x

2

−

5

x

−

12

=

0

is in the form:

a

x

2

+

b

x

+

c

=

0

with  

a

=

3

,  

b

=

−

5

,  

c

=

−

12

The roots are given by the quadratic formula:

x

=

−

b

±

√

b

2

−

4

a

c

2

a

x

=

5

±

√

(

−

5

)

2

−

4

(

3

)

(

−

12

)

2

(

3

)

x

=

5

±

√

25

+

144

6

x

=

5

±

√

169

6

x

=

5

±

13

6

That is:

x

=

5

+

13

6

=

18

6

=

3

or  

x

=

5

−

13

6

=

−

8

6

=

−

4

3

Length of the rectangle is 51 inches

Solution:

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

The formula for rectangle is given as:

[tex]\text { area of rectangle }=length \times width[/tex]

As given that Area of rectangle = 867 square inches

[tex]\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}[/tex]

On solving quadratic equation by using quadratic formula

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

[tex]\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}[/tex]

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

Answer:27

Step-by-step explanation: