The perimeter of a rectangle is 320mm. If its length increases by 10mm and its breadth decreases by 10mm then it its area will be 32 less. Calculate the length and breadth of the original rectangle. (20)

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

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:

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:

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]

One adult ticket costs £11 and one child ticket costs £8.5

Step-by-step explanation:

Let,

Adult ticket = a

Child ticket = c

According to given statement;

3a+4c=67   Eqn 1

5a+6c=106   Eqn 2

Multiplying Eqn 1 by 5;

[tex]5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 3;

[tex]3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17\\[/tex]

Dividing both sides by 2

[tex]\frac{2c}{2}=\frac{17}{2}\\c=8.5[/tex]

Putting c=8.5 in Eqn 1

[tex]3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33[/tex]

Dividing both sides by 3;

[tex]\frac{3a}{3}=\frac{33}{3}\\a=11[/tex]

One adult ticket costs £11 and one child ticket costs £8.5

Keywords: Linear equation, subtraction

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Live Fund receive [tex]\bold{\$2500 A}[/tex] it they sold half thier holding in Marks Brothers.

Solution:

Given: Sale price of Live Fund holding = 5000 dollar

To find: Amount that Live Fund will get if they sell half of their holding in Marks Brothers.

Assume the total number of shares held by Live Fund in Marks Brothers as A

Therfore, half the holdings (or half the number of shares) of Live Fund will be [tex]\frac{A}{2}[/tex].

Thus, if each share is valued at [tex]\$5000[/tex], then the total value of the number of shares sold will be as follows,

[tex]\Rightarrow5000\times\frac{A}{2}\text{ dollars }\rightarrow\frac{5000\times A}{2}\text{ dollars }[/tex]

[tex]\Rightarrow2500 A\text{ dollars }[/tex]

Hence, Live Fund will receive [tex]\$2500 A[/tex]

To minimize the cost, the packaging that should be used is the rectangular prism boxes.

From the complete information, the pencils needed is 2400. The prism can hold 60 pencils. Therefore, the number of prisms needed will be:

= 2400/60 = 40 prisms

The total cost for the prism will be:

= $0.50 × 40

= $20

The cylinder can hold 80 pencils. Therefore, the numbers needed will be:

= 2400/80

= 30

The cost of the cylinders will be:

= 30 × $0.75

= $22.50

Therefore, it implies that to minimize the cost, the packaging that should be used is the rectangular prism boxes.

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The company should use rectangular prism boxes, as they require fewer units and incur lower total cost.

To minimize cost, we need to find out which packaging option, between the rectangular prism box and the cylindrical container, requires fewer units and hence incurs lower total cost.

First, let's calculate how many units of each packaging option are needed to package 2,400 pencils:

1. **Rectangular Prism Box:**

  Each box holds 60 pencils.

  Number of boxes needed [tex]\(= \frac{2400}{60} = 40\)[/tex]

2. **Cylindrical Container:**

  Each container holds 80 pencils.

  Number of containers needed [tex]\(= \frac{2400}{80} = 30\)[/tex]

Now, let's calculate the total cost for each option:

1. **Cost for Rectangular Prism Boxes:**

  Number of boxes: 40

  Cost per box: $0.50

  Total cost: [tex]\(40 \times \$0.50 = \$20\)[/tex]

2. **Cost for Cylindrical Containers:**

  Number of containers: 30

  Cost per container: $0.75

  Total cost: [tex]\(30 \times \$0.75 = \$22.50\)[/tex]

Comparing the total costs, we can see that using the rectangular prism boxes incurs a lower cost $20 compared to using the cylindrical containers $22.50.

The reason for the lower cost with rectangular prism boxes is that each box holds fewer pencils (60) compared to cylindrical containers (80). Therefore, even though the cost per unit for the cylindrical containers is lower ($0.75) compared to the rectangular prism boxes ($0.50), the higher number of units required for cylindrical containers results in a higher total cost.

Therefore, to minimize cost, the company should use the rectangular prism boxes for packaging the pencils.

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:

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:

C)  It will take  14 weeks for Edurado to make a profit.

Step-by-step explanation:

The money spent on obtaining the merchandise = $ 7500

The general expense per week = $300

Let us assume Eduardo has to work for N weeks to break Even.

So, the general expense in N weeks  = N x( Expense per week)

=  N x ( $300)  = 300 N

So, the total expense in N weeks  =  Money spent on merchandise + general expense

or, the TOTAL EXPENSE =  $ 7500 +  300 N     .... (1)

Now, the earning per week = $850

So, the total earning in N weeks = N x ( Earning in 1 week) =  N x ( $850)

or, the TOTAL EARNING  =  850 N    .... (2)

Now, for N weeks ,

TOTAL EXPENSE  = TOTAL EARNING

⇒ $7500 +  300 N = 850 N

or, 7500 = 850 N -  300 N = 550 N

⇒ N  = 7500/550 = 13.63

So, number of weeks should at least be 13.63

Among the given options, N = 14 weeks is the most feasible answer.

Hence, it will take  14 weeks for Edurado to make a profit.

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:

4x+9

Step-by-step explanation:

x^2+8x+9-(x^2+4x)

x^2-x^2+8x+9-4x

8x-4x+9

4x+9

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

The equation for this would be 6x=42

Here's an explanation.

You have 6 sheets of paper, and you draw some number of stars on each paper. The number of stars are the same. Let's put the stars one each paper as x. Now it's also given that the total number of stars are 42. Since there are x stars on each paper, then 6 times x would be the total number of stars, which is 42. So 6x=42, and x=7

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

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:

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:

$100

Step-by-step explanation:

6 1/4=25/4

25/4%=0.0625

0.0625*1600=100

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

Answer:

80%

Step-by-step explanation:

=20/25  x 100

= 4/5 x 100

=4 x 20

= 80%

Law of Sines

[tex]\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a} \\ \\ \frac{sin\:40°}{5} = \frac{sin∠C}{7} → \frac{7sin\:40°}{5} = sin∠C → 0,8999026535... = sin∠C → 64,14527443...° = sin^{-1}\:0,8999026535... \\ \\ 64° ≈ m∠C[/tex]

As you can see, the inverse function had to be used towards the end, or the answer would have been thrown off.

I am joyous to assist you at any time.

Answer:

The number is -16.

Step-by-step explanation:

3/4x=-12

x=-12/(3/4)

x=(-12/1)(4/3)

x=-48/3

x=-16

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:

A u B = {3,5,6,7,8,11,12}

Step-by-step explanation:

A = {3,6,7,11}

B = {3,5,7,8,12}

A u B = {3,5,6,7,8,11,12}

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:

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:

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.

Answer:

u

Step-by-step explanation:

the endpoint will be the last one to the right

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]