Captain buys a 100g bar of chocolate. He eats 3/5 of his bar. How many grams of chocolate are left?

Number of students in senior class is 130

Solution:

Given that Every student in the senior class is taking history or science

85 of them taking both history and science

106 seniors takes history

109 seniors takes science

To find: number of students in senior class

Let A be the set of the students of the senior class that take history

Let B be the set of students of senior class that they science

The number of students in senior class is given by:

[tex]|A \cup B|=|A|+|B|-|A \cap B|[/tex]

Where,

A = 106 and B = 109 and |A n B| = 85

[tex]|A \cup B|=106+109-85=130[/tex]

Thus number of students in senior class is 130

Answer:

130

Step-by-step explanation:

Since 106 seniors are taking history and 109 seniors are taking science. If we add those numbers of seniors up we get 215, then we subtract the number of seniors that are taking both history and science because we counted them twice. So the total is 215 - 85 = 130. Therefore there are 130 students in the senior class.

The value which is equivalent to sin 51° is cos 39°. The correct option is B) cos 39°

From the complementary angle theorem, we have that

The sine of an angle is equal to the cosine of its complementary angle

That is,

sin θ = cos (90° - θ)

Recall: Complementary angles sum up to 90°

Then, we can write that

sin 51° = cos (90° - 51°)

sin 51° = cos 39°

Hence, the value which is equivalent to sin 51° is cos 39°. The correct option is B) cos 39°

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Answer:

(A) 40%

(B) 60%

Step-by-step explanation:

Given:

Total number of cars = 200

Cars in parking lot on Friday = 120

Total number of cars = Total cars on Friday + Total cars on Saturday.

⇒ 200 = 120 + Total cars on Saturday.

⇒ Total cars on Saturday = 200 - 120 = 80

So, 80 cars were in parking lot on Saturday.

(A)

Percentage of cars in parking lot on Friday is given as:

[tex]=\frac{\textrm{Cars in parking lot on Friday}}{\textrm{Total cars parked}}\times 100\\\\=\frac{120}{200}\times 100\\\\=\frac{120}{2}=60\%[/tex]

Therefore, 60% of the cars were in the parking lot on Friday.

(B)

Now, since 60% of the cars were parked on Friday, the remaining percent will be on Saturday.

Therefore, percentage of cars in parking lot on Saturday = 100% - 60% = 40%. This can be verified with the same formula used in part (A).

[tex]=\frac{\textrm{Cars in parking lot on Saturday}}{\textrm{Total cars parked}}\times 100\\\\=\frac{80}{200}\times 100\\\\=\frac{80}{2}=40\%[/tex]

We can use the Pythagorean theorem to solve. (a² + b² = c²)

Fill in with what we know → 6² + b² = 11²

Simplify → 36 + b² = 121

Subtract 36 to both sides → 36 - 36 + b² = 121 - 36

Simplify → b² = 85

Take the root of both sides → √b² = √85

Simplify → b = 9.2195...

Round if necessary → 9.2195 = 9.22

Hence, b equals 9.2195.. (unrounded) or 9.22 (rounded).

Best of Luck!

Answer:

length of rectangle=16 inches

width of rectangle=10.5 inches

Step-by-step explanation:

given ,perimeter of rectangle=53 inches

let ,length of rectangle= l=2b-5

  width of rectangle=b

p=2(l+b)

53=2(2b-5+b)

26.5=3b-5

31.5=3b

b=[tex]\frac{31.5}{3}[/tex]

b=10.5 inches

l=21-5=16 inches

Answer:

22,450

Step-by-step explanation:

the ones place is below 5 so you keep the number

Answer:

22,450

Step-by-step explanation:

22,451 rounded to the nearest 10 is 22,450, as 1 rounds down to 0.

:)

Answer:

"she could have sold between 14 and 24 glasses"

Step-by-step explanation:

7 to 12 glasses sold per hour

Min 7 glasses and Max 12 glasses

If she sold for 2 hours, her minimum would be:

7 * 2 = 14 glasses

and her max would be:

12 * 2 = 24 glasses

Hence,

she could have sold between 14 and 24 glasses

Solve for x.

8x=4x-32

Subtract 4x from both sides.

4x=-32

Divide by 4 on both sides.

x=-8

answer: x=-8

Answer:

x=-8

Step-by-step explanation:

8x=4x-32

4x-8x=32

-4x=32

x=32/-4

x=-8

The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6 so option (C) is correct.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given,

The sum of the quantity h and 3 = h + 3

It is divided by 6 so, (h + 3)/6

Hence "The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6".

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Answer:

1.) 26.2

2.) -22.9

Step-by-step explanation:

i took the test

There are 20 number of DVD's in Louis collection

Solution:

Let "J" be the number of DVD's with Jake

Let "B" be the number of DVD's with Bo

Let "L" be the number of DVD's with Louis

Given that Jake owns twice as many DVDs as Louis

So we can say,

number of DVD's with Jake = 2(number of DVD's with Loius)

J = 2L  ------ eqn 1

Given that Bo has sixty fewer DVDs than five times Louis’s collection

So we can say,

number of DVD's with Bo = 5 times number of DVD's with Louis - 60

B = 5L - 60 ---- eqn 2

Given that Jake and Bo have the same amount of DVDs

number of DVD's with Jake = number of DVD's with Bo

J = B ---- eqn 3

Let us solve eqn 1, 2, 3 to find value of "L"

From eqn 1 and eqn 3,

2L = B  ----- eqn 4

Substitute eqn 4 in eqn 2

2L = 5L - 60

2L - 5L = -60

-3L = -60

Thus there are 20 number of DVD's in Louis collection

Louis has 30 DVDs in his collection.

Let's denote the number of DVDs Louis has as L. According to the problem, Jake owns twice as many DVDs as Louis, so Jake has 2L DVDs. Bo has sixty fewer DVDs than five times Louis's collection, which means Bo has 5L - 60 DVDs.

Since Jake and Bo have the same amount of DVDs, we can set their quantities equal to each other:

2L = 5L - 60

Now, let's solve for L:

5L - 2L = 60

3L = 60

L = 60 / 3

L = 20

Louis has 20 DVDs in his collection.

To find the length of the diagonal path on a rectangular lawn, calculate the square root of the sum of the squares of its width and length.

The length of the diagonal path can be found using the Pythagorean theorem.

Given the dimensions of the rectangular lawn (10 m wide and 15 m long),

the length of the diagonal path (d) is calculated as:

d = √(10^2 + 15^2) = √(100 + 225) = √325 = 5√13 m.

Answer:

The function which represent the phone value after x years                      f = i [tex](0.37)^{x}[/tex]

Step-by-step explanation:

Given as :

The rate of depreciation of i-phone value each year = r = 63%

The initial value of i-phone = $ i

The final value of i-phone = $ f

The time period for depreciation = x year

Now, According to question

The final value of i-phone = The initial value of i-phone × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, $ f = $ i × [tex](1-\dfrac{\textrm r}{100})^{\textrm time}[/tex]

Or, $ f = $ i × [tex](1-\dfrac{\textrm 63}{100})^{\textrm x}[/tex]

Or, $ f = $ i × [tex](0.37)^{x}[/tex]

So, The function which represent the phone value after x years =                    f = i [tex](0.37)^{x}[/tex]

Hence, The function which represent the phone value after x years                     f = i [tex](0.37)^{x}[/tex]  Answer

x+y=23 and 10x+24y=426 can be used to determine the number of small and large boxes shipped where x represents the number of small boxes and y represent the number of large boxes.

Step-by-step explanation:

Given,

Volume of small box = 10 cubic feet

Volume of large box = 24 cubic feet

Total boxes shipped = 23

Combined volume = 426 cubic feet

Let,

x represent the number of small boxes.

y represent the number of large boxes.

x+y=23    

10x+24y=426

x+y=23 and 10x+24y=426 can be used to determine the number of small and large boxes shipped where x represents the number of small boxes and y represent the number of large boxes.

Keywords: linear equation, addition

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Sorry, but I don't see any information for me to use to answer that question.

Answer:

Step-by-step explanation:

line G :

5y = -2x - 20...put in slope intercept form (y = mx + b)

y = -2/5x - 4....the slope(m) = -2/5

Part A.) slope intercept form for line R...since R is parallel to G, it will have the same slope....so slope(m) = -2/5

(-10,8)...x = -10 and y = 8

slope(m) = -2/5

y = mx + b

8 = -2/5(-10) + b

8 = 4 + b

8 - 4 = b

4 = b

so ur equation is : y = -2/5x + 4 <=== part A answer

since line E is perpendicular to line G, it will have a negative reciprocal slope...all that means is flip the slope and change the sign....so the slope of line E is : (flip -2/5.....-5/2.....change the sign......5/2)

(-10,8)...x = -10 and y = 8

slope(m) = 5/2

y = mx + b

8 = 5/2(-10) + b

8 = -25 + b

8 + 25 = b

33 = b

so ur equation is : y = 5/2x + 33 <== part B answer

The equation for line R is y = -2/5x + 12. The equation for line E is y = 5/2x + 33.

Part A: To write the equation for line R in slope-intercept form, we need to find the slope and the y-intercept. Since line R is parallel to line G, it will have the same slope. The slope of line G can be determined by dividing the coefficient of x by the coefficient of y: -2/5. We can use the point-slope form, y - y1 = m(x - x1), to find the equation. Substituting the coordinates of the point (-10,8), the equation for line R is y - 8 = (-2/5)(x + 10). Simplifying, we get the equation for line R: y = -2/5x + 12.

Part B: To write the equation for line E in slope-intercept form, we need to find the slope and the y-intercept. Since line E is perpendicular to line G, its slope will be the negative reciprocal of the slope of line G. The slope of line G is -2/5, so the slope of line E will be 5/2. Using the point-slope form and substituting the coordinates of the point (-10,8), the equation for line E is y - 8 = (5/2)(x + 10). Simplifying, we get the equation for line E: y = 5/2x + 33.

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Answer:

43

Step-by-step explanation:

Remove parenthesis.

−6+3(2−4⋅−3+6)−5

Multiply −4 by−3.

−6+3(2+12+6)−5

Add 2 and 12.

−6+3(14+6)−5

Add 14 and 6.

-6+3(20)-5

Multiply 3 by 20.

-6+60-5

Add -6+60.

54-5

Subtract 54 and 5.

43

Answer:

-46y+48x

Step-by-step explanation:

Answer:

-46y + 48x

Step-by-step explanation:

-12(3y - 4x) -10y

-36y + 48x - 10y

-36y - 10y + 48x

-46y +48x

Answer:

(5-5)/(-3-0)= 0/-3= 0

y - 5 = 0(x - 0)

y - 5 = 0

y = 5

Answer:

see the attached figure

Step-by-step explanation:

we know that

If two triangles are similar, then its corresponding sides are proportional and its corresponding angles are congruent

Corresponding sides are named using pairs of letters in the same position on either side of the similarity statement

Corresponding angles are named using a letter in the same position on either side of the similarity statement.

therefore

Corresponding angles

∠D and ∠R

∠E and ∠S

∠F and ∠T

Corresponding sides

DE and RS

EF and ST

DF and RT

Answer:

The each coffee shops receives 4 cases of juice everyday.

Step-by-step explanation:

The juice company produced 8064 cartons of juice in 21 days each day they produced the same number of cartons.

Therefore, each day the company produces [tex]\frac{8064}{21} = 384[/tex] cartons.

The juice company delivers those cartons in 16 areas of coffee shops.

So, each coffee shop receives [tex]\frac{384}{16} = 24[/tex] cartons of juice.

Now, the cartons were delivered in cases of six cartons per case and each coffee shop received an equal number of cases in each delivery.

Hence, each coffee shops receives [tex]\frac{24}{6} = 4[/tex] cases of juice everyday. (Answer)

Answer:

The Table with Correct reasons are as follows.

Step-by-step explanation:

The Table with Correct reasons are as follows

       Answer                                                  Angle Relationship

c. Corresponding Angles                       ∠ 1 ≅ ∠ 5

d. Same Side Interior                             ∠ 4 + ∠ 5 = 180

a. Alternate Exterior Angles                    ∠ 3 ≅ ∠ 6

b. Alternate Interior Angles                    ∠ 4 ≅ ∠ 5

c. Corresponding Angles                       ∠ 2 ≅ ∠ 6

Answer  8.17

Step-by-step explanation:

1.divide 98 by twelve, since there are 12 inches in a foot

98 \ 12

2.then round to the nearest tenth. 8.16 is rounded to  8.17

Answer: The function is EVEN.

Step-by-step explanation:

For this exercise it is important to remember that:

1. A function f(x) is even if and only if:

[tex]f(-x) = f(x)[/tex] for all "x"

2. A function f(x) is odd if and only if:

[tex]f(-x) = -f(x)[/tex] for all "x"

So knowing that, and given the following function k(x):

[tex]k(x)=x^6 - x^2 + 7[/tex]

You can plug [tex]-x[/tex] in for "x", order to know if this is even. Then, you get:

[tex]k(-x)=(-x)^6 - (-x)^2 + 7\\\\k(-x)=x^6-x^2+7[/tex]

Therefore, since:

[tex]f(-x) = f(x)[/tex]

You can determine that that the given function [tex]k(x)=x^6 - x^2 + 7[/tex] is Even.

Answer: 10 and 23

Step-by-step explanation:

Let the first number be x and the second number be y.

Also , let x be the bigger number and y the smaller number.

From the first statement;

x + y = 33 ............................. equation 1

From the second statement

twice the smaller number = 2y

so, if the bigger number is 3 more than two times the smaller number, this means that

x = 2y + 3 .................................... equation 2

Solving the resulting linear equations by substitution method .

substitute x = 2y + 3 into equation 1 , that is

x + y = 33 becomes :

2y + 3 + y = 33

3y + 3 = 33

3y = 30  

y = 10

Substitute y = 10 into equation 2 , that is

x = 2y + 3 becomes

x = 2(10) + 3

x = 20 + 3

x = 23

Answer:

-3x^3+74x-5

Step-by-step explanation:

(x+5)(-3x^2+15x-1)

-3x^3+15x^2-x-15x^2+75x-5

-3x^3+15x^2-15x^2+75x-x-5

-3x^3+74x-5

The given expression can be simplified to obtain -3x³ + 74x - 5. The correct option is (a).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given algebraic expression is (x + 5)(-3x² + 15x - 1).

It can be evaluated as follows,

(x + 5)(-3x² + 15x - 1)

⇒ x(-3x² + 15x - 1) + 5(-3x² + 15x - 1)

⇒ -3x³ + 15x² - x - 15x² + 75x - 5

⇒ -3x³ + 74x - 5

Hence, the product of the given expression is -3x³ + 74x - 5.

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Answer: 1.5

Step-by-step explanation: To find 5% of 30, first write 5% as a decimal by moving the decimal point 2 places to the right to get .05.

Next, the word "of" means multiply, so we have (.05)(30) which is 1.5.

So 5% of 30 is 1.5.

Answer:

1.5

Step-by-step explanation:

To solve, you put (5%) in the calculator, then (30) next to it, and the calculator gives you your answer. I think that's the easiest way to do it.

Answer: j = 8

Step-by-step explanation: To solve for j in this equation, we want to get j by itself on the left side of the equation. Since j is being multiplied by 5, to get j by itself, we need to divide by 5 on the left side of the equation. Since we divided by 5 on the left side, we must also divide by 5 on the right side.

On the left side, notice that the 5's cancel out so we are simply left with j. On the right side, we have 40 divided by 5 which gives us 8 so we have j = 8.

Finally, remember to check your answer by substituting an 8 back into the original equation. So we have 5 (8) = 40 which is a true statement so our answer checks. Remember to show all your work when solving equations.

The Answer is :J=8  =)