label the sides opposite, adjacent, or hypotenuse, then find the missing side. Round to the nearest tenth for 25, 26, 27, 29, & 30
​

Carl has [tex]\( \frac{163}{36} \)[/tex] inches of string left out of the 20 inches he started with after tying the parcel and the box.

To find out how much string Carl has left after tying the parcel and the box, we'll subtract the lengths of string used from the total length he started with.

1. Convert the mixed numbers to improper fractions:

  -[tex]\(10 \frac{2}{9}\) inches = \(10 + \frac{2}{9} = \frac{90}{9} + \frac{2}{9} = \frac{92}{9}\)[/tex] inches

  - [tex]\(5 \frac{1}{4}\) inches = \(5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}\)[/tex] inches

2. Add the lengths of string used:

  [tex]\[\text{Total length used} = \frac{92}{9} + \frac{21}{4}\][/tex]

3. Find a common denominator to add the fractions:

  The common denominator for 9 and 4 is 36.

  [tex]\[\frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36}\] \[\frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36}\][/tex]

4. Add the fractions:

  [tex]\[\frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36}\][/tex] inches

5. Subtract the total length used from the total length Carl started with:

  [tex]\[20 - \frac{557}{36}\][/tex]

6. Convert the mixed number result to an improper fraction:

  \[20 = \frac{720}{36}\]

7. Subtract the fractions:

  [tex]\[\frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36}\][/tex] inches

Now, Carl has [tex]\(\frac{163}{36}\)[/tex] inches of string left.

We can convert this to a mixed number if necessary.

The correct question is:

Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?

Ans:          

Carl has [tex]\( {4 \frac{19}{36}} \)[/tex] inches of string left after tying both the parcel and the box.

1. Convert the mixed numbers to improper fractions:

  - 10 2/9 inches = [tex]\( \frac{92}{9} \) inches[/tex]

  - 5 1/4 inches = [tex]\( \frac{21}{4} \) inches[/tex]

2. Add the lengths of string used:

[tex]\( \frac{92}{9} \) inches (parcel) + \( \frac{21}{4} \) inches (box)[/tex]

  To add these fractions, find a common denominator:

  The least common multiple of 9 and 4 is 36.

[tex]\( \frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36} \)\\ \( \frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36} \)\\ \( \frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36} \) inches[/tex]

3. Subtract the total used from the initial length of string:

  Initial length of string = 20 inches

  Total used = [tex]\( \frac{557}{36} \) inches[/tex]

  To subtract, convert 20 inches to a fraction with the common denominator of 36:

[tex]\( 20 = \frac{720}{36} \)[/tex]

  Now, subtract:

[tex]\( \frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36} \) inches[/tex]

4. Convert the fraction to a mixed number (if necessary):

[tex]\( \frac{163}{36} \)[/tex] inches is already in its simplest form. To convert to a mixed number:

 [tex]\( 163 \div 36 = 4 \) remainder \( 19 \)[/tex]

  So, [tex]\( \frac{163}{36} = 4 \frac{19}{36} \) inches[/tex]

The correct question is:

Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?

Ans:_______

Answer:

Total amount of books in the bookcase =  225 books

Step-by-step explanation:

Each shelf is to have 15 books

Therefore total amount of books in the bookcase = {9×15} + {6×15} = 225 books

Answer:

radius = 6

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² - 12x + y² + 4y = - 4

Using the method of completing the square on the x and y terms

add (half the coefficient of the x/y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is

(x - 6)² + (y + 2)² = 36 ← in standard form

with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6

Answer:

6

Step-by-step explanation:

h = -12/-2 = 6

k = 4/-2 = -2

h² + k² - r² = 4

6² + (-2)² - 4 = r²

r² = 36

r = sqrt(36) = 6

Answer:

The minimum of cows he needs are: 2

Step-by-step explanation:

There's a relation between each animal:

5 chickens equals 1 pig

3 pigs equals 2 sheep

5 sheep equals 2 cows

You can understand it as the following three abstractions:

5c = 1p              (1)

3p = 2s             (2)

5s = 2o             (3)

Where:

c is for chickens

p is for pigs

s is for sheep

o is for cows

So now you have three equations with 4 variables. The next step is to obtain an equation that relates directly the variable c (chickens) with the variable o (cows). In order to do that from the equation 2 we obtain s in terms of p, as follow:

[tex]3p =2s\\s=\frac{3p}{2} \\[/tex]

Then we replace s in the equation 3 and we obtain v in terms of p:

[tex]5(\frac{3p}{2} )=2v\\\\2v=\frac{15}{2} p\\\\[/tex]

[tex]v=\frac{15}{2*2} p \\\\v=\frac{15}{4} p[/tex]

Now we replace v in the equation 1:

[tex]4c = \frac{4}{15} v[/tex]

[tex]c=\frac{1}{15} v[/tex]                    (4)

The equation 4 means that  1 chicken equals the fifteenth part of a cow. For this case the farmer needs 20 chikens, so we multiply per 20 each part of the equation 4:

[tex]20c = 20 * \frac{1}{15} v\\ \\\ 20c = \frac{20}{15}v = \frac{4}{3}v \\\\20c = 1.3333v[/tex]

As it is impossible to have 1.3333 cows, the answer  is 2 cows approximately.

Answer:

2

Step-by-step explanation:

Answer:

150 people took the test.

Step-by-step explanation:

Given:

Number of people liked the new flavor = 69

Percentage of people liked the new flavor = 46%

We need to find the number of people who took the test.

Solution:

Let the number of people who took the test be 'x'.

So we can say that;

Percentage of people liked the new flavor multiplied by the number of people who took the test is equal to Number of people liked the new flavor.

framing in equation form we get;

[tex]46\%\times x =69\\\\\frac{46}{100}x=69\\\\0.46x =69[/tex]

Dividing both side by 0.46 we get;

[tex]\frac{0.46x}{0.46}=\frac{69}{0.46}\\\\x= 150[/tex]

Hence 150 people took the test.

Answer:

The sampling method used is Convenience sampling.

Step-by-step explanation:

Convenience sampling is a non-probability sampling method that involves the selection of sample from the easiest source available. In this sampling method the samples are selected from the most convenient possible way.

Foe instance, samples taken from social media, nearest shopping mall, and so on.

In this case the students selected 10 friends to answer the survey.

This is an example of convenience sampling method because sampling your friend is the easiest sample anyone could collect.

Thus, the sampling method used is Convenience sampling.

Answer:

Yes, the approximate length of one side is a prime number less than 25.

The approximate dimensions of the room are 19 ft by 18 ft.

Step-by-step explanation:

Assuming the dining room is rectangular in shape

Approximate area of the dining room = 342 ft^2

The area of a rectangle is calculated by multiplying the length of the rectangle by the width.

Assuming the approximate length is a prime number less than 25

The closest prime number to 25 is 19

Approximate length = 19 ft

Approximate width = approximate area ÷ approximate length = 342 ft^2 ÷ 19 ft = 18 ft

Approximate dimensions of the room = 19 ft by 18 ft

Answer:

c= 1/26

Step-by-step explanation:

The joint probability mass function for X and Y must comply that:

[tex]\[\sum\]\sum\] c(x +y) = 1[/tex]   for  x∈{1,2,4} and  y∈{1,3}

thus, all the possible values for the pairs (x,y) are:

(1,1)  (1,3) (2,1) (2,3) (4,1) (4,3)

and then

c [(1+1)+(1+3)+(2+1)+(2+3)+(4+1)+(4+3)] = 1

c[26] = 1

c= 1/26

Answer:

y = 4/5x -3

Step-by-step explanation:

in order to do this :

use the formula :

[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]

= [tex]\frac{-5 + 5}{2} , \frac{-7 + 1}{2}[/tex]

midpoint =(0 , -3)

use the formula :

[tex]\frac{y2-y1}{x2-x1}[/tex]

= [tex]\frac{1-(-7)}{5-(-5)}[/tex]

=[tex]\frac{8}{10}[/tex]

simplified to 4/5

gradient = 4/5

formula for the equation of a line

(Y-y1) = m( X-x1)

now use the values of the midpoint and the gradient(m)

y +7 = 4/5 (x + 5)

y = 4/5x + 4-7

Answer:

y = 0.8x - 3

Step-by-step explanation:

Slope = (-7-1)/(-5-5) = -8/-10 = 0.8

When x = 5, y = 1

1 = 0.8(5) + c

1 = 4 + c

c = -3

y = 0.8x - 3

The domain is the X value ( input).

The line starts at (0,2) so 0 is the first part of the domain. The horizontal line has an arrow on it pointing to the right which means the line can continue to infinity.

The answer is the second choice, 0 to infinity

Answer:

2

Step-by-step explanation:do it on a piese of parer them it will make more sence

Answer:

3840 cubic inches

Step-by-step explanation:

The volume of a rectangular prism is 960 cubic inches

Let the dimensions be lXwXh,

l=length of the base

w=width of the base

h=height of the base

The volume, lwh=960 cubic inches

If the dimensions of the base are doubled and the height remains the same

Volume of the new rectangular prism=2l X 2w X h =4lwh

=4 X 960 =3840 cubic inches

Answer:

Boi

Step-by-step ex:

Answer:

Option 4

Step-by-step explanation:

x - 4 is negative for x < 4

Mod makes it positive,

-(x - 4) = 4 - x

4 - x for x < 4,

x - 4 for other x values (which are greater than/equal to 4)

Answer:

I) There are [tex]8.760\times 10^3[/tex] hours in 1 year.

II) The exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.

Step-by-step explanation:

Given : 1 hour=3600 seconds

1 year = 31556952 seconds.

To find :

I)  Use scientific notation to estimate the number of hours in one year.

1 day = 24 hours

1 year = 365 days

So, number of hours in one year is given by,

[tex]n=24\times 365[/tex]

[tex]n=8760[/tex]

In scientific notation,

[tex]8760=8.760\times 10^3[/tex]

So, there are [tex]8.760\times 10^3[/tex] hours in 1 year.

II) 1 year = 31556952 seconds.

1 hour = 3600 seconds

In one year the number of hour is given by,

[tex]n=\frac{31556952}{3600}[/tex]

[tex]n=8765.82[/tex]

In scientific notation,

[tex]8765.82=8.76582\times 10^3[/tex]

So, the exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.

III) In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.

Answer:

2884.8 millimeters squared

Step-by-step explanation:

Given:

The radius of the disc is 35 millimeters, so the area of it is:

π[tex]r^{2}[/tex] = 3.14*[tex]35^{2}[/tex] = 3846.5

Then, we find out the area of the circular hold cut out of the bigger one, its radius is a haft of the radius of the bigger circle = 35/2 = 17.5

π[tex]r^{2}[/tex] = 3.14*[tex]17.5^{2}[/tex] =961.6

=>  the area of the pendant = 3846.5  - 961.6  =2884.8 millimeters squared

The final result is the area of the pendant is 2887.1 mm².

To find the area of the pendant:

Therefore, the area of the pendant is 2887.1 mm².

Answer: the area of the original rectangle is 300 square meters.

Step-by-step explanation:

Let L represent the original length of the rectangle.

Let W represent the original width of the rectangle.

The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. This means that the length of the new rectangle is 2L and the width of the new rectangle is 3W

If the area of the new rectangle is equal to 1800 square meters, it means that

2L × 3W = 1800

6LW = 1800

LW = 1800/6

LW = 300 square meters

Answer:

Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.

Answer:

b m d j and k z y a

Step-by-step explanation:

The length of AB is 31 yd.

Solution:

Given data:

The side opposite to angle A is "a" = 22 yd

The side opposite to angle B is "b" = 26 yd

The side opposite to angle C is "c" = AB

Angle C = 80°

To find the length of AB:

Using cosine formula,

[tex]c^2=a^2+b^2-2ab \cdot \cos C[/tex]

Substitute the given values in the formula, we get

[tex]c^2=22^2+26^2-2(22)(26)\cdot \cos 80^\circ[/tex]

[tex]c^2=484+676-1144\cdot \cos 80^\circ[/tex]

[tex]c^2=1160-1144\cdot (0.1736)[/tex]

[tex]c^2=1160-198.5984[/tex]

[tex]c^2=961.4016[/tex]

Taking square root on both sides, we get

c = 31

AB = 31 yd

The length of AB is 31 yd.

Answer:

This is true

Step-by-step explanation:

10x1 is 10. 10x10 is 100. but if u did 100x10 you would add the amount of zeros total. which would be 1000. so 400x10 is 4000

Answer:

This system have 9000 different numbers.

Step-by-step explanation:

We know that the internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0.

We have total 10 digits.

In the first place we have 9 possibilities, because from the conditions of the task in the first place there cannot be 0.

In second, third and fourth place we have 10 possibilities.

Therefore, we get

[tex]N=9\cdot 10\cdot10 \cdot 10=9000[/tex]

This system have 9000 different numbers.

In this phone system, there are 9,000 different internal telephone numbers that can be assigned.

The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. To find the number of different numbers that can be assigned in this system, we need to consider the possibilities for each digit position. Since the first digit cannot be 0, there are 9 choices (1 through 9) for the first digit. For the remaining three digits, each digit can be any number from 0 to 9, resulting in 10 choices for each of the three remaining digits. Therefore, the total number of different numbers that can be assigned in this system is

9 * 10 * 10 * 10 = 9,000.

https://brainly.com/question/14986306

#SPJ12

Answer:

1.19 revolutions per second.

Step-by-step explanation:

Given:

A rotating object makes 5/6 of a revolution in 7/10 second.

To find:

Find the approximate speed in revolutions per second ?

Solution:

As here given that a rotating object makes 5/6 of a revolution in 7/10 second,

we will have to find that in one second how many revolution does this object make:

By unitary method:

In [tex]\frac{7}{10}[/tex] second, a rotating object makes = [tex]\frac{5}{6}[/tex]  revolution

In 1 second, a rotating object makes = [tex]\frac{5}{6}\div\frac{7}{10}[/tex]

                                                            [tex]=\frac{5}{6}\times\frac{10}{7} = \frac{50}{42}=1.190\ revolution[/tex]

Therefore, the approximate speed of object is 1.19 revolution per second.

We can also find by, [tex]speed = \frac{distance}{time}[/tex]

                                            [tex]=\frac{5}{6} \div\frac{7}{10} \\=\frac{5}{6} \times\frac{10}{7} =\frac{50}{42} = 1.19[/tex]

We can use any one to solve this type of question:

Finally, the approximate speed is 1.19 revolutions per second.

Answer:

a)  ¬p : I didn't buy a lottery ticket this week.

b) p ∨ q: I bought a lottery ticket this week or I won the million dollar jackpot.

c) p → q: If I didn't buy a lottery ticket this week, then I won the million dollar jackpot.

d) p ∧ q:  I bought a lottery ticket this week and I won the million dollar jackpot.

e) p ↔ q: I bought a lottery ticket this week if and only if I won the million dollar jackpot.

f ) ¬p → ¬q: If I didn't buy a lottery ticket this week, then I didn't win the million dollar jackpot.

g) ¬p ∧ ¬q: I didn't buy a lottery ticket this week and I didn't win the million dollar jackpot.

h) ¬p ∨ (p ∧ q): I didn't buy a lottery ticket this week or I bought a lottery ticket this week and I won the million dollar jackpot.

Step-by-step explanation:

In logic, a word or group of words that joins two or more propositions together to form a connective proposition it's called connective, also called sentential connective, or propositional connective

1. Negation: the symbol is ¬, or ~. It is use for saying that the proposition is false. This connective proposition only affects one statement.

2. Disjunction ("or"): the symbol is ∨. It is use for saying that at least one of the propositions are true.

3. Conjunction ("and"): the symbol is ∧. It is use for saying that both of the propositions, at the same time are true.

4. Conditional (“if . . . then”): the symbor is →. In this structure the first proposition it's called antecedent and the second one consecuent. For this connective the only case when it's not true is when the antecendent is true and the consecuent is false.

5. Biconditional ("if and only if"): the symbol is  ↔. This structure is a double conditional. And the proposition is true when antecent and consecuent are both true or both false.

Final answer:

The student's question involves translating logical propositions into English sentences. These include negation, disjunction, conjunction, conditional, and bi-conditional statements based on the scenarios presented.

Explanation:

The student wants to express each proposition as an English sentence. The propositions include notations for negation (¬), disjunction (∨), conjunction (∧), and implication (→), as well as bi-conditional (↔).

Each sentence corresponds to different logical statements found in propositional logic.

Answer:

Step-by-step explanation:

We are to find 62×1000

We can write in standard form

62×10³

6.2×10×10³

Using indices

a^m × a^n = a^(m+n)

Therefore,

6.2×10¹+³

6.2×10⁴

Using the normal multiplication

................1000

...............×. .62

...…......-------------

....., ... ..2 0 0 0

.......+.6 0 0 0

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

..........6 2 0 0 0

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

Answer:

Velocity of the 24.6 g marble is 31 cm/s.

Step-by-step explanation:

Given:

Marble 1:

Mass of the marble [tex](m_1)[/tex] = 12.3 gm

Velocity of [tex]m_1[/tex] before collision [tex]v_1_i[/tex] = 15.5 cm/s

Velocity of [tex]m_1[/tex] after collision [tex]v_1_f[/tex] = 77.5 cm/s

Marble 2:

Mass of the marble [tex](m_2)[/tex] = 24.6 gm

Velocity of [tex]m_2[/tex] before collision [tex]v_2_i[/tex] = 62 cm/s

Velocity of [tex]m_2[/tex] after collision [tex]v_2_f[/tex] = ?

From the law of conservation of momentum, we know that momentum before equals the momentum after :

So,

⇒ [tex]P(i)=P(f)[/tex]

⇒ [tex](m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)[/tex]

⇒ Plugging the values.

⇒ [tex](12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)[/tex]

⇒ [tex]190.65+1525.2=953.25+24.6\times v_2_f[/tex]

⇒ [tex]1715.85=953.25+24.6\times v_2_f[/tex]

⇒ [tex]1715.85-953.25=24.6\times v_2_f[/tex] ...subtracting both sides 953.25

⇒ [tex]762.6=24.6\times v_2_f[/tex]

⇒ [tex]\frac{762.6}{24.6}\ =v_2_f[/tex] ...dividing both sides with 24.6

⇒ [tex]31=v_2_f[/tex]

⇒ [tex]v_2_f =31[/tex] cm/s

The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.

Answer:

  50% of market value

Step-by-step explanation:

The actual tax rate on the Combs home is ...

  $8719.38/$361800 = 0.0241 = 24.1 mils

The rate of assessment is ...

  (24.1 mils)/(48.2 mils) = 0.50 = 50%

The Combs pay tax on 50% of their home's market value.

Answer:

There are a total number of 1656 students in the school.

Step-by-step explanation:

Let's set up this word problem in mathematical terms.

We can call the number of Left Handed Students as X,

and we can call the number of Right Handed Students as Y.

Since there are 276 more right handed pupils than left handed, we have the following equation:

X + 276 = Y   -Equation 1

Also, since there are 5/12 ratio of left handed students and 7/12 right handed students, we get:

Total Students = T

(5/12) T = X                  -Equation 2

(7/12) T = Y                  -Equation 3

Substituting equations 2 and 3 into equation 1 we get:

[tex]\frac{5}{12} T+276=\frac{7}{12} T[/tex]

Solving for Total number of students (T) we get:

T = 1656

Answer:

Therefore, Jane can create 80 different dinners.

Step-by-step explanation:

We know that Jane must select three different items for each dinner she will serve. If at least one of the selections must be vegetarian.

The items are to be chosen from among five different vegetarian and four different meat selections.

First we count the number of combinations for one vegetarian dinner and 2 meat dinners.

[tex]C_1^5\cdot C_2^4=5\cdot \frac{4!}{2!(4-2)!}=5\cdot 6=30[/tex]

Now we count the number of combinations for 2 vegetarian dinner and 1 meat dinners.

[tex]C_2^5\cdot C_1^4=10\cdot 4=40\\[/tex]

Now we count the number of combinations for 3 vegetarian dinner.

[tex]C_3^5=\frac{5!}{3!(5-3)!}=10\\[/tex]

We get 30+40+10=80.

Therefore, Jane can create 80 different dinners.

Answer:

Step-by-step explanation:

I think the photo below is your full question and my answer is presented in that too.

We create a table of values:

p      c

0      5

1       6

2       7

Then draw on the graph.

Hope it will find you well

Answer:

Step-by-step explanation:

a) The retail price (r) is the wholesale price (w) plus 20% of that price plus $2.50:

  r = w + 0.20w + 2.50

  r = 1.20w + 2.50

__

b) Substituting w=8.40, we have ...

  r = 1.20·8.40 +2.50 = 12.58

The retail price of the chair is $12.58.

__

c) Substituting r=13.30, we have ...

  13.30 = 1.20w +2.50

  10.80 = 1.20w . . . . . . . subtract 2.50

  9.00 = w . . . . . . . . . . . . divide by 1.20

The wholesale price of the chair is $9.00.