On a river you must release any fish that you catch ifvit measures less than 12 inches. Define a variable and then write an algebraic inequality for each senario. can you keep a fish that is 11.99 inches?

Answer:

  x^2 -11x +30 = 0

Step-by-step explanation:

If these two integers are solutions of the quadratic, then its factors are ...

  (x -5)(x -6) = 0

Multiplying this out, we get ...

  x^2 -11x +30 = 0

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:

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

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:

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:

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:

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:

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:

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:

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:

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: 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:

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:

  8

Step-by-step explanation:

The ratio of white paint to blue paint in the mix is ...

  40% : 20% = 2 : 1

We can multiply this ratio by 4 cups to find ...

  white : blue = 8 cups : 4 cups

There are 8 cups of white paint in the mixture.

Answer: the number of cups of white paint are used is 8

Step-by-step explanation:

Let x represent the total number of cups of paint used in the mixture.

40% of the mixture is white paint, this means that the number of cups of white paint used is 0.4x

20% of the mixture is blue paint, this means that the number of cups of blue paint used is 0.2x

If the rest is red, it means that the number of red cups used is

x - (0.2x + 0.4x) = 0.4x

There are 4 cups of blue paint used in a batch of lilac paint. This means that

0.2x = 4

x = 4/0.2 = 20

Therefore, the number of cups of white paint are used is

0.4 × 20 = 8

Answer:

600

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:

is d

Step-by-step explanation:

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.

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:

  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:

Amplitude is 17

Period = 12

Vertical shift of 50

Step-by-step explanation:

One complete cycle in 12 months

Mean line is at y = 50, so vertical shift of 50

Amplitude = 67-50 = 17

Or , 50 - 33 = 17

The vertical shift, amplitude, and period of the given equation would be as follows:

Amplitude [tex]= 17[/tex]

Period [tex]= 12[/tex]

Vertical Shift [tex]= 50[/tex]

Given that,

Duration of the cycle [tex]= 12[/tex] months

∵ Period [tex]= 12 months[/tex]

The Mean line lies at [tex]y = 50[/tex]

So,

The vertical shift [tex]= 50[/tex]

Now,

Amplitude [tex]= 67-50[/tex]

[tex]or[/tex]

[tex]50 - 33[/tex]

[tex]= 17[/tex]

Learn more about "Amplitude" here:

brainly.com/question/9351212

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.

Answer:

2

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

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:

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: the ship unloaded 1455 tons of cargo at the bahamas.

Step-by-step explanation:

Let x represent number of tons of cargo that the ship unloaded at the bahamas.

The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be

5678 - x

The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be

5678 - x + 3x

= 5678 + 2x

If the ship holds 8588 tons now, it means that

5678 + 2x = 8588

2x = 8588 - 5678

2x = 2910

x = 2910/2

x = 1455 tons of cargo

Answer:

It's D.

Step-by-step explanation:

Final answer:

The function f(x) = 3x⁴+5x²+1 is an even function because f(-x) equals f(x) for any value of x, confirming the student's statement as true.

Explanation:

The function f(x) = 3x4+5x2+1 is indeed an even function. This can be determined by checking if f(-x) = f(x) for any value of x. An even function is symmetrical about the y-axis and does not change when x is replaced with -x. Applying this to the given function:

f(-x) = 3(-x)4+5(-x)2+1 = 3x4+5x2+1

f(x) = 3x4+5x2+1

Since f(-x) and f(x) are indeed equal, the function is even. Therefore, the correct answer to the student's statement that the function is even is: 4) The student's claim is true, because for any input of x, f(x) = f(-x).

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.

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