A biologist uses a box-shaped fish trap that measures 1/4meter by 2/3meter by 3/5meter. What is the volume of the trap in the cubic meters.

Answer:

A. Obtuse

Step-by-step explanation:

Supplementary Angles: either of two angles whose sum is 180°

Adjacent: have a common side, a common vertex, and don't overlap

Answer:

12a+62b

Step-by-step explanation:

4a(2+3b)-5b(4a-10)

opening brackets

=8a+12b-20a+50b

=8a-20a+12b+50b

=-12a+62b

Answer: They can make 18 ornaments

Step-by-step explanation:

you make 4 and 1/2 into the common denominator of 4. So then you get 4 and 2/4 you multiply 4 by 4 to get 16 and then add it to the 2/4 to get 18/4 each takes 1/4 so you have 18(1/4)

Answer:

(A)[tex]128^{x/3}[/tex]

(D)[tex](4(2^{1/3}))^x[/tex]

Step-by-step explanation:

We want to determine which of the expression is equivalent to:

[tex]\sqrt[3]{128}^ x[/tex]

By the law of indices:

[tex]\sqrt[3]{128}=128^{1/3}\\$Therefore:\\\sqrt[3]{128}^ x \\=(128^{1/3})^x\\=128^{x/3}[/tex]

Similarly:

[tex]\sqrt[3]{128}^ x \\=\sqrt[3]{64*2}^ x\\=(4\sqrt[3]{2})^ x\\=(4(2^{1/3}))^x[/tex]

The expressions that are equivalent to (∛128)ˣ are; (128)^(x/3) and (4(2^(1/3))ˣ

We want to find the expression that is equivalent to (∛128)ˣ

From law of indices, we have that;

(∛128)ˣ = [(128)^(1/3)]ˣ

This can be further expressed as;

(128)^(x/3)

Similarly, we have the simplified expression at;

[(128)^(1/3)]ˣ = (64 * 2)^(x/3)

⇒ (4³ * 2)^(x/3)

⇒ (4(2^(1/3))ˣ

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Answer:

9 cm

Step-by-step explanation:

Since PQ and RS are opposite each other, then in a parallelogram, the lengths will be congruent.

Therefore 2x+5=4x+1

2x=4

x=2

If you plug x=2 into the the original equation, you get 9 cm.

The measure of PQ is 9 centimeters.

Important information:

The oppositie sides of a parallelogram are equal.

[tex]PQ=RS[/tex]

[tex]2x+5=4x+1[/tex]

[tex]5-1=4x-2x[/tex]

[tex]4=2x[/tex]

Divide both sides by 2.

[tex]2=x[/tex]

Now, find the measure of PQ.

[tex]PQ=2x+5[/tex]

[tex]PQ=2(2)+5[/tex]

[tex]PQ=4+5[/tex]

[tex]PQ=9[/tex]

Therefore, the measure of PQ is 9 centimeters.

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Answer:

b = a² + 2a

Step-by-step explanation:

a + 1 = √(b + 1)

(a + 1)² = b + 1 (Square both sides)

a² + 2a + 1 = b + 1 (Expand left side)

a² + 2a = b (Subtract 1)

Answer:

1/6

Step-by-step explanation:

Since we don't care what appears on the first roll

P( outcome) = 1

Second roll

P(1 or 2) = number of 1 or 2 / total number of outcomes

              =2/6 = 1/2

Third roll

odd numbers 1,3,5

P( odd number)= number of odd numbers/ total

                          =3/6 =1/2

P( outcome, 1or 2, odd)  = P( outcome) *P(1 or 2) *P( odd number)

                                       = 1* 1/3 * 1/2

                                       = 1/6

Answer:

x = 7

Step-by-step explanation:

-7x= -8x+7

Add 8x to each side

-7x+8x= -8x+8x+7

x = 7

Answer:

The value of [tex]x[/tex]:

[tex]x = 7[/tex]

Step-by-step explanation:

Solve for [tex]x[/tex]:

[tex]-7x = -8 x + 7[/tex]

Add both sides by [tex]8x[/tex]:

[tex]-7x + 8x = -8x + 8x + 7[/tex]

[tex]x = 7[/tex]

So, the final answer is [tex]x = 7[/tex] .

Answer:

111 units

Step-by-step explanation:

the diameter is double the radius so divide 222 by 2 to get 111 units.

Answer:

Mr Y got 10 votes

Step-by-step explanation:

The election of the housing society has 30 voters. Each of them gives the vote. The three person vying for the post of secretary are X, Y and Z.

Le us calculate the votes of each contestant

Mr X

He got 2/5 of the total votes

number of votes = 2/5 × 30

number of votes = 60/5

number of votes = 12

Mr Z

He got 1/4 of the total votes

number of votes = 1/4 × 30

number of votes = 30/4

number of votes = 1/4 × 30

number of votes = 7.5 ≈ 8 votes

Mr Y

The remaining votes will be 30 - 12 - 8 = 10 votes

Therefore,

Mr Y got 10 votes

Answer:

                                                                                                                                                     32

Step-by-step explanation:

2b+6=70

      -6=70-6=64

       [tex]\frac{2b}{2}[/tex]=64÷ 2

         b=32

beaten it's a visable line beween the equal line

Answer:

All possible are:

(G,L,S)

(G,L,R)

(G,L,P)

(G,S,R)

(G,S,P)

(G,R,P)

(L,S,R)

(L,S,P)

(S,R,P)

{L,R,P)

Probability of 1st/2nd/10th sample = 1/10

Step-by-step explanation:

All the possible combinations of the 3 size samples from a 5 size population have been listed without repetition.

Total Numbers of Samples = 10

To find the probability of finding the first sample from random sampling procedure,

Probability = Number of desired outcomes/ Total number of outcomes

Where Number of desired outcome is 1 and total number of outcomes is 10.

Probability = 1/10

Similarly, to find 2nd sample or 10th sample, the number of desired outcomes is same i.e 1, hecne the probability remains the same i.e 1/10

Possible samples:

(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).

a) Given:

Population size [tex]N=5[/tex].

Sample size [tex]n=2[/tex]

Possible sample (without replacement)

[tex]\Rightarrow 5C_{2}=\frac{5!}{2!\times 3!}[/tex]

[tex]=\frac{5\times 4}{2}[/tex]

[tex]=10[/tex]

[tex]10 samples:-[/tex]

Governor, Lieutenant Governor, secretary of state, Attorney General, Press (P)

Possible samples:

(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).

b) Event: [tex]E\to[/tex]choosing sample second and tenth.

[tex]E=\left\{\left ( G,S \right ),\left ( A,L \right ) \right\}\\n\left ( E \right )=2\\n(S) =10[/tex]

The Probability of that it is the first sample.

Second and tenth sample[tex]=\frac{n\left ( E \right )}{n(S)}[/tex]

                                           [tex]=\frac{2}{10}[/tex]

                                           [tex]=\frac{1}{5}[/tex]

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Answer= 13 years

Solution,

Let the age of grandmother be y

Let the age of grandson be X

according to question,

9x=y ( equation I)

X+56=y( equation ii)

Substituting,

9x=x+56

or,9x-x=56

or,8x=56

or,X=56/8

X=7

Again,

Age of grandson after 6 years

=7 years+6 years

=13 years

Hope it helps

Good luck on your assignment

The age of her grandson after 6 years is 13 years.

A mathematical statement in which two expressions are set equal to each other is known as an algebraic equation. A variable, coefficients, and constants are commonly included in an algebraic equation.

Let the age of the grandmother be x and the age of her grandson be y.

Since the grandmother is 9 times older than her grandson, we can write

x = 9y ...(1)

Since the grandmother is 56 years older than her grandson, we can also write

x = y + 56 ...(2)

We have to solve these two algebraic equations.

Equating the L.H.S. of (1) and (2),

9y = y + 56

i.e. 9y - y = 56

i.e. 8y = 56

i.e. y = 56/8 = 7

So, now the age of her grandson is 7 years.

Therefore the age of her grandson after 6 years is 6+7= 13 years.

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Answer:

Linear. The choice A is correct.

Step-by-step explanation:

Answer:

25/24

Step-by-step explanation:

Let

Sally=S

May=M

Sally is 5/6 as tall

S = 5/6

May is 4/5 as tall

M = 4/5

S/M = 5/6/4/5

=5/6×5/4

=25/24

Answer:

p ( 15p - 7)

Step-by-step explanation:

15 p^2 - 7p

The only common term is p so factor out p

p ( 15p - 7)

____________________________

15p^2-7p

take the common,

Ans: p(15p-7)

hope it helps

Good luck on your assignment

__________________________

Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]

Answer:1.8*10^-1

Step-by-step explanation:

Answer:     1.8 x 10^−1

Step-by-step explanation:

Answer:

2π/3 I believe !

Step-by-step explanation:

Answer:

C. x²+12x+36

Step-by-step explanation:

Since a square's area is figures out with [tex]length^{2}[/tex] and since the length is x+6, then we get:

(x+6)²=

(x+6)(x+6)=

Use FOIL method.

First: x²

Outer: 36

Inner: 6x

Last: 6x

x²+36+6x+6x=

x²+12x+36

The answer that fits is C. x²+12x+36.

Answer:

C. x²+12x+36

hope this helped

19/6

Step-by-step explanation:

3/4 + 5/3 +3/4

3/4 + 3/4 = 3/2

3/2 + 5/3 =19/6 or 3.16....

Answer: 700

84 is 12% of What Number:

12% of 700 is 84

100% of 700 is 700, therefore 12 percent of 700 equals 84.

To check this, 12% of 700 IS 84 (Check on Calculator)

Hope this helps!!

Answer:

$ 809.78

Step-by-step explanation:

Given that

F = future value = $50,000

Interest rate = r = 1.45% = 0.0145

Number of period per year = 12months

Time expressed in years = 5years

The present value of a periodic deposit

P =( F ×r/n)/{ (1+r/n)^nt} -1

Substituting the values into the above formula

P = (50000× 0.0145/12)/(1+0.0145/12)^12×5}-1

= 50000×0.001208/(1+0.0012)^60}-1

= 60.4/1.0012)^60}-1

60.416/1.074608-1

60.4/0.07460

= $ 809.779

His monthly deposit will be $ 809.78

Answer:

no solutions

Step-by-step explanation:

Subtract the two equations

3x+y=18

-(3x+y=16)

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

0 + 0 = -2

0 does not equal negative 2

This is never true so there are no solutions

Answer:

The number of solutions is 0.

Step-by-step explanation:

The x and y terms are equal. The constants are different. The lines are parallel. No solution.

Answer:

and 4x-5x-4x+3y+7y-3y-8z+10z-8z

-5x+7y-6z :this is the answer

Answer:

y-intercept is 3

Step-by-step explanation:

This equation is a linear equation [tex]y=mx+b[/tex].

m is the slope.

b is the y-intercept.

[tex]y=mx+b[/tex] is the same as [tex]y=7x+3[/tex]

7 would be the slope.

3 would be the y-intercept.

Answer:

Step-by-step explanation:

This right triangle is on a grid.

The area is the height * base/2

The base is on a line segment parallel to the x axis which is 6 squares.

The height is on a line segment parallel to the y axis which is 2 squares

The area is the height * base /2

Area = 6 * 2 /2 = 12/2 = 6 square units.

Answer:

(A) The independent variable is time (t) in minutes, and the dependent variable is rental cost (), in dollars. The linear function that models this situation is

R(t) = 30t +8

The time that can be rented for $26 = 1min

Step-by-step explanation:

Based on the information given:

Setup charge on Rent at local copy center = $9

an additional $150 for every 5 minutes. To determine the time that can be rented for $26, let's find the relationship between the rental cost and the time.

For every 5min = $150

For 1 min = $150/5

For t min = 150t/5

Where t = number of minutes of rental time

Rental cost = set up charge + additional cost

Let Rental cost = R(t)

R(t) = 9 + 150t/5

Writing it in form of a linear equation: y = mx + c

R(t) = 150t/5 +9

R(t) = (150/5) ×t + 9

R(t) = 30t + 9

The independent variable is time (t) in minutes, and the dependent variable is rental cost (), in dollars. The linear function that models this situation is

R(t) = 30t + 9

The time that can be rented for $26:

Rental cost = $26

R(t) = 30t +9

26 = 30t +9

26-9 = 30t

17 = 30t

t = 17/30 = 0.57

t is approximately = 1min (nearest minute)

The time that can be rented for $26 = 1min