An aquarium in a restaurant is a rectangular prism and measures 3.5 feet by 4 feet by 3 feet. What is the volume of the aquarium?
A) 42 cubic feet

B) 15.5 cubic feet

C) 36 cubic feet

D) 10.5 cubic feet

Answer:

Step-by-step explanation:

Parabola:

   [tex]\sf f(x) =\dfrac{-1}{2}x^2+7x - 5\\\\a = \dfrac{-1}{2} \ ; b = 7 \ ; \ c = -5[/tex]

[tex]\sf x = \dfrac{-b}{2a}\\\\x =\dfrac{-7}{2*\dfrac{-1}{2}}\\\\ = \dfrac{-7}{-1}[/tex]

x = 7

Now, to find the y-value substitute this in the equation

               [tex]\sf f(x) = \dfrac{-1}{2}*7^2+7*7-5\\\\ =\dfrac{-49}{2}+49-5\\\\ = \dfrac{-49}{2}+44\\\\ = \dfrac{-49}{2}+\dfrac{88}{2}\\\\= \dfrac{39}{2}[/tex]

[tex]\boxed{Vertex(7 ,\dfrac{39}{2})}[/tex]

b) The value of a is negative. So, the parabola is open down words and the maximum value is given by the y-coordinate of the Vertex.

             [tex]\sf \boxed{Maximum \ value= \dfrac{39}{2}}[/tex]

[tex]\sf c) Range = [\dfrac{39}{2}, -infinity)[/tex]

Answer:

(a) (7,39/2)

(b) Maximum, 39/2

(c) y ≤ 39/2

(d) Increase when x < 7 and decrease when x > 7

Step-by-step explanation:

Given the parabola:

[tex]\displaystyle \large{f(x)=-\dfrac{1}{2}x^2+7x-5}[/tex]

( A ) Find the vertex

In order to find the vertex, let’s use calculus for this one. Recall the power rules for differentiation:

Power Rules

[tex]\displaystyle \large{f(x)=x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant)}}[/tex]

Derivative Definition

Derive the parabola:

[tex]\displaystyle \large{f'(x)=-\dfrac{1}{2}(2)x^{2-1} + 7(1)x^{1-1} -0}\\\\\displaystyle \large{f'(x)=-x+7}[/tex]

Since vertex has slope = 0 —> e.g f'(x) = 0:

[tex]\displaystyle \large{0=-x+7}\\\\\displaystyle \large{-x=-7}\\\\\displaystyle \large{x=7}[/tex]

Substitute x = 7 in f(x):

[tex]\displaystyle \large{f(7)=-\dfrac{1}{2}(7)^2+7(7)-5}\\\\\displaystyle \large{f(7)=-\dfrac{1}{2}(49)+49-5}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+44}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+\dfrac{88}{2}}\\\\\displaystyle \large{f(7)=\dfrac{39}{2}}[/tex]

Therefore, the vertex is at (7,39/2)

( B ) Determine if max or min then find the value

Since the parabola opens downward then there only exists maximum value. The maximum value is the y-value of vertex at x-value of vertex. Henceforth:

( C ) Find range

For parabola, range is minimum value </≤ y </≤ maximum value. We know that parabola has maximum value of 39/2 but no minimum value so we can just ignore it then we’d have:

[Note: < and > are for open-dot meaning the value will not be included —> e.g x > 4 means 4 isn’t included in.]

( D ) Find the interval when function is increasing and when it’s decreasing

For parabola, the function will increase only if f'(x) or slope > 0 and will decrease only f'(x) < 0.

We know, from part A that the derivative is:

[tex]\displaystyle \large{f'(x)=-x+7}[/tex]

Therefore, when f'(x) > 0 —> e.g -x + 7 > 0:

[tex]\displaystyle \large{-x+7 > 0}\\\\\displaystyle \large{-x > -7}\\\\\displaystyle \large{x < 7}[/tex]

When f'(x) < 0 —> e.g -x + 7 < 0:

[tex]\displaystyle \large{-x+7 < 0}\\\\\displaystyle \large{-x < -7}\\\\\displaystyle \large{x > 7}[/tex]

Therefore, the function will increase when x < 7 and will decrease when x > 7.

Answer:

P(king or diamond) = P(king) + P(diamond) - P(king and diamond) P(king or diamond) = (4/52) + (13/52) - (1/52) P(king or diamond) = 16/52 Page 5 P(king or diamond) = 4/13.

Answer:

5.75

Step-by-step explanation:

If

1 box = 8 tomatoes

x boxes = 46 tomatoes

1 = 8

x = 46

You cross multiply giving you

8x = 46×1

8x = 46

8x/8 = 46/8

x = 5.75

Answer:

6

Step-by-step explanation:

The ratio of boys to girls is 2:5

let the number of boys be 2x -------(i)

and number of girls be 5x

and the total number of students is 21

therefore we know that..

2x+5x = 21

on solving for x,

7x=21

x= 21/7

x=3

now, by putting the value of x in (i),

2x = 2×3 = 6

therefore, there are 6 boys in the classroom.

you find the no. of girls similarly.

hope it helps !!...

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Answer:

133

Step-by-step explanation:

Line PYF is straight. Therefore, its angle measures 180°. One of the angles is 95°. The other angle measures (h-48)°.

Based on this info, we can form an equation:

95°+h°-48° = 180°

h°-48° = 180°-95°

h = 85°+48°

h = 133°

Hence, the value of h is 133°.

Hope this helps!!!

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Answer:

a=108;b=36;c=72

Step-by-step explanation:

Answer:

a = 108°

b = 36°

c = 72°

Step-by-step explanation:

Note : the sum of the interior angles of a regular pentagon = 540°

Then

The measure of one interior angle of a reg pentagon =540/5 = 108°

Therefore a = 108°

c = 180 - 108 = 72°

SRT is a new isosceles triangle then :

[tex]b=\frac{180-108}{2} = \frac{72}{2} =36[/tex]

For the basket with 4 different types of marbles, there are  4,096 combinations in which we can select 6 marbles (in order).

Here we need to identify the number of selections. We have 6 selections (assuming that order matters).

Now we need to find the number of options for each of these. We know that there are 4 different colors of marbles, then for each selection, we have 4 options:

The total number of combinations is given by the product between the numbers of options, so we have:

C = 4*4*4*4*4*4 = 4,096 combinations.

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Answer:

3

Step-by-step explanation:

The N1, N6 and N8 national highways meet in Bloemfontein,

Hope This Helped

Answer:

[tex]\boxed{\sf \dfrac{14}{95}}[/tex]

Explanation:

Black ribbons = 8 ribbons

Green ribbons = 12 ribbons

Total ribbons: 12 + 8 = 20 ribbons

[tex]\sf Probability = \dfrac{Favorable \ Outcomes}{Total \ Possible \ Outcomes}[/tex]

For Lila:

[tex]\sf Lila \ picks \ black \ : \ \dfrac{8}{20}[/tex]

Left black ribbons: 8 - 1 = 7 black ribbons

Left total ribbons: 20 -1 = 19 total ribbons

For Jessica:

[tex]\sf Jessica \ picks \ black \ : \ \dfrac{7}{19}[/tex]

Probability that they both pick black ribbons:

[tex]\sf \rightarrow \dfrac{8}{20} \ x \ \dfrac{7}{19}[/tex]

[tex]\sf \rightarrow \dfrac{14}{95}[/tex]

The solution of y= [tex]2x^{2} +x[/tex] given as:

x:   0      1       2       3

y:   0      3      10      21

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given function is:

y= [tex]2x^{2} +x[/tex]

For finding the solution of above expression, take value of x and solve for y.

y= 2(0)+0

y=0

y= [tex]2(1)^{2} +1= 3[/tex]

y=[tex]2(2)^{2} +2=10[/tex]

y= [tex]2(3)^{2} +3=21[/tex]

The required table is:

x:   0      1       2       3

y:   0      3      10      21

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The distribution of y is [tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]

The given parameters are:

Probability of success, p = 60%

Sample size, n = 5

The distribution of y is represented as:

[tex]P(y) = ^nC_y * p^y * (1 - p)^{n-y}[/tex]

So, we have:

[tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]

Hence, the distribution of y is [tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]

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Answer:

Step-by-step explanation:

Answer:

i agree with the other anwser!!

Step-by-step explanation:

Answer:

The answer to this question is -2.

Step-by-step explanation:

First, multiply one of the equations by something that can cancel out the other variable.

3x+2y=20

3(x+4y=0)

3x+2y=20

3x+12y=0

Now, subtract both equations.

-10y=20

Now, divide both sides by -10.

y=-2

Hope this helps!

Out of all 252 twelfth graders, 114 rode in a car to school

The proportion of students that rode in a car is given as:

p = 45.24%

So, the number of students that rode in a car is:

Students = 45.24% * 252

Evaluate the product

Students = 114.008

Approximate

Student = 114

Hence, 114 rode in a car to school

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Answer:

(amounts could be:)

Katia: $3.50

Mateo: $1.75

Step-by-step explanation:

Remember that a quarter = $0.25, 4 quarters = $1.00

after an hour of playing games in the arcade, Katia has $1.75 more than Mateo

lets say that Katia has (random amount)$3.50(14 quarters) and Mateo has $1.75 less than that.

$3.50 - $1.75 = $1.75

The circumference of the circle that Jason drew is gotten as; 62.80 inches

Since Jason lifted the pen and pulled the chain as far as it would reach before drawing a circle, then it means that;

radius of circle; r = 10 inches

Formula for circumference is;

C = 2πr

Thus;

C = 2 * 3.14 * 10

C = 62.80 inches

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Hey ! there

Answer:

Step-by-step explanation:

In this question we are provided with a cube having volume 27 cubic meters . And we are asked to find the value of n that is basically its edge .

For finding the value of n we need to know the volume of cube. So ,

[tex] \: \qquad \: \qquad \: \underline{ \boxed{ \frak{Volume_{(Cube)} = a {}^{3} }}}[/tex]

Where ,

SOLUTION : -

Substituting given volume that is 27 m³ and value of a as n in formula :

[tex] \quad \longrightarrow \qquad \: n {}^{3} = 27[/tex]

Applying cube root on both sides :

[tex] \quad \longrightarrow \qquad \: \sqrt[3]{n {}^{3} } = \sqrt[3]{27} [/tex]

We get ,

[tex] \quad \longrightarrow \qquad \:n= \sqrt[3]{27} [/tex]

We know that 3 × 3 × 3 is equal to 27 that means cube root of 27 is 3 . So ,

[tex] \quad \longrightarrow \qquad \: \blue{\underline{\boxed{\frak{ n = 3 \: m}}}} \quad \bigstar[/tex]

Verifying : -

Now we are checking our answer whether it is wrong or right by substituting value of n and equating it with given volume that is 27 cubic meters . So ,

Substituting values :

Therefore, our answer is correct .

Answer:

3

Step-by-step explanation:

Formula for volume of cube :

Here, V is given to be 27 m³.

Substitute the value of V in the formula.

Solving : Take the cubic root on each side.

The relative frequency table is:

Class         Frequency  Relative frequency

40 - 50         4                     0.1

50 - 60          6                     0.15

60 - 70           11                     0.18

70 - 80            9                     0.23

80 - 90              7                    0.18

90 - 100             3                   0.08

The relative frequency measures how often a value appears relative to the sum of the total values. The class width is 10. The class width is the difference between the upper and lower boundary (e.g. 100 - 90).

Frequency is the number of times the numbers in the class interval appear in the data set. Relative frequency is the frequency of a class interval divided by the total frequency of the data set.

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Answer:

4a^2+48a+288+(fraction)1800/a-6

Step-by-step explanation:

Answer:

arc BX = central angle BCX

inscribed BNX = 1/2 of central angle BCX

inscribed BNX = 1/2 of arc BX

Step-by-step explanation:

arc BX = central angle BCX

inscribed BNX = 1/2 of central angle BCX

inscribed BNX = 1/2 of arc BX

Answer:

See below ~

Step-by-step explanation:

Perimeter

Area

Answer:

Step-by-step explanation:

      The expanded value of n! is (n) * (n - 1) * (n - 2) until we reach one.

      Given:

4! - ((11-2)!) / 8!)

      Rewrite:

[tex]\displaystyle 4! - \frac{(11-2)!}{8!}[/tex]

      Subtract:

[tex]\displaystyle 4! - \frac{9!}{8!}[/tex]

      Expand:

[tex]\displaystyle 4*3*2*1 - \frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1}[/tex]

      Cancel out values that equal one in the fraction:

[tex]\displaystyle 4*3*2*1 - \frac{9}{1}[/tex]

      Multiply:

[tex]\displaystyle 24 - \frac{9}{1}[/tex]

      Simplify:

24 - 9

      Subtract:

15

Answer:

question is not correct

Step-by-step explanation:

3(x+2)=11+3x+5

3x+6=11+3x+5, once 3x is subjected from both sides it becomes unsolvable

Answer: Infinite solution

Step-by-step explanation: 3x + 6 = 11 + 3x - 5

                                             -3x

6 = 11 - 5

6 = 6

Answer:

1. Find the prime factorization of each number.

2. Write each number as a product of primes, matching primes vertically when possible.

3. Bring down the same numbers in each column and the remaining numbers in each column.

4. Multiply the factors to get the LCM.

for example the lcm of 24 and 36

= 24 = (2 × 2 × 2 × 3) = 2^3 × 3^1

 and 36 = (2 × 2 × 3 × 3) = 2^2 × 3^2

LCM(24, 36) = 2^2 × 3 × 2 × = 72

i hope my answer was helpful and please mark me as brainliest

Answer:

Step-by-step explanation:

Let Emma's age be 2x years, then:

Elsa's age is x years, also:

Bella's age is x - 2 years.

In one years time the sum of their ages

=  2x + 1 + x + 1 + x - 2 + 1

= 4x + 1  where x = Elsa's age now.

5 years before now

Sum of their ages

=  2x -5 + x - 5 + x - 2 - 5

= 4x - 17 where x = Elsa's age now,