The volume of an aquarium is 4,000 cubic feet and has a height of 10 ft. if a similar aquarium has a height of 1 foot, how many cubic feet would the smaller aquarium hold

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:

1st option

Step-by-step explanation:

the equation for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 7 and d = a₂ - a₁ = 3 - 7 = - 4 , then

[tex]a_{n}[/tex] = 7 - 4(n - 1)

Answer:

The answer is option A

Step-by-step explanation:

The solution is in the image

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:

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]

Answer:

3

Step-by-step explanation:

1/2 = 0.5

1/4 = 0.25

1/2 + 1/4

= 0.5 + 0.25

= 0.75

= 75/100

= 3/4

Quarter is 1/4.

3/4 can be written as 3 x 1/4

Hence,

1/2 + 1/4 is 3 times 1/4

1/2 + 1/4 = 3 quarters.

Answer:

3/4

Step-by-step explanation:

1*(1/2)= (2/2)*(1/2)= (2*1)/(2*2)=2/4

1/2+1/4=2/4+1/4=3/4

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!!!

Please give me brainliest!!!

Answer:

250 cm.

Step-by-step explanation:

Half = 50% so by proportion:

Half length of the rope =  75 *50/15

= 250

Answer:

250 cm

Step-by-step explanation:

15% to decimal:

15% = 15/100 = 0.15

Then, half of the lenght of rope is:

[tex](\frac{75}{0.15}) /2=500/2 = 250[/tex]

Hope this helps

Answer:
It will decrease cause there will be more deer. Deer eat blackberry bushes

Step-by-step explanation:

Answer:

It will decrease because there will be more deer

Step-by-step explanation:

Because of the lack of wolves, the deer population would increase. Since it would increase the amount of deer there would be less of the deer's food sources.

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,

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!

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.

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.

The formula of the function when the graph is analyzed will be y =1.5sin[(pi/4)x] - 3.

From the graph, the mid line is y = -3 and the amplitude will be:

= -1.5 - (-3)

= 1.5

From the mean line to the max is ¼ of a cycle. Therefore, the period will be:

= 4 × 2 = 8

Number of cycles in 2pi will be:

= 2pi/8

= pi/4

Hence, the formula of the function will be y= 1.5sin[(pi/4)x] - 3.

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Answer:

f(x)=1.5sin (pie/4 x)-3

Step-by-step explanation:

Kahn academy aproved

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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Answer:

11 1/2.

Step-by-step explanation:

23 / 2 = 11 remainder 1.
So it is 11 1/2.

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:

(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

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:

The base areas aren't same

Step-by-step explanation:

The base areas arent same

Answer:

He did not establish that heights are the same.

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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Step-by-step explanation:

$ 1: 2: 3: 4: 5: 6: 7: 7: in ratio

probability on two dice

1, 2, 3, 4, 5, 6, 7, 7.

The probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Let x be the probability of rolling a 1.

Ratios are 1:2:3:4:5:6

Then,

x + 2x + 3x + 4x +5x + 6x = 1

21x = 1

x = 1/21

The possible combinations of two rolls that total 7 are:

{(1,6) ; (2,5) ; (3,4) ; (4,3) ; (5,2) ; (6,1)}

The probability P of rolling a total of $7$ on the two dice is equal to the sum of the probabilities of rolling each combination.

[tex]\rm P = \dfrac{1}{21}\cdot\dfrac{6}{21}+\dfrac{2}{21}\cdot\dfrac{5}{21}+\dfrac{3}{21}\cdot\dfrac{4}{21}+\dfrac{4}{21}\cdot\dfrac{3}{21}+\dfrac{5}{21}\cdot\dfrac{2}{21}+\dfrac{6}{21}\cdot\dfrac{1}{21}\\\\=\dfrac{8}{63}[/tex]

Thus, the probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.

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If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32

This is the likelihood or chance that an event will occur. Mathematically;

Probability = expected/total

If you toss five fair coins, the total outcome will be:

T = 2^5
T = 32

If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32

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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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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:

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

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

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

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