240 Divided by8 is 30

The largest possible volume V is  4000[tex]cm^3[/tex]

Given,

Volume of a box = length × breadth × height= l× b× h

In this case the box have a square base. i.e.,  l = b

Volume V = [tex]l^2[/tex] × h

We using the formula of Surface area

The surface area of a square box

S = 2(lb +lh+ bh)

S = 2([tex]l^2[/tex] + lh + lh) since l=b

S = 2([tex]l^2[/tex] + 2lh)

Also, Given that the box is open top.

S = [tex]l^2[/tex] +4lh

And Surface Area of the box is 1200cm^2

1200 = [tex]l^2[/tex] + 4lh ....1

Making h the subject of formula

h = (1200 - [tex]l^2[/tex])/4l .....2

Volume is given as

V = [tex]l^2[/tex] × h

V = [tex]l^2[/tex] ×(1200 - [tex]l^2[/tex])/4l

V = (1200l - [tex]l^3[/tex])/4

the maximum point is at dV/dl = 0

dV/dl = (1200 - [tex]31^2[/tex])/4

dV/dl = (1200 - [tex]31^2[/tex])/4 = 0

[tex]31^2[/tex]= 1200

[tex]l^2[/tex] = 1200/3 = 400

l = √400

I = 20cm

Since,

h = (1200 - [tex]l^2[/tex])/4l

h = (1200 - [tex]20^2[/tex])/4×20

h = (800)/80

h = 10cm

Hence, The largest possible volume V is ;

V = [tex]l^2[/tex] × h

V = [tex]20^2[/tex] × 10 = 4000[tex]cm^3[/tex]

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(x² - 6 ) ( x + 3 ) is the completely factored form of this polynomial .

What is polynomial in maths?

= x³+3x² - 6x-18

= x² ( x + 3 ) - 6( x + 3 )

= (x² - 6 ) ( x + 3 )

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The range of this function f(x) = 3x + 9 is: B. {y | y > 9}.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.

Based on the given function f(x) = 3x + 9, we can reasonably infer and logically deduce that the range of this function in interval notation is given by:

Range = [10, ∞]

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The volume of the droplets in cubic meters would be = 1×10^-7 cubic meters.

Water droplets can be defined as the formation of small ball like structures with water due to the action of surface tension of liquid.

To convert cubic centimetres to cubic meters the following is carried out;

1 cubic meter = 1,000,000 cubic centimetres.

X cubic meters = 0.1 cubic centimetres

Make X cubic centimetres the subject of formula;

X cubic meters = 0.1× 1/1,000,000

X cubic meters = 1×10^-7.

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Answer:

Range is all real numbers.

Interval notation:

Range is

(-infinity,infinity)

Step-by-step explanation:

The range is all the y's on a graph of a function or all of the y's allowed to be used in an equation or able to be produced by the equation.

5x + 3y = 30

is a line. Except for a horizontal line, the range of any line is all real numbers. Somewhere on that line every single y value exists somewhere. You may put literally ANY value for y into that equation.

The range is all real numbers.

Using multiplication law of logarithm the value of logb 50 is 2.085

The logb 50 is rewritten in the multiples of 2, and 5 then laws of logarithm is applied to find the final answer

logb 50

= logb (2 * 5 * 5)

applying multiplication law of logarithm

= logb 2 + logb 5 + logb 5

= 0.401 + 0.842 + 0.842

= 2.085

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Answer:B

Step-by-step explanation:

A: Commutative property because the numbers in the parentheses change

B: Distributive property because you multiply the numbers out.

C: Commutative property because you change the numbers in the parentheses.

D: Associative property you move the parentheses to different numbers.

The number of weeks that it'll take Maru to fully pay off $43000 is 571.4 weeks.

From the information, Maru makes an initial down payment of $3000 then repays $70 per week and the total amount is $43000.

Let the number of weeks be represented as w.

This will be illustrated as:

3000 + (70 × w) = 43000

3000 + 70w = 43000

Collect like terms

70w = 43000 - 3000

70w = 40000

Divide

w = 40000 / 70

w = 571.4

The number of weeks is 571.4 weeks

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Answer:

I think it is $10.50 per hour. Hope this helps!!

Answer:

54°

Step-by-step explanation:

These are supplemental angles.  Supplemental angles add to 180

180-126 = 54

Answer:

Ounces of peanuts in the container

= 5 pounds × 16 ounces

= 80 ounces

Number of times Ronnie hit the ball

= 75% × 64 at-bat opportunities

= 48 times

Answer:

[tex]-9t^3+13t-1[/tex]

Step-by-step explanation:

Answer is attached.

The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁  , the correct option is (c) .

In the question ,

an explicit formula for the geometric sequence is given

that is aₙ = 16(-90)ⁿ⁻¹  ,

we know that the general explicit formula for the geometric sequence is given by

aₙ = a₁(r)ⁿ⁻¹

where aₙ is the nth term , r is the common ratio, a₁ is the first term of the sequence .

On comparing the given explicit formula with the general formula ,
we get ,

a₁ = 16

r = -90

So , the recursive formula is a₁ = 16 and aₙ = -90aₙ₋₁ .

Therefore, The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁  , the correct option is (c) .

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The measurement of each angle represented in terms of x is 156°

Here given the two angles : (13x-26)° and (9x+30)°.

We have to find each angle measurement.

From the given figure, it is clear that two angles are just vertically opposite angles.

So , we know that vertically angles are equal

So to find angles , we have to find x.

13x - 26 = 9x + 30

13x - 9x = 30 + 26

4x = 56

x = 56 / 4

x = 14

So the value of x = 14

Then we have to substitute the value of x in any of the given measurement.

By substituting x in (13x - 26)°

13 x 14 - 26

182 - 26

= 156

Similarly by substituting x in (9x + 30) °

9 x 14 + 30

= 126 + 30

= 156°

Therefore, the measurement  of each angle is 156°.

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The expression that represents the amount in dollars that each paid is (a) 1.2s - 1.2.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, Su's Sushi is $2 more than Darbi sushi and the cost of Su's sushi is represented by s.

Let the price of Darbi's sushi is $x.

Then, the price of Su's sushi is
s = x + 2

x = s -2

The total cost is:

  x + s

= s -2 + s

= 2s -2

Since they divided the total cost evenly, the cost each paid is:

(2s-2)/2

= s -1

Now, the cost after paying a 20% tip is:

(s - 1) + 20% of (s - 1)

= s- 1 + 20(s-1)/100

= s-1 + 0.2s - 0.2

= 1.2s - 1.2

Hence, the expression that represents the amount in dollars that each paid is (a) 1.2s - 1.2.

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Answer: x=-1 & y=2

Step-by-step explanation:

x = -3y+5

^^^substitute this equation into x in the second equation

(-3y+5)+9 = 4y

-3y+14 = 4y

Add +3y on both sides

14 = 4y+3y

14 = 7y

divide both sides by 7

y = 2

substitute y into either equation (I'm doing the first one)

x = -3(2)+5

x = -6+5

x = -1

The given quadratic function has two real zeros.

We are given a function. The function is quadratic in nature.  We need to check whether the given quadratic function has one, two, or no real solutions. We will use the quadratic formula to determine the answer. The equation of the quadratic function is given below.

f(x) = 4x² + 5x - 29

The general form of a quadratic equation is ax² + bx + c. The values of the variables a, b, and c for the given equation are 4, 5, and -29, respectively. The quadratic formula is given below.

x = (-b ± √D)/2a

The variable "D" represents the discriminant of the quadratic equation. If the value of D is less than zero, then no real roots exist. If the value of D is equal to zero, then only one real root exists. If the value of D is greater than zero, then two real roots exist. The formula for discriminant is D = b² - 4*a*c. We will calculate the discriminant for the given equation.

D = b² - 4*a*c

D = 5² - 4*(4)*(-29)

D = 25 + 464 = 489

The value of the discriminant is positive, so the function has two real roots.

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In the interval June to August and December to February rainfall decreasing.

What is average number of days?

7 days make up a week, there are roughly 365 days in a year, and there are 24 hours in a day. By adding all of your numbers together and dividing by the total amount of numbers, you can arrive at an average. Thus, 132 is the average amount of time periods when joined together.

From the given graph, in the interval June to August and December to February the average number of days of rainfall are decreasing.

Hence, June to August and December to February rainfall decreasing.

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The experiment is a binomial experiment as it had two outcomes which are success and failure.

A binomial experiment is one that has a fixed number of independent trials with only two outcomes. For example, the outcome could be a yes or no response.

A binomial experiment is a statistical test that has the following characteristics: The experiment consists of n trials that are repeated. Each trial has only two possible outcomes. One of these outcomes is referred to as a success, while the other is referred to as a failure. On each trial, the probability of success, denoted by P, is the same.

Tossing a fair coin n times, for example, with success defined as "heads up":

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Answer:

A would save Brenda the most money

Step-by-step explanation:

Answer:

Rewrite the equation as  w+ 2/5= 3/4

Move all terms not containing w to the right side of the equation.

so if u do that you should get your answer 7/20

Step-by-step explanation:

You need 5 gallon of the 45% acid solution 35 gallon of the 85% solution to get 40  gallon at 80%.

Let x represent the number of liters

0.45x+0.85(40-x) = 0.8(40)

0.45x+34-0.85x = 32

-0.4x = -2

Divide both sides by -0.4

x = -2/-0.4

x = 5

You need 5 gallon of the 45% acid solution

Gallon of the 85% solution to get 40  gallon at 80% = 40-5 = 35 gallon

Therefore 5 gallon and 35 gallon are needed.

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The trigonometric identities are verified that they are true.

What are trigonometric expressions?

Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.

1. LHS = sec x [ sec x - cos x]+(sin x+ cos x)/sin x- cot x

       = sec²x - sec x cos x +(sin x+ cos x)/sin x - cos x/sin x

       = sec²x - cos x/cos x +(sin x+ cos x- cos x)/sin x

       = sec²x - 1 + sin x /sin x

       = sec²x - 1 +1

      = sec²x

      = RHS

2. LHS = cos (π-Θ)+ sin (π/2 + Θ)

           = - cos Θ + cos Θ

           = 0

          = RHS

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The balance (future value) in Malik's account after 2 years of investing $7,550 at 1.95% compounded annually is $7,847.32.

The future value is the compounded present value of an investment or periodic deposit.

The future value can be determined using the FV formula, FV table, or an online finance calculator as below.

N (# of periods) = 2 years

I/Y (Interest per year) = 1.95%

PV (Present Value) = $7,550

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $7,847.32

Total Interest = $297.32

Thus, Malik's account balance (future value) after 2 years will be $7,847.32.

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Answer:

x = -1

Step-by-step explanation:

6x +5 = -7x - 8

6x +7x = -8 -5

13x = -13

13/13 x = -13/13

x = -1

The  expression G  is an integer when it's evaluated.

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

Negative numbers and all entire numbers are both considered integers. Accordingly, a set of integers can be formed by adding negative numbers as well as whole numbers.

Consider 9+(-3).

9+(-3)

Remove parenthesis

=9-3 = 6

6 is an integer.

So,  the  expression G  is an integer when it's evaluated.

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Answer:

Option 3

Step-by-step explanation:

[tex]-\frac{7}{5} =-\frac{14}{10} =-1.4[/tex]

[tex]-1\frac{3}{10} = -\frac{13}{10}=-1.3[/tex]

∴ ascending order of these rational numbers

[tex]=-1.5, -1.4, -1.3, -1.2[/tex]

[tex]= -1.5,-\frac{7}{5}, -1\frac{3}{10}, -1.2[/tex]

By solving a system of equations we will see that the exponential function is:

g(x) = 122.347*(0.589)^x

We know that our function is of the form:

g(x) = a*(b)^x

We also know that g(3)=25 and g(7)=3, then we can write:

a*(b)^3 = 25

a*(b)^7 = 3

So we have a little system of equations.

Taking the quotient between the second and first equations we get:

(a*(b)^7)/(a*(b)^3) = 3/25

b^4 = 3/25

b = (3/25)^(1/4) = 0.589

Replacing that in the first equation we get:

a*(b)^3 = 25

a*(0.589)^3 = 25

a = 25/(0.589)^3 = 122.347

The exponential function is:

g(x) = 122.347*(0.589)^x

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Give the guy above me a brainliest!!

The units price are:

Then brand A is the better option.

If you know that a set of N items has a price P, then the unit price is given by the quotient between the price and the number of items that you get, N.

For Brand A, we know that there are 25 spoons for $1.99, then in this case the unit price is:

a = $1.99/25 = $0.0796

For Brand B the set has 42 spoons for $3.89, then the unit price is:

b = $3.89/42 = $0.0926

So we can see that Brand A has a lower unit price, meaning that is a better option.

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