You can convert gallons to liters by using a factor of 3.79. That is, 1 gallon is about 3.79 liters. About how many liters are in 37 gallons? is your answers an underestimate or overestimate explain

Answer: 5w=w^3

Step-by-step explanation:

This is because the product means multiplication and so it would be 5w and then is in math is the same as equals so you have an equal sign and then it would w to the third power.

Answer:

I think 48!

Step-by-step explanation:

Solution of the expression are,

⇒ x = - 5, x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ [tex]12^{x^{2} + 5x - 4} = 12^{2x + 6}[/tex]

Now, We can compare as;

⇒ x² + 5x - 4 = 2x + 6

Solve for x as;

⇒ x² + 3x - 10 = 0

⇒ x² + 5x - 2x - 10= 0

⇒ x (x + 5) - 2 (x + 5) = 0

⇒ (x + 5) (x - 2) = 0

⇒ x = - 5, x = 2

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Step-by-step explanation:

(x+2)³ - (x)³ = 56

(x²+4x+4) (x+2) - (x)³ = 56

x³ + 2x² +4x²+ 8x + 4x + 8 -x³ = 56

6x² + 12x + 8 = 56

6x² + 12x - 48 = 0

x² + 2x - 8 = 0

(x+4) (x-2) = 0

x = -4

x = 2

the integers are 2 and 4

The required two consecutive positive even integers are 2, and 4.

A number which is not a fraction, and it is a whole number.

For example -1,-2,-3,0,1,2 etc. are integers.

Let two consecutive even numbers are x and x+2,

According to given condition, the difference of cube of x and x+2 is 56,

Implies that,

(x+2)³ - (x)³ = 56

x³ + 8 + 3.x².2+ 3.x.2² -x³ = 56

6x² + 12x - 48 = 0

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x = -4, 2

Both the integers are positive, so the value of x can't be negative.

Therefore, x=2 and x+2 = 4

So the integers are 2 and 4.

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Answer: $6.16

Step-by-step explanation:

Starting Amount: $30

30-6.97=23.03

23.03-11.37=11.66

11.66-5.50=6.16

Answer:

Step-by-step explanation:

You will use Pythagoreans Theroy. which is going to give you the anwser of square root of 13.

Answer:

3.6

Step-by-step explanation:

We can use the Pythagorean Theorem for this problem which is a²+b²=c² .

So we'll make 2 "a", and 3 "b". So 2*2=4. Then 3*3=9

4+9=13

Now we need to find the square root of 13.

√13 = 3.60555127546399

Let's now round that number, which is going to be 3.6

i) The volume of the candle is 48047.96 cubic cm. ii)the radius of the candle is 10.468 cm and iii)Volume of empty spaces in the box is 8749.73 cubic cm.

i) Slant height of the Pyramid = 39cm

Base length = 30 cm

Height of the pyramid part = √(39²-30²) = 24.92 cm

Volume of the pyramid part = 30 × 30 × 24.92 ÷ 3 = 7475.96 cm³

Height of the candle = 70 cm

Height of the cuboid= 70 - 24.92 = 45.08cm

Volume of the cuboid = 30 × 30 × 45.08 = 40572 cubic cm

Total volume of the candle = 7475.96 cm³ + 40572 cm³ = 48047.96 cm³

ii) Volume of the spherical candle = 0.1 × 48047.96 cm³ = 4804.79 cm ³

Now let the radius be r.

Hence 4/3 πr³ = 4804.79

or, r = 10.4679.. cm

or, r ≈ 10.468 cm

iii) Dimensions of the box = 10.468 × 2 = 20.94 cm

Height = 20.94cm

Width = 10.468 × 4 = 41.87 cm

Volume of the box = 41.87 × 20.94 × 20.94 = 18359.31 cubic cm

Volume of the candles = 4804.79 cm ³× 2 = 9609.58 cm³

Empty space in the box = 8749.73 cm³

Hence the empty spaces is 8749.73 cm³

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Answer: A

Step-by-step explanation: The dot is a filled-in circle, meaning it has to be A, B, or E. Then, B is saying that the arrow is going left, so that's wrong. E is saying that it is just 6 instead of -6, which leaves us with A.

hope this helps!

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The liters of water that the bucket hold is 5/7 liters of water.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 4/5 of a liter of water filled 4/7 of a bucket. The liters that it can hold will be:

= 4/7 ÷ 4/5

= 4/7 × 5/4

= 20 / 28

= 5/7

It can hold 5/7 liters.

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The fire truck, a mile away, traveling at 44 miles per hour towards the the bush fire, which is also traveling towards at 3 miles per hour towards it, reaches the fire's front in 1/47 hours or approximately 76.6 seconds

There are 60 seconds in a minute and 60 minutes in an hour, which makes 60 × 60 = 3600 seconds in one hour.

The rate at which the bush fire is moving, v₁ = 3 miles per hour

The direction the bush fire moves = Towards the fire station

Distance of the bush fire from the fire station, d = 1 mile

Speed of the fire truck, v₂ = 44 miles per hour

The equation that gives the time, t, the fire truck reaches the fire front is presented as follows;

v₁·t + v₂·t = d

Which gives; 3 × t + 44 × t = 1

47 × t = 1

[tex]t = \dfrac{1}{47}[/tex]

The time it takes the fire truck to reach the bush fire is 1/47 of an hour, which is approximately 76.6 seconds

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Answer: lb=48

l(l-8)=48

l^2–8l=48

l^2–8l-48=0

l^2–12l+4l-48=0

l(l-12)+4(l-12)=0

l=12inches &

b=12–8=4inches

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

cancel out the dilation by multiplying it by the reciprocal

18 x 3/2

27

I'm 80% sure

Answer:

12 is the answer

Step-by-step explanation:

you need to multiply the pre-image (the letters without an apostrophe beside it) with the dilation number (2/30)

The total cost of the car is 26,648.5 dollars.

The Latin word "per centum," which means by the hundred, is where the word "percent" comes from. Percentages are fractions with a denominator of 100. It is a relationship, in other words, where the value of the whole is always taken to be 100.

The cost of the car = $22300

The sales tax is given by

= 7% × 22300

= (7/100) × 22300

= 7 × 223

= 1561

The state requires a registration fee to be given by

= 12.5% × 22300

= (12.5/100) × 22300

= 12.5 × 223

= 2787.5

The total cost of the car is given by

Total cost = cost of car + sales tax + state registration fee

= 22300 + 1561 + 2787.5

= 26,648.5

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Considering the polynomial f(x) = x^4  - 16x³ + 70x² + 48x - 219, we have that:

a) The zeros are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

b) The linear factors are: (x + 1.995)(x - 1.995)(x - 8 + 3i)(x - 8 - 3i).

c) The solutions to f(x) = 0 are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

The given zero of the polynomial is:

8 + 3i

Hence it's conjugate is also a zero, that is:

8 - 3i.

Thus the first two factors are given as follows:

(x - 8 - 3i)(x - 8 + 3i) = x² - 16x + 64 + 9i² = x² - 16x + 55.

Then the polynomial can be written as follows:

x^4  - 16x³ + 70x² + 48x - 219 = (ax² + bx + c)(x² - 16x + 55).

As a fourth order polynomial can be the product of two second order polynomials. Applying the distributive property to the right side of the equality, we have that:

x^4  - 16x³ + 70x² + 48x - 219 = ax^4 + x³(b - 16a) + x²(55a + c - 16b) + x(55b - 16c) + 55c.

Then the coefficients are given as follows:

Hence the other two factors are given as follows:

x² - 3.98 = 0

x = ± sqrt(3.98)

x = ± 1.995.

The linear factors are:

(x - x')(x - x'')(x - x''')(x - x'''').

In which x', x'', x''' and x'''' are the roots.

The solutions to f(x) = 0 are the roots.

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A description of the quadrilateral VWXY that has equal length sides and equal length diagonals is that the quadrilateral is a square

A quadrilateral is a polygon that has four sides and four vertices or corners, such that a quadrilateral ABCD has sides AB, BC, CD, and AD, and interior angles ∠A, ∠B, ∠C, and ∠D

The given description of the quadrilateral VWXY are;

VW = 15, WX = 15, XY = 15, YV = 15

The lengths of the sides of the quadrilateral VWXY are the same

The length the diagonals are the same;

VX = WY = VX = WY

The properties of a square are;

The interior angles are congruent and equal to 90°

The four sides have equal length

Opposite sides of a square are congruent

The length of the diagonals are the same

The the same length diagonals of quadrilateral indicates that the quadrilateral can be either a square or a rectangle

The property of the quadrilateral of equal length sides indicate that the quadrilateral is a square.

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The total number of logs that are in the pile is 195.

From the information, the Logs are stacked in a pile where the bottom row has 24 logs, the next row has 23 logs, the following row has 22 logs and the pattern continues until the top row has 15 logs.

To calculate the total number, it simply means that you've to add the numbers for 15 to 24. This will be:

= 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24

=195

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The quotient of [13/(5-i)] in the form of (a + bi) is (2.5 + 0.5i).

A complex number is a number of the form a + bi, where a and b are real numbers

Given,

13/5-i

Rationalize the number

Multiply numerator and denominator by 5+i

13/5-i×5+i/5+i

13(5+i)/25+1

65+13i/26

65/26+13/26i

2.5+0.5i

Hence, the quotient of [13/(5-i)] in the form of (a + bi) is (2.5 + 0.5i).

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The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:

Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error

A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.

In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.

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The rocket reaches its maximum height at 1.25 second(s) after launch

The maximum height reached by the object is 32 feet.

The function is given as

h(t) = -16t² + 40t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 40

Set to 0

-32t + 40 = 0

So, we have

32t = 40

Divide by 32

t = 1.25

Hence, the time is 1.25 seconds

In (a), we have

t = 1.25

Substitute t = 1.25 in h(t) = -16t² + 40t + 7

h(1.25) = -16(1.25)² + 40(1.25) + 7

Evaluate

h(1.25) = 32

Hence, the maximum height is 32 feet

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Answer:

Step-by-step explanation:

3

Answer:

Step-by-step explanation:

If Tina is training for a biathlon. She runs the downhill portion of the course at 10 miles per hour.

(s-5) = speed on level ground

Time = distance /speed

Level time + downhill time = 1 hr

Hence,

3/(s-5) + 4/s =1

multiply by s(s-5), resulting in

3s + 4(s-5) = s(s-5)

3s + 4s - 20 = s^2 - 5s

Arrange as a quadratic equation on the right

0 = s^2 - 5s - 7s + 20

s^2 - 12s + 20 = 0

factors to

(s-2)(s-10) = 0

s = 10 mph

Therefore the speed is 10mph.

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a) i) P(x < 5) = 0.842

ii) P(X ≥ 7) = 0.0143

b) Given that P(X = 0) = 0.05, the value of p to 3 decimal places is; 0.221

c) Given the variances of x is 1.92 , the possible values of p are; 0.2 and 0.8

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.

The formula for binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

p = probability of "success"

n = number of trials, or the sample size

x = the number of "successes"

a) We are given;

p = 0.25

n = 12

Thus;

i)P(x < 5) using appendix tables online gives us;

P(x < 5) = 0.842

ii) P(X ≥ 7) can be expressed as;

1 – P(X ≤ 6)

Thus, using appendix tables online, we have;

P(X ≥ 7) =  1 – 0.9857

P(X ≥ 7) = 0.0143

b) We are given that  P(X = 0) = 0.05. Thus;

(1 - p)¹² = 0.05

1 - p = ¹²√0.05

p = 0.221

c) Variance is given by the formula;

Var = np(1 - p)

Var = 12p(1 - p) = 1.92

12 - 12p² = 1.92

12p² - 12 + 1.92 = 0

Using online quadratic equation calculator gives;

p = 0.2 or 0.8

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Complete question is;

a) A random variable has a Binomial distribution with n=12.

Given that p=0.25, find

(i) P(x < 5) ( From the table OF Appendix A)

(ii) P(x ≥ 7) ( From the table OF Appendix A)

b) Given that P(X = 0) = 0.05, find the value of p to 3 decimal places.

c)Given the variances of x is 1.92 , find the possible value of p

The dimensions that minimize the cost of construction are : 10/∛3 in,     10/∛3 in, 2 × [tex]3^{2/3}[/tex] in

Let the side of the square base be 'a'

The height of the box be 'h'

Then, the volume of the box is given by :

= (area of square base) × height

= a² × h

Given, volume of the box = 200 in³

⇒ a² × h = 200

⇒ h = 200/a²

The area of base = a²

Given, the cost of base is : 6 cents/in²

⇒ cost of square base with side 'a' = 6 × a² cents

The area of front of the box, which is a rectangle with dimensions (h×a) is:

= a × h

Given, the cost of decorating the front side of the box = 11 cents/in²

⇒ cost of decorating the front side of the box = (a × h) × 11 cents

The area of the other three sides of the box, which comprises of three rectangles of dimensions (h×a) is :

= 3(a  × h)

Given, cost of remaining sides = 3 cents/in²

Cost of remaining 3 sides = 3(a × h) × 3 = 9(a  × h) cents

Total cost = Cost for base + Cost for front + Cost for other sides

= 6a² + 11ah + 9ah

= 6a² + 20ah

Substitute h in terms of a² in the total cost,

Total cost, T = 6a² + 20a(200/a²) = 6a² + 4000/a

Differentiate T w.r.t a :

dT/da = 6(2a) + 4000(-1/a²)       = 12a - 4000/a²

For minimization, dT/da = 0

⇒ 12a - 4000/a² = 0

⇒ 12a = 4000/a²

⇒ a³ = 4000/12

⇒ a³ = 4×1000/4×3

⇒ a³ = 1000/3

⇒ a = ∛(1000/3)

⇒ a = 10/∛3

Then, h = 200/a² = 200/(10/∛3)² = 2 × [tex]3^{2/3}[/tex]

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The pairs of equations and their responses are below

(1/5)^2 + 1 and 2 12/25 No

(1 + 1/4)^2 and 2 - 7/16 Yes

This is done by solve both sides of the equation. If they have same answer then they can form equation. If otherwise they they cannot form equation

solving the first expressions

left hand side

(1/5)^2 + 1

= 1/25 + 1

= 26/25

right hand side

2 * 12/25

= 24/25

comparing the two sides shows that  the 26/25 ≠ 24/25

solving the second expressions

left hand side

(1 + 1/4)^2

= (5/16)^2

= 25/16

right hand side

2 - 7/16

= 25/16

comparing the two sides shows that  the 25/16 = 25/16solving the first part

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Diagonalization is the process of converting a matrix into diagonal form. Diagonal matrices plainly depict a matrix's eigenvalues. A diagonal matrix is a square matrix in which all of the elements except the primary diagonal members are zero.

The primary goal of diagonalization is to determine the functions of a matrix. If P1AP = D, where D is a diagonal matrix, the entries of D are the eigenvalues of matrix A, and P is the matrix of A's eigenvectors.

If and only if the nilpotent component of a matrix is zero, it is diagonalizable. In other words, a matrix is diagonalizable if no nilpotent portion exists in its Jordan form.

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The maximum profit for soybeans is 30 acres and the maximum profit for wheat is 60 acres.

The maximum profit from these 70 acres is $12600

Mathematically profit is considered the amount of gain from any business activity. Whenever a shopkeeper sells a product, his motive is to take advantage of the buyer in the name of profit. .

Given,

Total land = 70 acres

For soyabeans,

1 acre = $60 for 3days

⇒Profit=$180

Foe wheat,

1 acre = $30 for 4days

⇒Profit=$100

Working days must ≤ 120

Preparation cost ≤ 1800

For soyabeans,

60$ for 3 days

1800$ for ?

x = (1800×3)/60

x = 90 days

1 acre = 3 days

? = 90 days

x = 90/3

x = 30 acres

For wheat,

30$ for 4 days

1800$ for ?

x = (4×1800)/30

x = 240 days

1 acre for 4 days

? for 240 days

x = 240/4

x = 60 acres

The maximum profit for soybeans is 30 acres and the maximum profit for wheat is 60 acres.

Maximum profit is:

1 acre for 180$

70 acres for ?

x = (180×70)/1

x = $12600

The maximum profit from these 70 acres is $12600

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The inverse of the cubic function is f⁻¹(x) = ∛(x+5/6) and the inverse relationship is valid

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

f(x) = x³-5/6

y = x³-5/6

make x the subject:

x³= y+5/6

x = ∛(y+5/6)

x = f⁻¹(y) = ∛(y+5/6)

Thus, f⁻¹(x) = ∛(x+5/6)

To confirm the inverse relationship using composition.

Let g(x) = f⁻¹(x)

For valid confirmation f(g(x)) must be equal to g(f(x))

Let's confirm:

f(g(x)) = f(∛(x+5/6))

          = ( ∛(x+5/6) )³ - 5/6

         = x+5/6-5/6

        = x

g(f(x)) = g(x³-5/6)

         = ∛(x³-5/6+5/6)

         = ∛x³

         = x

Since  f(g(x)) = g(f(x)) then the inverse is valid

Therefore, the inverse of the cubic function is ∛(x+5/6) and the inverse is valid

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Answer:

4(2x +1)(2x-3)

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

We have already determined that the first person is just a place holder. Therefore, there is only one choice for the first spot.

The number of ways "n" number of people can sit around a circular table will be (n - 1)! thus 5 people can sit in 24 ways.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

The number of ways that n person can sit around a table is written as,

n!/n=n(n−1)!/n=(n−1)!

As per the given n = 5

(5 - 1)! = 4! = 4 x 3 x 2 = 24 ways

Hence "The number of ways "n" number of people can sit around a circular table will be (n - 1)! thus 5 people can sit in 24 ways".

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Answer:

6x-

7y

=

-11

6x-7y=-11