A large container holds 4.7 gallon of water. Use the following information to convert this amount of water to liters.1 gallon =4 quarts 1L =1.057 quarts

Answer:

3?

Step-by-step explanation:

Answer:

The square root of 34 with one digit decimal accuracy is 5.8.

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

Answer:

3, -1, 1 and 0

Step-by-step explanation:

An expression is undefined when the denominator is equal to 0 as you cannot divide by 0 in Mathematics. Therefore you are looking for the values of x which will result in either or both denominators equaling 0.

This simply means finding the solutions to the quadratics in the denominators.

First equation is \(x^{2} -2x-3\).

One way you can solve this equation is using factorization (putting the equation into two sets of brackets which show the solutions) which puts the equation in the solvable form: (ax+b)(cx+d).

Firstly, we can deduct that a and c are both 1 as ax and cx multiply to give the x^2 term, the co-efficient of which is 1. Since only 1 and 1 can multiply to 1, a and c must both be 1.

Now, in order to work out b and d we need to find the possible factor combinations for -3 as b and d multiply to give the constant term. The only possible combination is 1x3, therefore b and d can either be -1 and 3, or -3 and 1.

To work this out we look at the x term. We see it is -2x. b and d will add to give the co-efficient.

Therefore we know that they are -3 and 1 as -3+1 = -2

We now have the equation: (x+1)(x-3)

Setting it to 0 gives us: \((x+1)(x-3)=0\)

This tells us the solutions to this equation are x= -1 and x= 3 as substituting these values for x will result in a bracket adding to 0 so both those options can be selected as your answer.

The second equation \(2x^{2} +2x\) can be approached with a slightly easier method. Both terms have a 2x, so we can condense it into a bracket by dividing both terms by the common factor and moving the factor outside. Factorizing this equation in this fashion gives us: \(2x(x+1)=0\)

Now our solutions are x=0 and x=1.

Combined from both equations the correct options are: 3, -1, 1 and 0.

Hope this helped!

Answer:

3 * 3

4    1

Step-by-step explanation:

To convert division problems with fraction into multiplication problems use the KCF rule

Answer:

\(\frac{27}{8}\)

Step-by-step explanation:

using the rules of  exponents/ radicals

• \((\frac{a}{b}) ^{-m}\) = \((\frac{b}{a}) ^{m}\)

• \(a^{\frac{m}{n} }\) = \((\sqrt[n]{a}) ^{n}\)

then

\((\frac{16}{81}) ^{-\frac{3}{4} }\)

= \((\frac{81}{16}) ^{\frac{3}{4} }\)

= \(\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }\)

= \(\frac{3^3}{2^3}\)

= \(\frac{27}{8}\)

Answer:

D. \( 4\frac{2}{5} \)

Step-by-step explanation:

Area of fabrics = 2¾ square yards

Width of fabrics = ⅝ yard

Length of fabrics = x

Area = length * width

Therefore:

2¾ = ⅝*x

Change the mixed fraction to improper fraction

\( \frac{11}{4} = \frac{5x}{8} \)

Cross multiply

\( 4*5x = 11*8 \)

\( 20x = 88 \)

Divide both sides by 20

\( \frac{20x}{20} = \frac{88}{20} \)

\( x = \frac{22}{5} \)

\( x = 4\frac{2}{5} \)

\( length = 4\frac{2}{5} \)

Answer:

Option 4.

Step-by-step explanation:

The only viable choice is the fourth option, this is because it is the only choice that adds up to 180:

35  + 65 + 80 = 180

And all interior angles must add up to 180 in a triangle.

Hope this helps!

Answer:

b = 34°

Step-by-step explanation:

b + 115° + 31° = 180°

b + 146° = 180

b = 180° - 146°

b = 34°

Answer:

\( {b}^{o} = {34}^{o} \)

Step-by-step explanation:

Hint :

Sum of angles = 180°

Simplify :

\( {115}^{o} + {31}^{o} + {b}^{o} = {180}^{o} \)

\( {146}^{o} + {b}^{o} = {180}^{o} \)

\( {b}^{o} = {180}^{o} - {146}^{o} \)

\( {b}^{o} = {34}^{o} \)

Answer:

27

Step-by-step explanation:

15x-31 = 9x+11

6x-31 = 11

6x = 42

x = 7

15x -31 + 9x + 11 + s = 180

15(7) -31 + 9(7) + 11  + s = 180

105 - 31 + 63 + 11 + s = 180

153 + s = 180

s = 27

Answers:

See the diagram below.

======================================

Explanation:

Let's say we replaced 3x with y for now.

3x+1 is the same as y+1

So we have y+1 = 10

To isolate y, we undo the addition and subtract 1 from both sides.

That means -1 will go in the first two boxes.

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

After that step is done, we have y = 9 which is the same as 3x  = 9 after replacing y with 3x.

3x means "3 times x".

To undo the multiplication, we divide both sides by 3.

Therefore, boxes 3 and 4 will have "3" each.

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

Box 5 has 3 as well because 9/3 = 3.

The final answer is x = 3.

As a check,

3x+1 = 10

3*3+1 = 10

9+1 = 10

10 = 10

It works out.

Refer to the diagram below.

The students in 8th class who choose music are 16 in number,

The students in 7th class who choose music are 32 in number

The total who choose world language is 270

The totals who are in 7th grade be 194

The number of students who choose world language in 7th class are 162

Let x be the students in 8th class who choose music

x+108=124

x=124-108

x=16 students

Now  y be the students in 7th class who choose music

16+y=48

y=48-16

y=32

Let z be the total who choose world language

48+z=318

z=318-48

z=270

Now the totals who are in 7th grade be A

124+A=318

A=318-124

A=194

B be the number of students who choose world language in 7th class

Now 32+B=194

B=194-32

B=162

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Answer:

y"= 2 wich is positive

Step-by-step explanation:

Step-by-step explanation:

Our equation is: y=(x-3)²

x should be replaced by x-4

y=(x-3)²

y=[(x-4)-3]²

y=(x-4-3)²

y=(x-7)²

The graph is still a parabola but with a different vertex

The vertex here is :

y= (x-7)²

y= x²-14x-49

y'= 2x-14

solve y'=0

2x-14=0

2x=14

x=7

You can easily find it without derivating by dividing -14 by -2

since: x²-14x-49

a=1 b= -14  c=-49

-b/2a = 14/2 = 7

the image of 7 is:

y=(7-7)² = 0

so the coordinates of the new vertex are (7,0) and it's a maximum

since y">0

y'= 2x-14

y"= 2 wich is positive

Answer:

X ~ (350, 0.5)

0.00009

Step-by-step explanation:

Given that:

Daily passenger volume = 350

Since both airlines A and B have equal probability ;

p = 0.5

n = 350

X ~ (n, p)

X ~ (350, 0.5)

B.)

Mean, m= np = 350 * 0.5 = 175

Standard deviation, s = sqrt(np(1-p)) = sqrt(350*0.5*0.5) = sqrt(87.5)

Obtaining standardized score, Z

Z = (x - m) / s

x = 210

Z = (210 - 175) / sqrt(87.5)

Z = 35 / sqrt(87.5)

Z = 3.74

P(Z > 3.74) = 0.00009 (Z probability calculator)

The equation (x + 3)²+ (y - 5)² = 16 represents a circle with center Z(-3,5) and a radius of 4 units.

The correct option is D.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

Given:

A circle with center Z(-3,5) and a radius of 4 units.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

So, the equation is,

(x + 3)²+ (y - 5)² = 4²

(x + 3)²+ (y - 5)² = 16

Therefore, the equation is (x + 3)²+ (y - 5)² = 16.

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Answer:

i believe your answer would be 5 and 3, FD

Step-by-step explanation:

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

LM = 1.5

LN = 3

Step-by-step explanation:

From the question given:

M is the midpoint of LN

LM = 3x

LN= 2x + 2

LM =.?

Next, we shall determine the value of x. This is illustrated below:

Since M is the midpoint of LN, it means that when we divide LN by 2 the result will be LM i.e

LN /2 = LM

With the above formula, we can obtain the value of x as follow:

LN= 2x + 2

LM = 3x

x =..?

LN /2 = LM

2x + 2/ 2 = 3x

Cross multiply

2 × 3x = 2x + 2

6x = 2x + 2

Collect like terms

6x - 2x = 2

4x = 2

Divide both side by 4

x = 2/4

x = 0.5

Finally, we can obtain LM and LN as follow:

LM = 3x

x = 0.5

LM = 3 × 0.5

LM = 1.5

LN= 2x + 2

x = 0.5

LN = 2(0.5) + 2

LN = 1 + 2

LN = 3

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Using it's concept, it is found that:

a) For the Jumping Jackrabbits, the MAD is of 3.6 and for the Leaping Lizards, the MAD is of 6.8.

b) Due to the higher value of the MAD, the Leaping Lizards have less consistent scores than the Jumping Jackrabbits.

Item a:

For the Jumping Jackrabbits, the mean and the MAD are given by:For the Jumping Jackrabbits, the MAD is of 3.6 and for the Leaping Lizards, the MAD is of 6.8.

M = (70 + 65 + 72 + 80 + 73)/5 = 72

MAD = (|70 - 72| + |65 - 72| + |72 - 72| + |80 - 72| + |73 - 72|)/5 = 3.6.

For the Leaping Lizards, the mean and the MAD are given by:

M = (61 + 47 + 70 + 63 + 54)/5 = 59

MAD = (|61 - 59| + |47 - 59| + |70 - 59| + |63 - 59| + |54 - 59|)/5 = 6.8.

For the Jumping Jackrabbits, the MAD is of 3.6 and for the Leaping Lizards, the MAD is of 6.8.

Item b:

Due to the higher value of the MAD, the Leaping Lizards have less consistent scores than the Jumping Jackrabbits.

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Answer:

$199.89

Step-by-step explanation:

The bike costs 266.52

The parents are contributing one fourth of this (1/4)

We need to find 1/4th of 266.52

Divide 266.52 by 4 to find out how much Justin's parents are contributing to the bike

The answer is 66.63

Now subtract 66.63 from 266.52

Justin has to pay a total of 199.89

The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.

However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.

This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.

As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.

It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.

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Answer:

5 ft

Step-by-step explanation:

Using the formula,

A = 6a²

a² = A/6

a = √(A/6)

a =√(150/6)

a = √25

a = 5

The area of a 2D form is the amount of space within its perimeter. The length of the edge of the cube is 5 ft. The correct option is B.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The total surface area of a cube is 6 times the area of a face which is equal to the square of side of the cube. Therefore, the total surface area of the cube is,

Total surface area of cube = 6a²

Given that the total surface area of the cube is 150 square feet. Therefore,  the length of the side of the cube can be written as,

Total surface area of cube = 6a²

150 square feet = 6a²

150 square feet / 6 = a²

25 ft² = a²

a = √(25 ft²)

a = 5 ft

Hence, the length of the edge of the cube is 5 ft.

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1) If the sales of McDonald's for one year is $650,000 and increasing at 4% annually (exponential growth), their sales after 5 years will be $790,824.

2) If the population of a school is 800 students and is increasing at a rate of 2% per year (exponential growth), after 6 years, the population will be 901.

3) With 70 northern sea otters growing at a rate of 18% annually (exponential growth), after 4 years, the population will be 136.

4) If the annual sales for a furniture stores are $375,000 and increasing (exponential growth) at a rate of 6.75% each year, the sales after 9 years will be $675,060.

5) If the population of Indiana showed an annual growth rate of 0.6% (exponential growth) and their population in 1999 was 273,000, the population in 2007 will be 286,383.

Exponential growth refers to the consistent increase in quantity over time and at a constant growth rate.

Exponential growths are modeled using the exponential growth function y = a(1+r)^t.

1. McDonalds:

y= a(1+r)^t

Where a = $650,000

r = 0.04 (4%)

t = 5 years

Sales after 5 years, y= a(1+r)^t

= $650,000 (1.04)^5

= $650,000 × 1.2166529

= $790,824

2) School Population:

Current population = 800

Annual increasing rate = 2%

a = 800

r = 2%

t = 6 years

Population after 6 years, y= a(1+r)^t

= 800(1.02)^6

=901

3) Northern Sea Otters:

a = 70

r = 18% or 0.18

t = 4 years

Population after 6 years, y= a(1+r)^t

= 70(1.18)^4

= 136

4) Furniture Stores:

a = $375,000

r = 6.75% or 0.0675

t = 9 years

Sales after 9 years, y = a(1+r)^t

= 375,000(1.0675)^9

= $675,060

5) Indiana Population:

a = 273,000

r = 0.6% or 0.006

t = 8 years (2007 - 1999)

Population after 8 years, y = a(1+r)^t

= 273,000(1.006)^8

= 286,383

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Answer

Steven has an account with $350 in it and he withdrawals $15 per day. Jessica has an account with $200 and withdrawals $10 per day.