A train travels 110 miles per hour. How fast does the
train travel in feet per second?

The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Jane bought 3 shirts and returned 2 pairs of pants

Laura bought 4 shirt and 3 pairs of pants.

Let, s = cost of shirt

and, p = cost of a pair of pants

The equation for Jane is

3s - 2p = $5

Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.

Now, the equation for Laura is

4s + 3p = $120

Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.

So, the system of equation we get

3s - 2p = $5

4s + 3p = $120

After solving  simultaneously we get the values s = 15 and p = 20.

Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,

for 1st equation,

3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)

for 2nd equation,

4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)

Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.

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Answer:

x = [tex]\frac{y-b}{a}[/tex]

Step-by-step explanation:

y = xa + b ( subtract b from both sides )

y - b = xa ( isolate x by dividing both sides by a )

[tex]\frac{y-b}{a}[/tex] = x , that is

x = [tex]\frac{y-b}{a}[/tex]

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

y = xa - b ( add b to both sides )

y + b = xa ( isolate x by dividing both sides by a )

[tex]\frac{y+b}{a}[/tex] = x , that is

x = [tex]\frac{y+b}{a}[/tex]

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

assuming you mean

y = [tex]\frac{x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

2y = x + 2 ( subtract 2 from both sides )

2y - 2 = x , that is

x = 2y - 2

Answer:

y = 0.028t + 230,000

Step-by-step explanation:

We know

t = number of years since the start of the study

y = be the city's population

Each year the population has grown by 2.8%, this is the slope

The city had 230,000 people, this is the y-intercept

2.8% = 0.028

The equation is y= mx + b

So, our equation in this case is

y = 0.028t + 230,000

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The value of the original integral is 42, as expected.

What must an answer about a indefinite integral of a function include?

A definite integral is an infinitesimal sum derived from a integrable function, that is, a function that exist for all value x within the range of integration.

To evaluate this integral, we can interpret it in terms of the area of a region. To do this, we can rewrite the integral as:

∫0 36 − x2 dx −6

= ∫0 36 x2 dx + ∫0 36 dx

= ∫x2 dx + ∫dx

The first integral on the right-hand side represents the area under the curve y = x^2 from x = 0 to x = 6.

The second integral on the right-hand side represents the area of the rectangle with base 6 and height 1, which is just 6.

Therefore, the original integral can be interpreted as the sum of the area under the curve y = x^2 from x = 0 to x = 6 and the area of the rectangle with base 6 and height 1. This area is equal to 36 + 6 = 42. Thus, the value of the original integral is 42.

We can also verify this result using the formula for the area under a curve:

∫x2 dx = (1/3) x3 + C

Substituting the limits of integration, we get:

∫0 6 x2 dx = (1/3) * 6^3 - (1/3) * 0^3

= (1/3) * 216

= 72

Therefore, The value of the original integral is 42, as expected.

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(a) {2, 3, 4, 5, 6, 7, 8}

(b) {2, 4, 5, 9, 11, 12, 14}

(c) No next largest 7-subset; this is the last one in lexicographic order.

(d) {2, 4, 5, 6, 11, 12, 13}

(e) No next largest 7-subset; this is the last one in lexicographic order.

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

For instance, if A represents the set of natural numbers and B represents the set of all whole numbers, then B is a subset of A since the set of whole numbers contains all natural numbers. This is how we may comprehend it: Natural numbers 1, 2, 3, and so on make up the set A. B = A collection of whole numbers, such as "0, 1, 2, 3,..."

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Answer:

distance between two cities will be 9 000 000 km

Answer:

Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km

Answer: 6 and 7

Step-by-step explanation: The square root of 41 is 6.4. Since you multiply it by itself, it’s the nearest square root to 41.

The measure of angle EBF is 40 degrees

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

EBF = 6x + 4

CBF = 7x - 2

Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent

This can be represented mathematically as follows

EBF = CBF

Substitute the known values in the above equation, so, we have the following representation

6x + 4 = 7x - 2

Multiply through by 1

6x + 4 = 7x - 2

Collect the like terms

7x - 6x = 4 + 2

Evaluate the like terms

x = 6

Recall that

EBF = 6x + 4

Substitute the known values in the above equation, so, we have the following representation

EBF = 6 x 6 + 4

Evaluate

EBF = 40

Hence, the measure is 40 degrees

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Complete question

If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF

Most of the kinetic energy of the water is transferred into the water, then the thermal energy will increase. Hence, option C is correct.

Kinetic energy is the term used in physics to describe the force that a moving item has. It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except variations in speed, the body retains the kinetic energy it gains during acceleration.

The body uses exactly the same amount of energy when slowing down from its current rate to a state of rest. Formally, kinetic energy refers to any term in a system's Lagrangian that has a derivative with respect to time.

As per the given information in the question,

When the kinetic energy of the diver is transferred into the water, the thermal energy will increase.

The entity's thermal energy grows as the average kinetic energies of its particles rise. As a result, an object's thermal energy rises as its temperature does.

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The simplified form of the given expression is, 1/4d + f.

What is simplified form of the expression?

To simplify an expression, create an equivalent expression without any terms that are similar.

The expression will then be rewritten using the fewest terms possible.

Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.

Consider the given expression,

1/2d - 3/4d + 3f - 2f

Here the like terms are '1/2d  and 3/4d' and '3f and 2f'.

To simplify the expression,

1/4d  + f

Hence, the simplified form of the given expression is, 1/4d + f.

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There are 60 different ways could you choose a car and this can be determined by using arithmetic operations.

What are arithmetic operations?

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-") Multiplication ("×") Finding the quotient in division ("÷").

Given :

A car dealership has five exterior color choices.

A car dealership has six interior color choices.

A car dealership has two model choices.

The following steps can be used to determine the different ways could you choose a car:

Multiply 5 and 6 that is multiply five exterior color choices and six interior color choices.

= 5 * 6

Multiply the above expression by 2 which is with two model choices.

= 30 * 2

Further, simplify the above expression.

= 60

Hence, There are 60 different ways could you choose a car.

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Answer: Shape P is similar to shape Q, however, shape P, is smaller than shape Q.

A single transformation that takes shape P to shape Q is; a dilation by a scale factor of 3 with a center of dilation at .

Reasons:

The give figure shows;

The preimage figure = P

The image figure = Q

The image P is larger than the preimage Q, therefore, the figure, Q is a

dilation of the preimage P

(x₁, y₁) = A point on the preimage, P = (2, 3)

(x₂, y₂) = The corresponding point on the dilated image, Q = (4, 9)

k = The scale factor = 3

Therefore;

The center of dilation, (x₀, y₀) = (1, 0)

Therefore;

The single transformation that takes shape P to shape Q is a dilation by a scale factor of 3 with a center of dilation at (1, 0).

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Step-by-step explanation:

Answer:

Infinite

Step-by-step explanation:

2x + 12 = 2x + 12

they both are equal

The cost of the milk from the supplier can be calculated as follows:

Cost of milk = (price per kg of milk) * (number of kg of milk) + delivery fee

= $0.5/kg * 9250 kg + $15

= $<<0.5*9250+15=4675>>4675

The holding cost of the milk can be calculated as follows:

Holding cost = (holding cost per kg per month) * (number of kg of milk)

= $0.03/kg/month * 9250 kg

= $<<0.03*9250=277.5>>277.5

Therefore, the total cost of the milk for Bruno's production facility is $4675 for the milk from the supplier and $277.5 for the holding cost, for a total of $4952.5.

The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

Time t = 11 sec

Initial velocity u = 25 kmph

u = (25 × 1000)/(60 × 60) = 6.9 m/s

final velocity v = 75 kmph

v = (75 × 1000)/(60 × 60) = 20.83 m/s

From the first equation of motion;

v = u + at

Put the values;

20.83 = 6.9 + 11a

20.83 - 6.9 = 13a

11a = 13.93

a = 13.93 / 11

a = 1.26 m/s²

Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

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Answer:

10 cups

Step-by-step explanation:

120minutes divided into 60minutes = 2 hours

20 divided by 2 = 10 cups

If 5 dollars can be exchanged for 7.7095 units of some foreign​ currency, the unit of that currency that can be obtained for 6 ​dollars will be

5 dollars can be exchanged for 7.7095 units. This means that 1 dollar equals to:

5 dollars / 5 = 7.7095 units / 5

1 dollar = 7.7095 units / 5

1 dollar = 1.5419 units.

Now, for 6 ​dollars, the foreign currency that can be obtained is:

= 6 * 1.5419 units

= 9.2514 units. Therefore, 9.2514 unit of the foreign​ currency can be obtained for 6 ​dollars.

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The coefficient and constant in the system of linear equations are identified below

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

In this question, we are given two equations to define the variables.

3x + 7y = 18 ...eq(i)

2x - 4y = 9 ..eq(ii)

In the equations above;

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Answer:

angle B = 55°

.............

The statement that can be concluded from the fact that the area of square ABHI plus the area of square BCDE is equal to the area of square EFGH is of:

D. BE² + BH² = EH².

The area of a square of side length s is given by the side length squared, as follows:

A = s².

Hence the areas of each square on the image given at the end of the answer are given as follows:

Hence the correct statement regarding the areas is given as follows:

BE² + BH² = EH².

Meaning that statement D is correct.

The problem is given by the image shown at the end of the answer.

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The relation between the vertices of a cube or cuboid is  V, the side is E, and the surface, F is  V - E + F = 2. Option 3) is the correct answer.

The vertice, face, and side of a cube or cuboid are related by Euler's Theorem. This theorem states that the number of faces, vertices, and edges of any polyhedron are related by Euler's formula.

Euler's formula can be stated as:

F + V = E + 2.

or

F + V - E = 2

where,

F = equal to the number of faces,

V = equal to the number of vertices

E = equal to the number of edges.

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The given formula would be used to find the first quartile of a data set using the exclusive method.

What is quartile?

A quartile is a type of quantile used in statistics that divides the total number of data points into four roughly equal parts, or quarters. To compute quartiles, the data must be arranged from smallest to largest; therefore, quartiles are a type of order statistic.

The given formula is [tex]L_P = (n + 1)\frac{25}{100} \\[/tex]

This formula can also be written as,

[tex]R = (n + 1)\frac{25}{100}[/tex]

where 25 is the percentile of the data set.

So, the option (c) is correct.

The first quartile of a data set using the exclusive method.

Hence, the given formula would be used to find the first quartile of a data set using the exclusive method.

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We know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.

An identity element, also known as a neutral element, in a binary operation on a set is a set element that, when the operation is applied, leaves each element of the set untouched.

In algebraic structures like groups and rings, this idea is applied.

The left side of the equation equals the right side of the equation in an algebraic identity.

As an illustration, (a+b)2 = a2+2ab+b2 is true for all values of and b.

So, we have the equation:

(x + y)³ - (x³ + y³)

Now, get factors as follows:
Use the algebraic identity: (a + b)³ = a³ + b³ + 3ab (a + b)

x³ + y³ + 3xy (x + y) - x³ - y³

Simplify one more step to obtain:
3xy (x + y)

Therefore, we know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.

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Correct question:

Which of the following is a factor of (x + y)3 - (x3 + y3 )

a. x² + y² + 2xy

b. x² + y² - xy

c. xy²

d. 3xy

Answer: 8

Step-by-step explanation:

From our knowledge, we know two things.

From here, we can work out what f(3) is by substituting n as 2

f(2 + 1) = f(2) + 2

f(3) = 4 + 2 = 6

And we can work out f(4) by substituting n as 3

f(3 + 1) = f(3) + 2

f(4) = 6 + 2 = 8

Eventually, if you continue doing this, you will see a sequence forming where the next number is the previous number added by 2.

Hypothesis is tested as H₀: σ   = 0.05 mm versus H₁: σ  <  0.05 mm.

The type I error occurs if we accept a shipment that should have been rejected .

A type II error occurs if we reject a shipment that should have been  accepted.

Given that,

A corporation wants to see concrete proof that the genuine standard variation of sheath thickness is less than 0.05mm before committing to a significant order of polyethylene sheaths for a certain kind of high-pressure oil-filled submarine power line.

We have to find what theories need to be tested and what exactly are types I and ii errors.

We know that

H₀: σ   = 0.05 mm

versus

H₁: σ  <  0.05 mm.

In this context,

The type I error occurs if we accept a shipment that should have been rejected .

A type II error occurs if we  reject a shipment that should have been  accepted.

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Answer:

The second hiker is farther away from the visitor center as all things being equal cos 128 < cos 140

from distance^2 = 4^2 + 1.8^2 -- 2*4*1.8 cos (angle turned).

Step-by-step explanation:

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Answer:

The first hiker is the farthest from camp since 140° > 128°.

Step-by-step explanation:

The journeys of both hikers can be modelled as triangles (see attachment).

Even though they hike the same distance of 4 miles plus 1.8 miles, as the angles of their turns between the two legs of their journeys are different, the final distance they are from camp is also different.

The first hiker turns 40° south so the included angle of the triangle is 140°.

The second hiker turns 52° north, so the included angle of the triangle is 128°.

As 140° > 128°, the distance between the first hiker and camp is farther than the distance between the second hiker and camp.

To prove this, use the cosine rule to find the missing length of each triangle.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Cosine Rule} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

First hiker:

[tex]\implies c^2=4^2+1.8^2-2(4)(1.8) \cos 140^{\circ}[/tex]

[tex]\implies c^2=19.24-14.4\cos 140^{\circ}[/tex]

[tex]\implies c=\sqrt{19.24-14.4\cos 140^{\circ}}[/tex]

[tex]\implies c=5.501912393[/tex]

Second hiker:

[tex]\implies c^2=4^2+1.8^2-2(4)(1.8) \cos 128^{\circ}[/tex]

[tex]\implies c^2=19.24-14.4\cos 128^{\circ}[/tex]

[tex]\implies c=\sqrt{19.24-14.4\cos 128^{\circ}}[/tex]

[tex]\implies c=5.301464443[/tex]

As 5.50 > 5.30, this proves that the first hiker is farthest from the camp.

Answer:

[tex]\sqrt{4100}[/tex]

Step-by-step explanation:

Step 1 Substitute Using Pythagorean Theorem:

x = [tex]\sqrt{50^2+40^2}[/tex]

Step 2 Solve:

[tex]50^2=2500[/tex]

[tex]40^2=1600[/tex]

Therefore,

[tex]\sqrt{50^2+40^2}=\sqrt{4100}[/tex]

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The equation of the line is

y = x - 10.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line has,

Slope = 1

Passes through = (-3, -13)

Now,

The equation of a line is given as,

y = mx + c

Put (-3, -13) = (x, y)

-13 = 1 x (-3) + c

-13 = -3 + c

c = -13 + 3

c = -10

Now,

The equation of the line.

y = 1x - 10

y = x - 10

Thus,

The equation of the line is

y = x - 10.

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The equation to represent the given situation is [tex]500(2)^x=16000[/tex] after 5 hours. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a bacteria has an initial population of 500 and is doubling every hour.

Let x be the number of hour bacteria population to reach 16,000

The bacteria reaches a population of 16,000 bacteria.

So, the equation is [tex]500(2)^x=16000[/tex]

⇒ [tex]2^x[/tex]=16000/500

⇒ [tex]2^x[/tex]=160/5

⇒ [tex]2^x=2^5[/tex]

⇒ x=5

Therefore, after 5 hours the bacteria population reaches 16,000.

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