the greatest common factor of 24 56 and 96

Answer: m= -6

Step-by-step explanation: 2 = 11 + 3m + 9

3m = 2 - 11 - 9

3m = -18

Divide both sides by 3.

m= -6

Answer:

m = -6

Step-by-step explanation:

Step by step explanation:

2-11 = 3m+9 ==》3m = -18 ==》m = -18/3 ==》m= -6

The number of applicants that were not accepted are calculated to be 1260.

The number of applicants that were not accepted can be determined as follows;

Since 2 out of every 9 applicants are accepted; therefore the total number of applicants out of which 360 applicants were accepted can be calculated as follows;

360 × 9 / 2 = 3240 / 2 = 1620

Therefore the total number of applicants is calculated to be 1620, out of these 1620 applicants, 360 were accepted therefore the number of applicants that were not accepted can be determined by subtraction.

The number of applicants that were not accepted can be determined by subtracting the accepted applicants from the total number of applicants as follows;

Applicants not accepted = 1620 - 360

Applicants not accepted = 1260

Therefore 1260 applicants were not accepted by the program.

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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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For the given line y = 1/2x - 4,

Consider a line with the equation ax+by+c=0

It is given that, the equation of a line is given as y = 1/2x - 4.

The slope of the given line is m = 1/2; (since it is in the form of y=mx+c)

Then, the slope of the line parallel to the given line is m = 0.

And the equation of the parallel line passing through the point (-4, 2) is

a(x - x1) + b(y - y1) = 0; where a = 1; b = -2 (y = 1/2x-4 ⇒ 2y = x - 8)

⇒ 1(x + 4) - 2(y - 2) = 0

⇒ x + 4 -2y + 4 = 0

⇒ x - 2y +8 = 0

So, the point on the parallel line is (0, 4).

The slope of the line perpendicular to the given line is m = -1/1/2 = -2.

And the equation of the perpendicular line passing through the point (-4, 2) is

b(x - x1) - a(y - y1) = 0; where a = 1; b = -2;

⇒ -2(x + 4) - 1(y - 2) = 0

⇒ -2x - 8 - y +2 = 0

⇒ y = -2x - 6

So, the point on the perpendicular line is (-2, -2).

All of these are shown in the graph below:

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The no: of solutions that the equation -1/2(-8x+14) = 3x +9+x  has is 1

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

The no: of solutions that the equation is -1/2(-8x+14) = 3x +9+x is 1

as the equation is 1 degree polynomial.

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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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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.

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: -5/4

Step-by-step explanation:

The slope is rise/run or y2 - y1/ x2 - x1

The two points are (-6,-3) (-2, -8)

The y decreases by 5 and the x increase by 4

So the slope is -5/4

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:

Yes

Step-by-step explanation:

y = 2x - 8  Plug is 6 for x and 4 for y

4 = 2(6) - 8

4 = 12 - 8

4 = 4

(6,4) is a solution for this equation

y = -1/3 x + 6

4 = -1/3(6) + 6

4 = -2 + 6

4 = 4

(6,4) is a solution for this equation too.

(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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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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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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(A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

A polynomial is a mathematical equation made up of coefficients and indeterminates that exclusively uses the operations of addition, subtraction, multiplication, or powers of positive numbers of the variables.

x² - 4x + 7 is an illustration of a quadratic with a solitary indeterminate x.

(A) 4x² - 3x + 7:

'x' is the only variable in the provided polynomial.

As a result, the polynomial 4x² - 3x + 7 has one variable.

(B) y² + √2:

'Y' is the only variable in the provided polynomial.

y² + √2 is a polynomial in one variable as a result.

(C) 3√t + t√2:

Since the power of the variable in the first term is 1/2, which is not a whole integer, 3√t + t√2 is not a polynomial.

(D) y + (2/y):

Because the power of the variable in the second term is -1, which is not a whole number, y + 2y⁻¹ is not a polynomial.

(E) x¹⁰ + y³ + t⁵⁰

Due to the fact that x, y, and t are all three variables, x¹⁰ + y³ + t⁵⁰ is not a polynomial in one variable.

Therefore, (A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

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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:

brainliest pls

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.

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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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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413 bricks are needed to build a wall whose area is equivalent to 10.32 m².

Given is that a brick wall of dimension 4.3 m by 2.4 m is to be built. There are 40 bricks per m².

The area of the wall will be -

[A] = 4.3 x 2.4 = 10.32 m²

[A] = 10.32 m²

Now, for the area of 1 m², 40 bricks are needed. So, for 10.32 m², we can say that -

10.32 x 40

412.8

413 bricks.

Therefore, for the area of 10.32 m², to only 413 bricks are needed to build it.

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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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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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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 number of balls that must be chosen to be certain we have One red and one green is; 5 balls.

We are given;

Number of green balls in box = 95 balls

Number of red balls in box = 90 balls

Thus;

Total number of balls in the box = 95 + 90

Total number of balls in the box = 185 balls

Now, the probability of getting one red from selection = 90/185

Probability of getting one green ball = 95/185

P(Red and Green) = P(R) * P(G)

P(R and G) =  = (90/185) * (95/185) = 0.2418

However, in this case we will make use of the unitary method which is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Thus, minimum number of balls to get the given selection = 95 - 90 = 5 balls

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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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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.

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.

Answer:

angle B = 55°

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

Answer:

Infinite

Step-by-step explanation:

2x + 12 = 2x + 12

they both are equal

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]