Which of the following expressions is equivalent to: 4x-12 *
16x
O
-8x
4(x-3)
O
4 + X-12
O
4(x-12)

Answer:

50 centimetres

Step-by-step explanation:

The true statements about the quadratic function f(x) = x² – 5x + 12 are

A second-order polynomial equation with a single variable, x, is known as a quadratic equation.

The graph of a quadratic equation traces a parabolic path

For the given function, f(x) = x² – 5x + 12 the coefficient of x² is positive hence the curve opens down

The graphs is attached and it does not contain the points (20, –8). and (0, 0)

Substituting  f(–10) = x² – 5x + 12

= (-10)² – 5(-10) + 12

= 100 + 50 + 12

= 162

hence not equal to 82

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

#2 and #4

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The fraction formed in the lowest form is \(\frac{3}{20}\)

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

6 persons for 40 dresses;

So, here

The numerator is 6;

and,

The denominator is 40;

So, The fraction that will be formed is: \(\frac{6}{40}\)

In order to simplify to the simplest form, we have to divide it by the common divisor of 6 and 40.

So,

The fraction formed in the lowest form is \(\frac{3}{20}\)

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Answer:

80736

Step-by-step explanation:

Answer:

The product of 841 × 96 is 80736.

The solution is also given in the attachment.

Hope it's helpful!

Answer:

Step-by-step explanation:

(0, 2) (2, 0)

(0-2)/(2-0)= -2/2= -1

y - 2 = -(x - 0)

y - 2 = -x + 0

y = -x + 2

Answer:

Step-by-step explanation:

x=0.5, y=12.

x=3, y=2.

x=4, y=1.5.

x=6, y=1.

Answer:

1.B 2.C 3.C

Step-by-step explanation:

Answer:

BCC

Step-by-step explanation:

Answer:

Negative relationship

Step-by-step explanation:

It is going in a negative direction.

Pls mark brainliest :)

The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.

To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.

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Answer:

the average number of car(s) in the system is 1

Step-by-step explanation:

Given the data in the question;

Arrival rate; λ = 2.5 cars per hour

Service time; μ = 5 cars per hour

Since Arrivals follows Poisson probability distribution and service times follows exponential probability distribution.

Lq = λ² / [ μ( μ - λ ) ]

we substitute

Lq = (2.5)² / [ 5( 5 - 2.5 ) ]

Lq = 6.25 / [ 5 × 2.5 ]

Lq = 6.25 / 12.5

Lq = 0.5

Now, to get the average number of cars in the system, we say;

L = Lq + ( λ / μ )

we substitute

L = 0.5 + ( 2.5 / 5 )

L = 0.5 + 0.5

L = 1

Therefore, the average number of car(s) in the system is 1

12% of 284 is about ,14% of 100, or 14.2.

Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Now,

Let start by finding 10% of 284,

= 10% of 284

= 10/100 x 284

= 28.4.

Then, The half of 28.4,

= 28.4 / 2

=  14.2.

So, 12% of 284 is about 14% of 100, which can be written as;

= 14% of 100 = 14.2.

Therefore, the answer is ,14% of 100, or 14.2.

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Answer:

A. 32

Step-by-step explanation:

1+2+3+4+5+6+7+8+9+10=55

55-32=23

55-36=19--can

55-34=21--can

55-40=15--can

55-38=17--can

combo of 3

1,3,5=9

137=11

139=13

157=13

159=15

179=17

357=15

359=17

379=19

579=21

Discuss measures that can be taken to develop the spirit of hard work

Answer:

Step-by-step explanation:

The mean value theorem for integrals for the function f(c) over a given interval [a, b] is expressed as g prime(c) = g(b) - g(a)/b-a. The idea is that there is a value c in between the interval [a, b] for the function given.

Given the function g(x) = 5√x within the interval [4,9]

g prime (c) = g(9) - g(4)/9-4

g(9) = 5√9

g(9) = 5*3 = 15

g(4) = 5√4

g(4) = 5*2 = 10

g prime c) = 15-10/9-4

g prime (c) = 5/5

g prime(c) = 1

So we are to find the number for which g prime (x) = g prime(c)

If g(x) = 5√x = \(5x^{1/2}\)

g prime (x) = \(5/2 \ x^{-1/2}\)

g prime (x) = 5/2√x

Since g prime (c) = 1 then;

5/2√x = 1

5 = 2√x

√x = 5/2

x = (5/2)²

x = 25/4

The value of c guaranteed by the mid value theorem is 25/4

The possible value of c for \(\mathbf{f(x) = 5\sqrt x\ [4,9]}\) is 6.25

The function is given as:

\(\mathbf{f(x) = 5\sqrt x\ [4,9]}\)

Calculate f(4) and f(9)

\(\mathbf{f(4) = 5\sqrt 4 = 10}\)

\(\mathbf{f(9) = 5\sqrt 9 = 15}\)

Substitute c for x in f(x)

\(\mathbf{f(c) = 5\sqrt c }\)

Calculate f'(c)

\(\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}\)

So, we have:

\(\mathbf{f'(c) = \frac{f(9) - f(4)}{9 - 4}}\)

\(\mathbf{f'(c) = \frac{f(9) - f(4)}{5}}\)

This gives

\(\mathbf{f'(c) = \frac{15 -10 }{5}}\)

\(\mathbf{f'(c) = \frac{5 }{5}}\)

\(\mathbf{f'(c) = 1}\)

Also, we have:

\(\mathbf{f'(x) = \frac 52x^{-1/2}}\)

Substitute c for x

\(\mathbf{f'(c) = \frac 52c^{-1/2}}\)

Substitute 1 for f'(c)

\(\mathbf{\frac 52c^{-1/2} = 1}\)

Multiply through by 2/5

\(\mathbf{c^{-1/2} = \frac 25}\)

This gives

\(\mathbf{c^{1/2} = \frac 52}\)

Square both sides

\(\mathbf{c = \frac{25}4}\)

\(\mathbf{c = 6.25}\)

Hence, the possible value of c is 6.25

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The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.

From the attached line segment graph, we see the coordinates as;

J (1, -10) and K (7, 2)

Let us assume that, point L divides the directed line segment from J to K into a ratio of 5:1.

From the properties of coordinate geometry we know that, the coordinates of point that divides the line joining (x₁, y₁), (x₂, y₂) in m:n, are;

[(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]

Plugging in the relevant values gives;

[(5 * 7 + 1 * 1)/(5 + 1)], [(5 * 2 + 1 * -10)/(5 + 1)]

⇒ (6, 0)

Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.

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Answer:

c. 0

Step-by-step explanation:

Hey There , Here is your Answer :-

Answer:

78

Step-by-step explanation:

Formula is already provided

2pir

2×3×13

Answer: 34/100

Step-by-step explanation:

it is 34% out of 100, so it is 34/100. Reduced is 17/50

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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Answer: 425

Step-by-step explanation:

Think of this problem as 4% of a number equals 17

since in math, the word 'of' usually means multiplication, we can think of it that way.

Also, 4% = 0.04

\(x*0.04=17\)

\(0.04x=17\)

\(\frac{0.04x}{0.04} =\frac{17}{0.04}\)

\(x=425\)

Answer:

2.5

Step-by-step explanation:

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

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Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

Answer:

24c+9

Step-by-step explanation:

I assume these equations are the sides so we just add all of them together

(10c+4)+(6c+4)+(8c+1)

We combine like terms

(10c+6c+8c)+(4+4+1)

24c+9

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