What is the range of f(x) = (3/4)^x – 4

Answer:

Step-by-step explanation:

y=−7x+3x intercept when y = 0so-7x + 3 = 0-7x = -3   x = 3/7y intercept when x = 0 so y = 3

answer

x intercept (3/7 , 0)y intercept (0, 3)

The ratio of 1 foot 4 inches to 1 yard is 16:36 or 4:9.

To find the ratio of 1 foot 4 inches to 1 yard, we first need to convert both measurements to the same unit. Since there are 3 feet in a yard and 12 inches in a foot, we can express both measurements in inches.

1 foot is equivalent to 12 inches.

Therefore, 1 foot 4 inches is:

1 [tex]\times[/tex] 12 + 4 = 12 + 4 = 16 inches

Now, since there are 3 feet in a yard, and each foot has 12 inches, 1 yard is equivalent to:

3 [tex]\times[/tex] 12 = 36 inches

Now we have both measurements in inches, and we can set up the ratio:

16 inches: 36 inches

Therefore, the simplified ratio is:

16:36.

We can further simplify this ratio by dividing both numbers by 4:

(16/4):(36/4) = 4:9.

It would take the newer pump 4.5 hours to drain the pool working alone.

Given that,

It takes an older pump twice as long to drain a certain pool as it does a newer pump.

Let us assume that,

The time it takes for the newer pump to drain the pool alone is x hours.

Hence, According to the information given, the older pump takes twice as long, so it would take 2x hour to drain the pool alone.

Now, When both pumps work together, their combined rate of draining the pool is additive.

Therefore, the equation is,

[tex]\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{1}{3}[/tex]

Simplify the equation for x,

[tex]\dfrac{(2 + 1)}{2x} = \dfrac{1}{3}[/tex]

[tex]\dfrac{(3)}{2x} = \dfrac{1}{3}[/tex]

Cross multiplication,

[tex]3 \times 3 = 2x[/tex]

[tex]2x = 9[/tex]

Dividing both sides by 2:

[tex]x = 4.5[/tex]

Therefore, it would take the newer pump 4.5 hours to drain the pool working alone.

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a =16 is the solution of the given equation.

To solve the equation 6 = a/4 + 2, we'll perform two steps to isolate the variable 'a'.

Step 1: Subtract 2 from both sides of the equation:

6 - 2 = a/4 + 2 - 2

4 = a/4

Step 2: Multiply both sides of the equation by 4 to get rid of the fraction:

4 * 4 = (a/4) * 4

16 = a

Therefore, the solution to the equation is a = 16.

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Answer:

Option C) is correct

Step-by-step explanation:

Given :  y is the daily production cost at a canning company such that [tex]y=650-15x+0.45x^2[/tex] wherex is the number of canned items .

To find : Minimum daily production cost

Solution :

[tex]y=650-15x+0.45x^2[/tex]

On differentiating both sides with respect to x, we get

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=-15+0.9x[/tex]

On putting [tex]\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex] , we get [tex]-15+0.9x=0\Rightarrow 15=0.9x\Rightarrow x=\frac{15}{0.9}=\frac{150}{9}=\frac{50}{3}[/tex]

We get intervals as \left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty  \right )[tex]\left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty  \right )[/tex]

For [tex]x=0\epsilon \left ( -\infty ,\frac{50}{3} \right )[/tex] , [tex]f'(0)=-15< 0[/tex]

For [tex]x=16\epsilon \left ( \frac{50}{3},\infty  \right )[/tex] , [tex]f'(18)=-15+0.9(18)=-15+16.2=1.2> 0[/tex]

Therefore, [tex]y=\frac{50}{3}[/tex] is a point of minima.

So, minimum cost is equal to [tex]y\left ( \frac{50}{3} \right )[/tex]

[tex]y\left ( \frac{50}{3} \right )=650-15\left ( \frac{50}{3} \right )+0.45\left ( \frac{50}{3} \right )^2=650-250+125=\$ 525[/tex]

So, option C) is correct .

In two column proof the right column states your reasons is true statement.

In a two-column proof, the right column typically contains the statements of reasons or justifications for each step taken in the left column.

The left column contains a sequence of statements that represent the logical progression of the proof, while the right column provides the reasoning or logical basis for each step to show that it follows from the previous statements.

This format is commonly used in geometry to provide a clear and organized presentation of the proof's logical structure.

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The probability that the kicker makes his first two kicks is 0.63, or 63%.

Let's denote the events:

A: The kicker makes his first kick

B: The kicker makes his second kick

Given:

P(A) = 0.7 (probability that the kicker makes his first kick)

P(B|A) = 0.9 (probability that the kicker makes his second kick given that he made his first kick)

To find the probability of both events A and B occurring (the kicker making his first two kicks), we can use the multiplication rule of probability:

P(A and B) = P(A) * P(B|A)

Substituting the given probabilities, we have:

P(A and B) = 0.7 * 0.9 = 0.63

Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.

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The probability that the kicker makes his first two kicks is 0.63, or 63%.

To find the probability that the kicker makes his first two kicks, we need to multiply the probabilities of each individual kick.

The kicker has a 70% chance of making his first kick, which means he has a 30% chance of missing it.

If the first kick is made, his success rate rises to 90%. So, the probability of making the second kick, given that he made the first kick, is 90%.

To find the probability of both kicks being made, we multiply the probability of making the first kick (0.7) with the probability of making the second kick given that the first kick was made (0.9).

0.7 * 0.9 = 0.63

Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.

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Final answer:

The expected number of heads and tails when tossing a coin 10 times is 5 each.

Explanation:

If you toss a coin ten times:

Expected number of heads: 5

Expected number of tails: 5

This is because for each toss, the probability of getting a head is 0.5 (50%) and the same for a tail. Over multiple tosses, the outcomes tend to approach these expected values.

It is found that there are 43,800 minutes in a month.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We knowt that there are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour.

1 day = 24 hour

1 hour = 60 minutes.

1 minutes = 60 seconds

Therefore, 24 hours = 24 x 60 = 1440 minutes

There are 1440 minutes in one day.

Then 30 days = 30 x 1440 = 43,800

Hence, It is found that there are 43,800 minutes in a month.

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Answer:

The correct answer is f(-2)= -2

Step-by-step explanation:

Answer:

S''(-3/2, 9/2)

Step-by-step explanation:

In a dilation, the coordinates of every ordered pair in the pre-image are multiplied by the scale factor to create the ordered pairs of the image.

The first dilation has a scale factor of 1/2.  This maps:

R(-6, 10)→R'(-6/2, 10/2) = R'(-3, 5)

S(-2, 6)→S'(-2/2, 6/2) = S'(-1, 3)

T(-10, 0)→T'(-10/2, 0/2) = T'(-5, 0)

The second dilation has a scale factor of 3/2:

R'(-3, 5)→R''(-9/2, 15/2)

S'(-1, 3)→S''(-3/2, 9/2)

T'(-5, 0)→T''(-15/2, 0)

This makes S'' have coordinates (-3/2, 9/2).

Answer: a :)

Step-by-step explanation:

Ques 1)

                   [tex]g(x)=-12x+48[/tex]

Ques 2)

                 [tex]g(x)=|3x|+4[/tex]

Ques 1)

We know that if a graph is stretched by a factor of a then the transformation if given by:

    f(x) → a f(x)

Also, we know that the translation of a function k units to the right or to the left is given by:

  f(x) →  f(x+k)

where if k>0 then the shift is k units to the left

and if k<0 then the shift is k units to the right.

Here the graph of f(x) ​is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.

This means that the function g(x) is given by:

[tex]g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48[/tex]

Ques 2)

We know that the transformation of the type:

  f(x) → f(x)+k

is a shift or translation of the function k units up or down depending on k.

If k>0 then the shift is k units up.

and if k<0 then the shift is k units down.

Here, The graph of the function f(x)=|3x| is translated 4 units up.

This means that the transformed function g(x) is given by:

                 [tex]g(x)=|3x|+4[/tex]

Answer:

-12(x-4)

Step-by-step explanation:

I just took the test this is the answer!! Basically you take -3 and 4 and times it which would be -12. You then have x and another 4 left over. Since you are translating to the right you will be negative therefore giving us the answer -12(x-4).

In mathematics, specifically geometry, the least angle measure by which a regular, symmetric figure can be rotated to map onto itself is usually 90°. This concept falls under the umbrella of rotational symmetry.

The question is about rotation of objects in geometry. To identify the least angle measure for a figure to map onto itself, we need to know the shape of the figure. However, assuming the figure is regular and symmetric (a square or a rectangle for example), the least angle measure by which it can be rotated to map onto itself is 90°.

It's important to remember the concept of rotational symmetry. A figure has rotational symmetry if it can be rotated less than 360° around a central point and still appear the same. For instance, a regular rectangle or square has a rotational symmetry of 90°, since we can rotate it 90 degrees and it appears the same.

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the value of (t) that satisfies the equation is approximately (37.6992).

Let's solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\).[/tex]

Step 1: Multiply both sides by \(-4\) to isolate \(t\).

[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4)\][/tex]

This simplifies to:

[tex]\[ t = 12\pi \][/tex]

Step 2: Substitute the value of \(\pi\) to get the final answer.

[tex]\[ t = 12 \times 3.14159 \][/tex]

[tex]\[ t = 37.6992 \][/tex]

Therefore, the value of ( t ) is approximately ( 37.6992 ).

To solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\)[/tex] , we first want to isolate (t) on one side of the equation. To do this, we can multiply both sides of the equation by (-4). This cancels out the fraction and leaves us with (t) on the left side:

[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4) \\t = 12\pi\][/tex]

Now, to get the numerical value of \(t\), we substitute the value of \(\pi\), which is approximately \(3.14159\), into the equation:

[tex]\[ t = 12 \times 3.14159 \][/tex]

[tex]\[ t \approx 37.6992 \][/tex]

Therefore, the value of (t) that satisfies the equation is approximately (37.6992).

complete question

−t/4=−3π

What is the answer to T

Answer:

the answer is C. -5/7

Answer:

x ≤ 7

Yuuupeeee

Answer: 1. A) 3x−4y=10

2. [tex]y=-\frac{x}{4}+3[/tex]

3. In the attachment.

Explanation:

1. Given equation=[tex]y=\frac{3}{4}x-\frac{5}{2}[/tex]

To reduce it into standard form , multiply both sides by 4,we get

[tex]4y=4(\frac{3}{4}x-\frac{5}{2})\\\Rightarrow4y=3x-10......[distributive\ property]\\\Rightarrow3x-4y=10[/tex] which is option A.

2. Given linear equation : x+4y=12

The standard slope intercept form is given by y=mx+c where m is the slope and c is the constant.

To reduce given linear equation subtract x from both sides, we get

4y=12-x

Divide 4 on both sides.

[tex]\Rightarrow\ y=\frac{12-x}{4}=3-\frac{x}{4}\\\Rightarrow\ y=-\frac{x}{4}+3[/tex] is the slope-intercept form of the linear equation x + 4y = 12.

3. To graph equation [tex]y=\frac{1}{2}x[/tex] on the coordinate plane.

We need to find points to plot the line

Put x=0,we get y=0

Put x=2,we get y=1

Thus we have points (0,0) and (2,1) to plot the line on the graph.

Answer: 1. A) 3x−4y=10

Step-by-step explanation:

Answer:

not 480, answer is 453 according to K12.

Step-by-step explanation:

took the k12 test, the answer is in fact, 453.

The population of the bacteria after 30 hours will be 400.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the population of bacteria doubles every 12 hours initially the population of bacteria is 80 what is the population of bacteria after 30 hours?

The population will be calculated as,

12 hours = 2 times of 80

1 hour = 2 / 12 times of 80

30 hours = ( 30 x 2 x 80 ) / 12

30 hours = 400 bacterias

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Answer:  The required slope-intercept form is [tex]y\leq 3x+21.[/tex].

Step-by-step explanation:  We are given to write the following inequality in slope-intercept form :

[tex]-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope-intercept form of an inequality of the given form is as follows :

[tex]y\leq mx+c,[/tex] where m is the slope and c is the y-intercept.

From inequality (i), we have

[tex]-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.[/tex]

Thus, the required slope-intercept form is [tex]y\leq 3x+21.[/tex].

the measure of angle ABC (m∠ABC) is 130 degrees. it's essential to recognize that the sum of the angles along a straight line is always 180 degrees.

In this case, we have two angles, 2x and 5x+5, forming a straight line with an unknown angle (m∠ABC). So, we set up the equation:

2x + 5x + 5 = 180

Next, combine the like terms on the left side:

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25

Therefore, the measure of angle ABC = 5x + 5

= 5(25) + 5

=130 degree

So, the measure of angle ABC (m∠ABC) is 130 degrees.

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