4+7a=12+8a
with steps pls

Answer:

Your answer is going to Be b

There are 7 strings in T⁶ that are balanced.

What is a  bijection?

A bijection, also known as a bijective function, is a type of function between two sets that establishes a one-to-one correspondence or mapping between the elements of the sets. In other words, a bijection ensures that each element in the first set is uniquely associated with an element in the second set, and vice versa.

a) To show a bijection between the set of strings in T^6 that are balanced and T⁵, we can define a function f: T⁶ -> T⁵ as follows:

For any string x = x1x2x3x4x5x6 ∈ T⁶, we define f(x) = y = y1y2y3y4y5 ∈ T⁵, where:

y1 = (x1 + x2 + x4) mod 3

y2 = (x2 + x3 + x5) mod 3

y3 = (x3 + x4 + x6) mod 3

y4 = (x4 + x5) mod 3

y5 = (x5 + x6) mod 3

Now, let's prove that f(x) is a bijection.

Injectivity (One-to-One):

Assume f(x1) = f(x2) for some x1, x2 ∈ T⁶. We need to show that x1 = x2.

Let's consider the components of f(x1) and f(x2):

y1 = (x1 + x2 + x4) mod 3

y2 = (x2 + x3 + x5) mod 3

y3 = (x3 + x4 + x6) mod 3

y4 = (x4 + x5) mod 3

y5 = (x5 + x6) mod 3

If f(x1) = f(x2), then y1 = y1, y2 = y2, y3 = y3, y4 = y4, and y5 = y5.

From the equations, we can deduce that x1 = x2, x2 = x2, x3 = x3, x4 = x4, x5 = x5, and x6 = x6.

Thus, x1 = x2, proving the injectivity of f(x).

Surjectivity (Onto):

For any y = y1y2y3y4y5 ∈ T⁵, we need to show that there exists an x = x1x2x3x4x5x6 ∈ T⁶ such that f(x) = y.

We can choose x1 = y1, x2 = y2, x3 = (y2 + y3) mod 3, x4 = (y1 + y3) mod 3, x5 = y4, and x6 = (y4 + y5) mod 3.

By substituting these values into the equations for f(x), we can see that f(x) = y.

Therefore, f(x) is surjective.

Hence, we have shown that f(x) is both injective and surjective, making it a bijection between the set of strings in T⁶ that are balanced and T⁵.

b) To count the number of strings in T⁶ that are balanced, we can analyze the possible values of each digit in the string.

In a balanced string, the sum of the digits must be an integer multiple of 3. Since each digit can only take values from T = {0, 1, 2}, there are three possibilities for the sum of three digits: 0, 3, or 6.

Sum of three digits = 0: There is only one way to achieve this, which is to have all three digits equal to 0. Thus, there is only one string with this property.

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Function notation is an important tool in mathematics and is used to express the relationship between two variables.

A function is a process or set of actions that is used to complete a specific task. It is a self-contained unit of code that takes input from the user and produces a desired output. Functions are important for programming, as they help to organize code and make it easier to read, debug, and maintain.

A function is a rule that assigns a unique output to every input. The inputs are listed in the domain of the function and the associated outputs are listed in the range of the function. The notation used for a function is usually f(x), where x is the input to the function and f(x) is the output.

The function notation is used to express the relationship between the input and output of a given function. The notation is composed of the function name, followed by the input in parentheses. For example, a function named f with an input of 3 can be written as f(3). The function notation is also used to express the rules used to calculate the outputs from the inputs. For example, if the function f has the rule f(x) = -5 when x is 3, then it can be written as f(3) = -5.

Function notation can also be used to express the composition of two or more functions. For example, if the functions f and g are composed, then the notation to express this is (f o g)(x). This notation is read as “f composed with g of x” and means that the output of g is used as the input for f.

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Answer:

BCF

Step-by-step explanation:

Step-by-step explanation:

÷ and 1/2 are both division but one is a fraction with a little more potential

The values of a and b in the exponential function f(x) = \(ab^x\) can be found by using the two given points and solving a system of two equation.

To find the values of a and b in the exponential function f(x) = \(ab^x\) given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.

Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:

11 = \(a * b^0\)

Since \(b^0\) = 1 for any value of b, we have:

11 = a * 1

So a = 11.

Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:

1375 = \(11 * b^3\)

Dividing both sides of the equation by 11, we have:

125 = \(b^3\)

By combining the cube roots of the two sides, we obtain:

b = 5

So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = \(11 * 5^x\).

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The complete question is:

an exponential function f(x) = \(ab^x\) passes through the points (0, 11) and (3, 1375). Find the values of a and b?

Answer:

6.4% of the lights are faulty

Step-by-step explanation:

Well you can make a proportion out of this question.
so lets do faulty/total

16/250 = x/ 100

Since x/100 is basically finding the percent since percent means out of a hundred.

Cross multiply to solve.

250x= 1600

SOlve for x

X=6.4

6.4 percent of the lights are faulty.

Step-by-step explanation:

Given

g(x) = x² + 4x - 7

g(-6)= ( - 6)² + 4 * ( -6) - 7

= 36 - 24 - 7

= 5

Hope it will help :)❤

Answer:

i wold but can we just be frends

Step-by-step explanation:

i have a discord if you wanna join it?

Answer:

Not sure if this has been answerd but its 6

Step-by-step explanation:

if u are really gonna give brain that would be cool

Option C is correct, , the expression 6.1+7.7-5.4 can be used to find  find the value of the expression.

The given expression is 6.1 - 5.4 - (-7.7).

We have to find the expression which is used to find the value of the given expression.

Which means we have to simplify the given expression.

When negative sign is multiplied with negative sign we get positive.

6.1 - 5.4 +7.7

We get 8.4.

Hence, the expression 6.1+7.7-5.4 can be used to find  find the value of the expression.

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Answer:

4, 3, -2 are the 3 roots of the function

Answer:

-2, 3 & 4

Step-by-step explanation:

The integer roots of the polynomial function f(x)=x^3-5x^2-2x+24f(x)=x

3

−5x

2

−2x+24 can be only among the divisors of free term.

The divisors of free term are:

\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24.±1,±2,±3, ±4,±6,±8,±12,±24.

Check them:

1. f(1)=1^3-5\cdot 1^2-2\cdot 1+24=18\neq 0f(1)=1

3

−5⋅1

2

−2⋅1+24=18



=0 , 1 is not a root.

2. f(-1)=(-1)^3-5\cdot (-1)^2-2\cdot (-1)+24=20\neq 0f(−1)=(−1)

3

−5⋅(−1)

2

−2⋅(−1)+24=20



=0 , -1 is not a root.

3. f(2)=2^3-5\cdot 2^2-2\cdot 2+24=8\neq 0f(2)=2

3

−5⋅2

2

−2⋅2+24=8



=0 , 2 is not a root.

4. f(-2)=(-2)^3-5\cdot (-2)^2-2\cdot (-2)+24=0f(−2)=(−2)

3

−5⋅(−2)

2

−2⋅(−2)+24=0 , -2 is a root.

5. f(3)=3^3-5\cdot 3^2-2\cdot 3+24=0f(3)=3

3

−5⋅3

2

−2⋅3+24=0 , 3 is a root.

6. f(-3)=(-3)^3-5\cdot (-3)^2-2\cdot (-3)+24=-42\neq 0f(−3)=(−3)

3

−5⋅(−3)

2

−2⋅(−3)+24=−42



=0 , -3 is not a root.

7. f(4)=4^3-5\cdot 4^2-2\cdot 4+24=0f(4)=4

3

−5⋅4

2

−2⋅4+24=0 , 4 is a root.

The cubic function has at most 3 roots, then

Answer: roots of the function are -2, 3 and 4.

Answer:

90

Step-by-step explanation:

342-252=90

So, therefore, 252+90=342

Answer:

90

Step-by-step explanation:

Since the sum is 342 and we already know the first number is 252 we would take away 252 from 342 to get the amount of the second number.

(342-252=90)

We got 90 and to check we would add 252+90 which is =

(252+90=342)

The answer is 90

I hope this helped:)

Answer:

83438143e + 21

Step-by-step explanation:

83438143e + 21

Answer:

No.

Step-by-step explanation:

(h represents the hours; y represents years; m represents the total money they'd get!)

If you put this into an equation, for James it would be:

14h +2y = M

For Tyree, it would be:

7h + 2y = M

Because the numbers don't match up, the answer is no. The relationship is not proportional.

Answer:

Step-by-step explanation:

All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power. So the length of the edge of a cube with a volume of 125 is 5.

Answer:

triangle STU and WEK are CONGRUENT

ST=WK SIDE OF A CONGRUENT TRAINGLE ARE EQUAL

2M=N.....1

SU=WE

3M+5=N+8

3M+5=2M+8

3M-2M=8-5

M=3

NOW

N=2M=2×3=6CM

TU=WK=N=6CM.

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

When the water flows through the sprinkler nozzle, it speeds up, creating a low-pressure area that sucks water up from the supply pipe and distributes it over the lawn.

Archimedes' principle, Pascal, and Bernoulli's principle have been proved to be the most fundamental principles of physics. Here is a detailed explanation of the similarities and differences between the three and three examples of daily life for each of the principles:

Archimedes' principle: This principle of physics refers to an object’s buoyancy. It states that the upward buoyant force that is exerted on an object that is submerged in a liquid is equal to the weight of the liquid that is displaced by the object.
It is used to determine the buoyancy of an object in a fluid.
It is applicable in a fluid or liquid medium.
Differences:
It concerns only fluids and not gases.
It only concerns the buoyancy of objects.

Examples of daily life for Archimedes' principle:

Swimming: Swimming is an excellent example of this principle in action. When you swim, you’re supported by the water, which applies a buoyant force to keep you afloat.
Balloons: Balloons are another example. The helium gas in the balloon is lighter than the air outside the balloon, so the balloon is lifted up and away from the ground.
Ships: When a ship is afloat, it displaces a volume of water that weighs the same as the weight of the ship.

Pascal's principle:
Pascal's principle states that when there is a pressure change in a confined fluid, that change is transmitted uniformly throughout the fluid and in all directions.
It deals with the change in pressure in a confined fluid.
It is applicable to both liquids and gases.
Differences:
It doesn’t deal with the change of pressure in the open atmosphere or a vacuum.
It applies to all fluids, including liquids and gases.

Examples of daily life for Pascal's principle:

Hydraulic lifts: Hydraulic lifts are used to lift heavy loads, such as vehicles, and are an excellent example of Pascal's principle in action. The force applied to the small piston is transmitted through the fluid to the larger piston, which produces a greater force.
Syringes: Syringes are used to administer medicines to patients and are also an example of Pascal's principle in action.
Brakes: The braking system of a vehicle is another example of Pascal's principle in action. When the brake pedal is depressed, it applies pressure to the fluid, which is transmitted to the brake calipers and pads.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Step-by-step explanation:

Let's call the number of girls in the school "g". We know that there are 1000 boys, so the total number of students is 1000 + g.

The problem states that 48% of the total number of students were successful in the examination. Therefore, we can write an equation:

0.48(1000 + g) = 0.5(1000) + 0.4(g)

Simplifying and solving for g:

480 + 0.48g = 500 + 0.4g

0.08g = 20

g = 250

Therefore, the number of girls in the school is 250.

Answer:

250

Step-by-step explanation:

Hi dear,

Firstly, let the girls be G

1000 + G = Total number of students

50% of boy = 1000 × 0.5 = 500

40% of girls = G × 0.4 = 0.4G

0.48 • (1000 + G) = 480 + 0.48G

480 + 0.48G = 500 + 0.4G

Collect Like Terms

0.48G - 0.4G = 500 - 480

0.08G = 20

G = 20/0.08

G = 250

Therefore, the girls are 250( two hundred and fifty)in the school

Answer:

5,674,200,000,000

Step-by-step explanation:

The expression equivalent to\(-4x^2 + 2x - 5(1 + x)\)  is \(4x^2 + 8x + 5.\)

This expression matches the form \(x^2 + x + c,\) where c = 5.

To simplify the given expression \(-4x^2 + 2x - 5(1 + x)\) and make it equivalent to the expression \(x^2 + x + c,\) where c is a constant term, we need to perform some algebraic operations.

First, let's distribute the -5 to the terms inside the parentheses:

\(-4x^2 + 2x - 5 - 5x\)

Next, we can combine like terms:

\(-4x^2 + (2x - 5x) - 5 - 5x\)

Simplifying further:

\(-4x^2 - 3x - 5 - 5x\)

Now, let's rearrange the terms to match the form \(x^2 + x + c:\)

\(-4x^2 - 3x - 5x - 5\)

To make the leading coefficient positive, we can multiply the entire expression by -1:

\(4x^2 + 3x + 5x + 5\)

Now, we can combine the x-terms:

\(4x^2 + 8x + 5\)

So, the expression equivalent to \(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)This expression matches the form \(x^2 + x + c,\) where c = 5.

It's important to note that the original expression and the equivalent expression have different coefficients and constants, but they represent the same mathematical relationship.

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Answer:

216 different cakes are possible.

Step-by-step explanation:

Given that a bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes, if one option is chosen from each list, to determine how many different cakes are possible the following calculation must be performed:

4 x 3 x 6 x 3 = X

12 x 18 = X

216 = X

Therefore, 216 different cakes are possible.

Answer: 5(x-1)

Step-by-step explanation:

5*x = 5x

5*-1 = -5

therefore the answer is 5(x-1)

5x-5 distributed is 5(x-1).

The common factor of 5x and 5 is 5.

5x divided by 5 is 1x or x.

5 divided by 5 is 1.

So the answer is 5(x-1).

Answer: 26

Step-by-step explanation:

Answer:

5(2x-3)-7x=x-10

or, 10x -15 -7x = x-10

or, 3x-15=x-10

or, 3x- x = 15-10

or, 2x = 5

or, x= 5/2

The value of the variable b = -4, 4, based οn the prοvided data.

72 isn't a perfectly square number because its square base isn't a whοle integer. The real number οf 72 in its simplest versiοn is 62, where 2 is indeed an irratiοnal integer and 72 is therefοre alsο irratiοnal.

Starting with b² - 1 = 15,

we can add 1 tο bοth sides tο get b² = 16.

Taking the square rοοt οf bοth sides, we get b = ±4.

Therefοre, the sοlutiοns are b = -4 οr b = 4.

We can write the sοlutiοns as (b = -4, 4).

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The pre-image and image have the same shape after dilatation, but they are not the same size.

In the given question, we have to explain what is true about an image after a dilation.

The pre-image and image have the same shape after dilatation, but they are not the same size.

The figure is the same from every perspective. The midpoints of the figure's sides and the dilated shape's midpoint are both unchanged. Lines that are parallel and perpendicular to one another in the figure are identical to those in the dilated figure. The pictures stay the same.

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There are a total of 7 ways to seat eight people around a table if Alice and Bob won't sit next to each other. This is because the seating arrangement must be a permutation of the seven people not including Alice and Bob.

We can calculate this by taking the factorial of the number of people not including Alice and Bob, which is seven. Since a factorial is the product of an integer and all the integers below it, we can calculate the factorial of seven by multiplying all the integers from one to seven.

This gives us 7=5040, which is the total number of ways to seat eight people around a table if Alice and Bob won't sit next to each other.

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Answer: I am terrible at these kinds of "sit-uating" problems (haha). My idea is that the three people can be situated in (3−1)!

ways and that the rest can be situated in (5−1)!

ways. Then, the ordering of the five people depends on the partitions of 5 into 3 groups:

Step-by-step explanation: