4 - 7/x = 5 + 6/x help me guys

Answer:

1/16

Step-by-step explanation:

For 1/4 you multiply the four with the four friends. And you'll get 4x4. You multiply it and get 16. Same as you for it with 1/2. 4x1/2=? Try it out! Hope this helps!

Answer:

\((\frac{4\sigma}{2.056})^2\), rounded up, if needed, citizens should be included in the sample, in which \(\sigma\) is the standard deviation of the population.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.96}{2} = 0.02\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.02 = 0.98\), so Z = 2.056.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

Within 4 years of the actual mean

We have to find n for which M = 4. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(4 = 2.056\frac{\sigma}{\sqrt{n}}\)

\(2.056\sqrt{n} = 4\sigma\)

\(\sqrt{n} = \frac{4\sigma}{2.056}\)

\((\sqrt{n})^2 = (\frac{4\sigma}{2.056})^2\)

\(n = (\frac{4\sigma}{2.056})^2\)

\((\frac{4\sigma}{2.056})^2\), rounded up, if needed, citizens should be included in the sample, in which \(\sigma\) is the standard deviation of the population.

Answer:

lesser x = - 1 , greater x = 1

Step-by-step explanation:

- 4x² - 7 = - 11 ( add 7 to both sides )

- 4x² = - 4 ( divide both sides by - 4 )

x² = 1 ( take square root of both sides )

x = ± \(\sqrt{1}\) = ± 1

then

lesser x = - 1

greater x = 1

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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Answer:

295= 210+X

Step-by-step explanation:

If she has a total of 295 dollars deposited and she had 210 before then you could just subtract 295-210 to find how much she deposited. The answer would be that she deposited 85 dollars in her savings account and the equation is listed above.

Answer:

the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Step-by-step explanation:

We can use the concept of minimum distance to find the minimum possible time for Emma to reach the island. Let's assume that Emma walks to some point P along the shoreline and then swims to the island. We want to find the point P that minimizes the total distance that Emma has to cover.

Let the distance from the cottage to point P be x km. Then the distance from point P to the island is (3 - x) km. Using the Pythagorean theorem, we can find the distance from the cottage to the island as follows:

distance^2 = x^2 + (3 - x)^2 + 2^2

distance^2 = 10x - 6x^2 + 13

To minimize the distance, we can take the derivative of the distance equation with respect to x and set it equal to zero:

d(distance^2)/dx = 10 - 12x = 0

x = 5/6 km

Substituting x = 5/6 km into the distance equation, we get:

distance^2 = 25/3 km^2

distance = 5/sqrt(3) km

Therefore, the minimum possible time for Emma to reach the island is the time it takes her to walk to point P (distance x) plus the time it takes her to swim to the island (distance 3 - x), divided by her swimming speed:

time = x/4 + (3 - x)/3

time = (3x + 12 - 4x)/12

time = (12 - x)/4

time = (12 - 5/6)/4

time = 2.9583 hours (rounded to 4 decimal places)

Therefore, the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Let's call the point where Emma starts swimming P. We can draw a diagram to visualize the situation:

Cottage ---------- Q ---------------- Island

x km 3 km 2 km

The distance from the cottage to Q is x km, and the distance from Q to the island is 2 km. The total distance Emma will have to travel can be expressed as:

d = √(x^2 + 2^2)

The time it will take Emma to walk the distance from the cottage to point P is:

t1 = x / 4

The time it will take Emma to swim from point P to the island is:

t2 = √((d - x)^2 + 2^2) / 3

The total time it will take Emma to reach the island can be expressed as:

T = t1 + t2

To find the minimum possible value of T, we can take the derivative of T with respect to x and set it equal to zero:

dT/dx = (1/4) - (d-x)/3√((d-x)^2+4) = 0

Solving for x, we get:

x = (3/5)d

Substituting this value of x back into the expression for T, we get:

T = (3/20)d + (2/5)√(5)

Rounding to the nearest hundredth, we get:

T ≈ 0.96 hours

Therefore, the minimum possible time it will take Emma to reach the island is approximately 0.96 hours.

Answer:

Step-by-step explanation:

Chanclas

Answer:

$110.94

Step-by-step explanation:

221.88 divided by 2 is 110.94

Answer:

Hello,

Step-by-step explanation:

\(\displaystyleV=2*\pi*\int\limits^4_2 {(\dfrac{1}{x}-\dfrac{1}{x^3} )*x } \, dx \\=2*\pi*\int\limits^4_2 {(1-\dfrac{1}{x^2} ) } \, dx \\=2*\pi* [x+\dfrac{1}{x}]^4_2\\\\\boxed{V=\dfrac{7\pi}{2}}\\\)

The doubling time of a bank account balance is the amount of time it takes for the balance to double. In this case, the doubling time is 10 years, which means that the balance will double every 10 years.

Let's say the initial balance in the bank account is B. After 10 years, the balance will have doubled to 2B. After another 10 years (i.e., 20 years from the initial balance), the balance will have doubled again to 4B. Finally, after another 10 years (i.e., 30 years from the initial balance), the balance will have doubled one more time to 8B.

Therefore, after 30 years, the balance in the bank account will have grown by a factor of 8B/B, which simplifies to just 8. This means that the balance in the bank account will be 8 times the initial balance after 30 years.

To summarize, the balance in the bank account will double every 10 years due to the given doubling time. After 30 years, it will have doubled three times, resulting in a growth factor of 2 x 2 x 2 = 8, which means the balance will be 8 times the initial balance.

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Finding the values of d and the value of m with the algebraic working will give us the the value of d to be 7 and the value of m to be 3.

Finding the value of d, we know that the sum of the first n terms of an arithmetic series is given by:

S = n/2 * (2a + (n-1)d)

Since the sum of the first n terms is S and the sum of the first 2m terms is S2m, we can set up the following equation:

S = m/2 * (2a + (m-1)d)

S2m = 2m/2 * (2a + (2m-1)d)

Substituting the given values for S and S2m into these equations, we get:

39 = m/2 * (2a + (m-1)d)

320 = 2m/2 * (2a + (2m-1)d)

Solving for d in each equation, we find that d = -7 in the first equation and d = 7 in the second equation. Since d must be a prime number, the only possible value for d is 7.

Now that we know the value of d, we can solve for m. Substituting the value of d back into one of the equations and solving for m, we get:

39 = m/2 * (2a + (m-1)7)

78 = m * (2a + (m-1)7)

78 = m * 2a + 7m^2 - 7m

7m^2 - m - 78 = 0

We can solve for m using the quadratic formula:

m = (-1 +/- sqrt(1^2 - 4*7*(-78)))/(2*7)

= (-1 +/- sqrt(2521))/14

= (-1 + 49)/14 = 3

= (-1 - 49)/14 = -7

Since m must be a positive integer, the only possible value for m is 3.

Therefore, the value of d is 7 and the value of m is 3.

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Answer:

A

Step-by-step explanation:

remember y=Mx+b where M is slope mad B is y intercept

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

The number of units sold increased by \(\mathbf{11.2\%}\)

Step-by-step explanation:

Vacuum dealer sold units in 2011 = 420

Vacuum dealer sold units in 2012 = 467

We need to find percent increase or decrease

Since, In 2012 units sold are greater than 2011, so there will be percent increase.

The formula used is: \(Percent\:Increase=\frac{New\:Value-Original\:Value}{Original\:Value}\times 100\)

We have New Value (Units sold in 2012) = 467

Original Value (Units sold in 2011) = 420

Percent increase is:

\(Percent\:Increase=\frac{New\:Value-Original\:Value}{Original\:Value}\times 100\\Percent\:Increase=\frac{467-420}{420}\times 100\\Percent\:Increase=\frac{47}{420}\times 100\\Percent\:Increase=11.2\%\)

So, The number of units sold increased by \(\mathbf{11.2\%}\)

Answer:

I might be wrong but i think C sorry if im wrong tho

Step-by-step explanation:

<3

Answer:

2827 m²

Step-by-step explanation:

The equation for volume of a sphere is:

\(V=\frac{4}{3}\pi r^3\)

Using this equation and the given volume of the sphere, we can find the radius of the sphere.

\(V=\frac{4}{3}\pi r^3\)

\(4500\pi = \frac{4}{3}\pi r^3\)

Divide both sides by π

\(4500=\frac{4}{3}(r^3)\)

Multiply both sides by 3

\(13500=4( r^3)\)

Divide both sides by 4

\(3375=r^3\)

Take the cube root of both sides

\(r=15\)

Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.

The equation for surface area of a sphere is \(4\pi r^2\). Substituting the value we found for the radius into the equation, we find:

\(SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2\)

The surface area of the sphere, rounded to the nearest square meter, is 2827 m².

Answer:

B C. F

Step-by-step explanation:

(a) Given \(f(x) = x^3\), the derivative is

\(f'(x)=3x^2\)

which is exists for all \(x\) in the domain of \(f\), so \(]f\) is differentiable everywhere and satisfies the mean value theorem. There is some number \(c\) in the open interval (0, 2) such that

\(f'(c) = \dfrac{f(2) - f(0)}{2-0} \iff 3c^2 = \dfrac{8-0}2 = 4\)

Solve for \(c\) :

\(3c^2 = 4 \implies c^2 = \dfrac43 \implies \boxed{c = \dfrac2{\sqrt3}}\)

We omit the negative square root since it doesn't belong to (0, 2). Graphically, the MVT tells us the tangent line to the curve \(f(x)=x^3\) at \(x=\frac2{\sqrt3}\) is parallel to the secant line through the endpoints of the given interval.

(b) \(f(x)=1+x+x^2\) has derivative

\(f'(x)=1+2x\)

By the MVT,

\(f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff 1+2c = \dfrac{7-1}2 \implies \boxed{c = 1}\)

(c) \(f(x) = \cos(2\pi x)\) has derivative

\(f'(x) = -2\pi \sin(2\pi x)\)

By the MVT,

\(f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff -2\pi \sin(2\pi c) = \dfrac{0-0}2 \implies \sin(2\pi c) = 0 \\\\ \implies 2\pi c = n\pi \implies c = \dfrac n2\)

where \(n\) is any integer. There are 3 solutions in the interval (0, 2),

\(\boxed{c = \dfrac12, c = 1, c = \dfrac32}\)

(Pictured is the situation with \(c=\frac12\))

The different sums are possible are 18.

As, the number of different sums possible is given by the equation:

Number of different sums = n x m

In other words, we multiply the number of outcomes for the first spinner by the number of outcomes for the second spinner to get the total number of unique sums.

So, the different sums are possible

= 2 x 3 x 3

= 18

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When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, the signs in the binomials should be both positive

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The form of the polynomial is given as:

ax2 + bx + c

Where a, b, and c are positive real numbers.

Since a, b, and c are positive real numbers. then the form of the expansion would be:

ax2 + bx + c = (dx + e)(fx + g)

Take for instance, we have the following quadratic equation

x^2 + 6x +  8

Expand the equation

x^2 + 6x +  8 = x^2 + 4x + 2x +  8

Factorize the equation

x^2 + 6x +  8 = (x + 2)(x + 4)

Hence, the signs in the binomials should be both positive

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Answer:

23/10

Step-by-step explanation:

i know its right

Answer:

80

Step-by-step explanation:

Answer:

Investment is a source of Income.

Self Employment Income

Answer: Business ownership

Step-by-step explanation: took the quiz

For given functions, The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

What is the definition of a function?

A function is a mathematical rule that gives each input value a distinct output value. A function is officially defined as a collection of ordered pairs (x, y) in which each input value x is coupled with exactly one output value y. The domain of the function refers to the input values, while the range refers to the output values. A graph, table, equation, or verbal explanation can all be used to depict a function. When the input value is x, the notation f(x) is commonly used to express the output value of a function f.

Now,

From given function f(x) and g(x)

For f(x) when x=0 then y=1 or y-intercept=1

for g(x), the y-intercept is 1 from equation y=4x+1

and slope of g(x)=4

and slope of f(x)=(11-1)/(2-0)

=10/5

=2

Hence,

           The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

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Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Problem

Make Sense and Persevere Randyand Carla like to walk the path around their town park. The path is 2 miles long. Last month Randy walked the path 13 times, and Carla walked it 22 times. How many more miles did Carla walk than Randy last month?​

Solution

For this case we need to start finding the difference of times between the two persons:

22-13= 9 times

And then the total more miles that Carla walk are:

9* 2= 18 miles

Answer:

32.4 dollars

Step-by-step explanation:

The value of angle C to the nearest tenth is 21.6°

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

c² = a² + b² - 2ab cosC

8² = 14² + 19² - 2 × 14 × 19 cos C

64 = 196+ 361 - 532cosC

64 = 557 - 532 cosC

532cos C = 557 -64

532cos C =

cosC = 493/532

cos C = 0.93

C = 21.6°( nearest tenth)

Therefore the value of angle C is 21.6°

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