What is the missing numerator?
\(\frac{5}{7} + \frac{?}{6} = \frac{51}{42}\)
a. 2
b. 3
c. 8
d. 10

Answer: K = 8

Step-by-step explanation:

For these kinds of problems you have to isolate the variable, the one we're trying to isolate is k.

First step is adding 4 to both sides to get rid of the -4 on the left.

Once you do that youll have 4k = 36.

Now divide both sides by 4 to get the k by itself, this'll give you k = 8.

You can plug it in to see if it's right.

4(8) - 4 = 32

36 - 4 = 32

32 = 32

So its correct

Answer:

1) 7+(-3)=

7-3=4

Step-by-step explanation:

The answer is:

4

Work/explanation:

Adding a negative is the same as subtracting a positive;

\(\sf{a+(-b)=a-b}\)

Similarly,

\(\sf{7+(-3)=7-3=4}\)

Answer:

the probability: (4,4) it is certain to happen. (6,3) it is not likely nor unlikely

because it is half. (9,5) it is likely to happen.

Step-by-step explanation:

Answer:

5 cm

Step-by-step explanation:

Area= 1/2 base×altitude

let base be x cm hence altitude = x+7 cm

30 = 1/2 (x) (x+7)

60= x^2 + 7x

x = 5 or - 12

but measurements can't be in negative form hence -12 is discarded. Thus x= 5 cm

x= base hence base = 5cm

Answer:

base = 5 cm

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the altitude )

let base be b then h = b + 7

Given A = 30, then

\(\frac{1}{2}\)b(b + 7) = 30 ( multiply both sides by 2 to clear the fraction )

b(b + 7) = 60 ← distribute left side

b² + 7 = 60 ( subtract 60 from both sides )

b² + 7 - 60 = 0 ← in standard form

(b + 12)(b - 5) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 12 = 0 ⇒ b = - 12

b - 5 = 0 ⇒ b = 5

However, b > 0, thus b = 5

That is the base is 5 cm

Answer:

A) (2, 6)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

The solution set of the systems of equations would be where the 2 lines intersect. According to the graph, the equations intersect at (2, 6). Therefore, our answer is A.

Answer:

Step-by-step explanation:

\(y = \frac{1}{3}x+6\\\\\)

When x = 0 , y = 0 + 6 = 6    

(0 , 6)

When x = 3,

\(y = \frac{1}{3}*3 + 6 = 1 + 6 = 7\)

(3, 7)

When x = -3

\(y =\frac{1}{3}*(-3)+6=-1 + 6 = 5\)

(-3, 5)

Plot (0,6) ; (3, 7) and (-3, 5) in the graph and join the points.

Answer:

n=9

Step-by-step explanation:

Subtract 4n and 2n ( 2n =18 )

Divide 2 on both sides ( 18/2 )

Once you divide, you get the answer of 9

Hope this helped, Have an amazing day!!

it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.

No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.

When conducting hypothesis testing, the significance level (in this case, 0.01 or 1%) is the probability of rejecting the null hypothesis when it is actually true. This means that there is a 1% chance of observing a significant result purely by chance, even if the null hypothesis (in this case, that the subjects do not have ESP) is true.

In this scenario, nine subjects performed significantly better than random guessing, which may suggest that they have ESP. However, due to the possibility of observing significant results by chance, it is not proper to conclude that these nine people have ESP. There is still a chance that these results are purely coincidental.

Additionally, it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.

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The Length x in terms of the trigonometric ratios is  b / (√3 - 1).

Given, In a right triangle ABC,

angle A = 30° and angle C = 60°.

We have to find the length x in terms of trigonometric ratios of 30°.

Now, In a right-angled triangle ABC,

AB = x,

angle B = 90°,

angle A = 30°, and angle C = 60°.

Let BC = a.

Then, AC = 2a.

By applying Pythagoras theorem in ABC, we get;

\({(x)^2} + {(a)^2} = {(2a)^2}\)

⇒\({(x)^2} + {(a)^2} = 4{(a)^2}\)

⇒\({(x)^2} = 3{(a)^2}\)

⇒ x = a√3 …….(i)

Now, consider a right-angled triangle ACD with angle A = 30° and angle C = 60°.

Here AD = AC / 2 = a.

Let CD = b.

Then, the length of BD is given by;

BD = AD tan 30°

= a / √3

Now, in a right-angled triangle BCD,

BC = a and BD = a / √3.

Therefore,

CD = BC - BD

⇒ b = a - a / √3

⇒ b = a {(√3 - 1) / √3}

Therefore,

x = a√3 {From equation (i)}

= a {(√3) / (√3)}

= a {√3}

Hence, x = b / (√3 - 1)

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An all-night study session can help you catch up on school assignments. The only way to become a straight-A student is efficient study habits.

Most students pseudo-work and end up wasting valuable time.

The correct option is (C)

This is based on an article about pseudo-working which is something that students do where they read for long hours and appear very serious in reading when in fact they do not focus on the reading and therefore end up not grasping much.

The author was trying to express that most students do this and that it is simply a waste of time which could have been spent actually studying.

The correct option is (C).

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The given question is incomplete, complete question is:

What central idea about studying does the author express in Passage 1?

A Straight-A students know how to work harder than other students.

B The only way to become a straight-A student is efficient study habits.

C Most students pseudo-work and end up wasting valuable time.

D An all-night study session can help you catch up on school assignments.

The variables of farmer are independent variables and dependent variables.

In this scenario, the farmer is testing the impact of different amounts of nitrogen on corn plant height. Her variables are as follows:

1. Independent variable: The amount of nitrogen infused in the soil (one pot has nitrogen-infused soil and the other has regular soil).

2. Dependent variable: The height of the corn plants (measured in feet).

However, it's important to note that the experimental setup has a potential confounding variable, which is the location of the pots (one is outside and the other is in the bathroom). This might influence the results and make it difficult to solely attribute the differences in height to the nitrogen content in the soil.

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Answer:

(3x+5)(7x^2+3)

Step-by-step explanation:

Factor : 21x^3+35x^2+9x+15

21x^3+35x^2+9x+15

=(3x+5)(7x^2+3)

______________________

Hope this helps!

O....M.....G.....?!

i am only in 6th grade....

but i could do it.....but i have no idea...

BIG OOOOOF!

Answer:

4

Step-by-step explanation:

Answer:3

Step-by-step explanation:

The inequality that represents the cost, c, that Mr. Daniels can spend on the class trip is; c < 300

We are told that;

Mr. Daniels is organizing a class trip.

Mr. Daniels wants to spend less than $300

Thus, if the cost that Mr. Daniels can spend on the class trip is given as c, then it means that c has to be less than the amount which he wants to spend which is $300.

Thus, since c has to be less than $300, then it means that the inequality to be used would be a less than sign which can be expressed as;

c < 300

Thus, we conclude that it is the required inequality.

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The derivative is negative, the equilibrium point y = 0 is locally stable.

(a) To find all  stability and determine if each is locally stable or unstable, follow these steps for the equation y' = 5 - 3y:

1. Set y' equal to 0 and solve for y: 0 = 5 - 3y.
2. Isolate y: 3y = 5, so y = 5/3.

Now, let's use the local stability criterion:

3. Calculate the  derivate of y' with respect to y: dy'/dy = -3.
4. Evaluate the derivative at the equilibrium point y = 5/3: -3.

Since the derivative is negative, the equilibrium point y = 5/3 is locally stable.

For the phase plot, sketch the slope field of the differential equation y' = 5 - 3y. You will notice that the slopes are positive for y < 5/3 and negative for y > 5/3, which confirms the stability of the equilibrium point.

(b) To find all equilibria and determine if each is locally stable or unstable, follow these steps for the equation y' = 2y - 3y:

1. Simplify the equation: y' = -y.
2. Set y' equal to 0 and solve for y: 0 = -y, so y = 0.

Now, let's use the local stability criterion:

3. Calculate the derivative of y' with respect to y: dy'/dy = -1.
4. Evaluate the derivative at the equilibrium point y = 0: -1.

Since the derivative is negative, the equilibrium point y = 0 is locally stable.

For the phase plot, sketch the slope field of the differential equation y' = -y. You will notice that the slopes are positive for y < 0 and negative for y > 0, which confirms the stability of the equilibrium point.

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(a) The derivative of y = \((3x^2 - 5) / (2x + 3)\) with respect to x is given by:

dy/dx = \([(6x)(2x + 3) - (3x^2 - 5)(2)] / (2x + 3)^2\)

Simplifying this expression yields:

\(dy/dx = (12x^2 + 18x - 6x^2 + 10) / (2x + 3)^2\\dy/dx = (6x^2 + 18x + 10) / (2x + 3)^2\)

(b) The derivative of y = √(1 + √x) with respect to x can be found using the chain rule. Let's denote u = 1 + √x. Then y = √u. The derivative dy/dx is given by:

dy/dx = (dy/du) * (du/dx)

To find dy/du, we apply the power rule for derivatives, resulting in 1/(2√u). To find du/dx, we differentiate u = 1 + √x, which gives du/dx = 1/(2√x).

Combining these results, we have:

dy/dx = (1/(2√u)) * (1/(2√x))

dy/dx = 1 / (4√x√(1 + √x))

(c) The equation \(x^2y - (y^2/3) - 3 = 0\) can be rewritten as \(x^2y - y^{2/3} = 3\). To find dy/dx, we differentiate both sides with respect to x using the product rule and chain rule.

Using the product rule, we get:

\(x^2(dy/dx) + 2xy - (2/3)y^{-1/3}(dy/dx) = 0\)

Rearranging the equation and isolating dy/dx, we have:

\(dy/dx = -(2xy) / (x^2 - (2/3)y^{-1/3})\)

This is the derivative of y with respect to x for the given equation.

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The equation rearranged so that m is the independent variable is n = (9/11)m

To rearrange the equation -2m - 5n = 7m - 3n so that m is the independent variable, we need to isolate the term that contains m on one side of the equation. We can do this by adding 2m to both sides and then subtracting 3n from both sides. This gives us:

-2m - 5n + 2m = 7m - 3n + 2m - 3n

-5n = 9m - 6n

Now, we can further isolate the term containing m by subtracting 6n from both sides and then dividing both sides by 9:

-5n - 6n = 9m - 6n - 6n

-11n = 9m - 12n

-11n + 12n = 9m

n = (9/11)m

Therefore, the equation rearranged so that m is the independent variable is:

n = (9/11)m

This equation expresses n in terms of m, where m is the independent variable, and n depends on m. We can use this equation to determine the value of n for a given value of m.

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Answer:

Step-by-step explanation:

X-intercept: y=0:

6x +2×0 = 12

6x = 12

 x = 2          

Y-intercept: x=0:

6×0 + 2y = 12

2y = 12

 y = 6      

The square of the centimeter of the area is calculated by the square of the centimeter. The area of the rectangle is calculated by the formula width x length. So the rectangles area is 94cm  

Squares have only one side that is squared to find the area of the shape. But in rectangle there will be two sides given that width and length of the shape. So to find the area the width and the length of the rectangle is given so the numerical must be multiplied. In the given question the width of the rectangle is 8.5 and the length of the rectangle is 11.

o the area of the rectangle can be found by the formula= w x l

=8.5 x 11

=93.5

approximately can be taken as 94 cm.

A rectangle can is a four sided shape that includes the length, width and height and that opposites sides are equal in the rectangle. The adjacent sides of the rectangle is perpendicular and the angle is right angle that is it is measured as 90 degree. A rectangle can be a parallelogram but parallelogram can not be equal to the rectangle.

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The question has an area because the square because the square has only one side and the area of the square can be found by squaring one side of square. So the actual question should be What is the area, in rectangle centimeters, of an 8.5 inch by 11 inch sheet of paper?

Answer:

Maya is hiking down at a speed of 100 feet per hour.

Step-by-step explanation:

Given that Maya is hiking down a mountain, and after one hours she is at 500 feet elevation while after three hours she is at 300 feet elevation, to determine the speed at which Maya is hiking down the following calculation must be performed:

3-1 = 2

500-300 = 200

200/2 = 100

Thus, Maya is hiking down at a speed of 100 feet per hour.

The coefficient of x³ in the binomial expansion is k = 0

Given data ,

Let the binomial expansion be represented as A

Now , the value of A is

A = ( 2x + 1 )²

On simplifying the equation , we get

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

( 2x + 1 )² = ( 2x + 1 ) ( 2x + 1 )

( 2x + 1 )² = 4x² + 2x + 2x + 1

( 2x + 1 )² = 4x² + 4x + 1

Hence , the coefficient of x³ in the expansion of (2x + 1)² is 0

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Answer:

-7 & 1

Step-by-step explanation:

\( - 7 \times 1 = -7 \\ \\ - 7 + 1 = - 6\)

Hope it helps you in your learning process.

f(0.9) ≈ 2.0808 This is a good approximation of f(1.08), given that we only used the first four nonzero terms of the Taylor series.

a. To find the first four nonzero terms of the Taylor series centred at 0 for the function f(x) = (1 + x)⁻², we need to compute the first four derivatives of the function and evaluate them at x = 0.
f(x) = (1 + x)⁻²
f'(x) = -2(1 + x)⁻³
f''(x) = 6(1 + x)⁻⁴
f'''(x) = -24(1 + x)⁻⁵
Now, evaluate the derivatives at x = 0:
f(0) = (1 + 0)⁻² = 1
f'(0) = -2(1 + 0)⁻³ = -2
f''(0) = 6(1 + 0)⁻⁴ = 6
f'''(0) = -24(1 + 0)⁻⁵ = -24
Thus, the first four nonzero terms of the Taylor series are:
1 - 2x + 6x² - 24x³

b. To approximate the given quantity 1.08, we can use the first four terms of the Taylor series. Start by determining a value of x such that f(x) equals the value to be approximated:
1.08 ≈ 1 - 2x + 6x² - 24x³
To solve for x, we can use trial and error or numerical methods, such as the Newton-Raphson method or the bisection method. In this case, we find that x ≈ 0.0254. Therefore, to approximate f(x) ≈ 1.08, we can use the value x ≈ 0.0254 in the Taylor series expansion:
1.08 ≈ 1 - 2(0.0254) + 6(0.0254)² - 24(0.0254)³

a. The Taylor series centred at 0 for f(x) is given by:
f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...
where f(0) = 1, f'(0) = 1, f''(0) = 0, f'''(0) = 2, f''''(0) = 0, and so on.
So, the first four nonzero terms of the Taylor series are:
f(x) = 1 + x + (2/3)x³ + (4/15)x⁴ + ...

b. We want to approximate f(1.08) using the first four terms of the Taylor series. Let's first check if f(1.08) is a valid value to use: f(1.08) = 1 + 1.08 = 2.08
Now, we need to find a value of x such that f(x) equals 2.08. We can use the approximation we just found (f(1.08) ≈ 2.08) and solve for x in the first four terms of the Taylor series:
2.08 ≈ 1 + x + (2/3)x³ + (4/15)x⁴
Simplifying and rearranging, we get:
(2/3)x³ + (4/15)x⁴ ≈ 1.08
Multiplying both sides by 15/4 to clear the denominators, we get:
5x³ + 3x⁴ ≈ 4.05
We can solve for x using numerical methods (e.g. Newton's method), but for simplicity let's use trial and error. We can try x = 1 first:
5(1)³ + 3(1)⁴ = 8
This is too large, so let's try x = 0.9:
5(0.9)³ + 3(0.9)⁴ ≈ 3.993
This is close enough, so we'll use x = 0.9. Plugging this into the first four terms of the Taylor series, we get:
f(0.9) ≈ 1 + 0.9 + (2/3)(0.9)³ + (4/15)(0.9)⁴
Simplifying, we get:
f(0.9) ≈ 2.0808
This is a good approximation of f(1.08), given that we only used the first four nonzero terms of the Taylor series.

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ToS is a bijection and has an inverse that is also a linear transformation, we conclude that ToS is an isomorphism.

To show that the composition ToS is an isomorphism, we need to show that it is a bijection and that its inverse exists and is also a linear transformation.

First, we'll show that ToS is injective. Suppose that ToS(x) = ToS(y), where x, y are vectors in U. Then we have:

ToS(x) = T(S(x)) = T(S(y)) = ToS(y)

Since T is an isomorphism, it is injective, so we can cancel it on both sides to obtain:

S(x) = S(y)

Again, since S is an isomorphism, it is injective, so we can cancel it on both sides to get:

x = y

This shows that ToS is injective.

Next, we'll show that ToS is surjective. Let z be any vector in W. Since T is an isomorphism, it is surjective, so there exists some y in V such that T(y) = z. Similarly, since S is an isomorphism, it is surjective, so there exists some x in U such that S(x) = y. Then we have:

ToS(x) = T(S(x)) = T(y) = z

This shows that ToS is surjective.

Since ToS is both injective and surjective, it is a bijection. The last thing we need to show is that its inverse exists and is also a linear transformation.

Let R = (ToS)^(-1) be the inverse of ToS. We claim that R = S^(-1)oT^(-1). To see why this is true, consider the following calculation:

(RoToS)(x) = R(ToS(x))

= S^(-1)oT^(-1)(T(S(x)))  [definition of R]

= S^(-1)(S(x))            [since T^(-1)oT and S^(-1)oS are identity maps]

= x

This shows that R is the inverse of ToS, and it is also a linear transformation since it is the composition of two linear transformations.

Therefore, since ToS is a bijection and has an inverse that is also a linear transformation, we conclude that ToS is an isomorphism.

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Joaquin draws a circle on a sheet of grid paper.

The circumference of the circle that Joaquin drew is 25 1/7 units.

r=4 units

Circumference=2πr=2.(22/7).4 = 176/7= 25 1/7 units

The notion of a circle is a two-dimensional plane shape formed from a set of points with a constant or regular distance from a fixed point in a plane.

The fixed point on a circular plane shape is also called the origin or center point of the circle. While the distance of a fixed point from the starting point of a circle is also known as the radius of the circle.

As an object, a circle has special characteristics that make it different from other flat shapes.

This is also useful for identifying whether the object is included in a flat circular shape or not. The circle has at least 4 specific characteristics, as follows.

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a. To determine the probabilities associated with different service lives, we can use the properties of the normal distribution. Given that the mean service life is six years with a standard deviation of one-half year, we can calculate the probabilities as follows:

(1) Probability of service lives of at least five years:

We need to calculate the area under the normal curve to the right of five years. Using the Z-score formula, we find the Z-score corresponding to five years: Z = (5 - 6) / 0.5 = -2. We can then look up the corresponding probability in a standard normal distribution table or use statistical software to find the probability associated with a Z-score of -2. This gives us the probability of service lives of at least five years.

(2) Probability of service lives of exactly six years: Since the service life follows a normal distribution, the probability of exactly six years is zero since it is a continuous distribution. We can assign a very small positive probability to approximate "exactly" six years. (3) Probability of service lives of seven and one-half years: Similarly, we calculate the Z-score corresponding to seven and one-half years: Z = (7.5 - 6) / 0.5 = 3. We find the probability associated with a Z-score of 3 to determine the probability of service lives of seven and one-half years or longer. b. If the manufacturer offers service contracts of four years, we want to find the percentage of televisions that fail from wear-out during this period. We can calculate this by finding the area under the normal curve to the left of four years. Using the Z-score formula, we find the Z-score corresponding to four years: Z = (4 - 6) / 0.5 = -4. The corresponding probability gives us the percentage of televisions expected to fail during the four-year service period.

c. To achieve an expected wear-out rate of 2 percent or 5 percent, we need to determine the service period corresponding to these rates. We can use the Z-score formula in reverse to find the Z-score that corresponds to the desired wear-out rate. From there, we can calculate the corresponding service period by rearranging the Z-score formula and substituting the desired wear-out rate and the given mean and standard deviation values.

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If the recipe is for 1 gallon of punch , then the amount of punch needed to make 1/4 of the recipe is 1/8 cups of powdered punch .

the number of cups of powdered punch required to make 2/3 gallons of punch is = 1/3 cups ;

So , the number of cups of powdered punch required to make 1 gallons of punch is = (1/3)×(3/2) = 1/2 cups  ;

Since this is the recipe for 1 gallons of punch , to find the amount of punch mix needed to make 1/4 of the recipe , we multiply the ratio by (1/4) ,

On multiplying ,

We get ;

⇒ (1/2) × (1/4)

⇒ 1/8 .

Therefore , 1/8 cups of punch mix is required to make 1/4 of recipe .

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The given question is incomplete , the complete question is

It takes 1/3 cups of powered punch mix to make 2/3 gallons of punch. If the recipe is for 1 gallon of punch, how much punch is need to make 1/4 the recipe ?