Share £20 in the ratio of 3:2

Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

1. The tangent of an acute angle in a right triangle equal to 17 greater than 1 that measure angle is 57.29 degrees.

2. The tangent of an acute angle in a right triangle equal to 17 less than 1 that measure angle is 45 degrees.

3. The tangent of an acute angle in a right triangle equal to 17 equal to 1 that measure angle is 45 degrees.

In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite to the angle to the length of the adjacent side. Let us denote the acute angle by θ, the length of the side opposite to the angle by a, and the length of the adjacent side by b. Then we have:

tan(θ) = a/b

Since the angle θ is acute, we have a > 0 and b > 0. We can use the Pythagorean theorem to relate the lengths of the two sides to the length of the hypotenuse c:

a^2 + b^2 = c^2

Solving for b, we get:

\(b = \sqrt{c^2 - a^2}\)

Substituting this into the expression for tangent, we get:

tan(θ) = a/ \(\sqrt{c^2 - a^2}\)

Now, we can use the given conditions to find the possible values of the angle θ.

1. If tan(θ) is 17 greater than 1, we have:

tan(θ) > 1 and tan(θ) = 17 + 1 = 18

Using the expression for tangent above, we get:

a/sqrt(c^2 - a^2) > 1 and a/√(c^2 - a^2) = 18

Squaring both sides of the inequality and simplifying, we get:

a^2 < (c^2 - a^2) and a^2 = 324(c^2 - a^2)

Solving for a/c, we get:

a/c = √(324/325)

Since a/c is the sine of the angle θ, we have:

sin(θ) = a/c = √(324/325)

Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.9999 radians or 57.29 degrees satisfies the given condition.

2. If tan(θ) is less than 1, we have:

tan(θ) < 1

Using the expression for tangent above, we get:

a/√(c^2 - a^2) < 1

Squaring both sides and simplifying, we get:

a^2 > (c^2 - a^2)

Solving for a/c, we get:

a/c > √(2)/2

Since a/c is the sine of the angle θ, we have:

sin(θ) > √(2)/2

Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition.

3. If tan(θ) is equal to 1, we have:

tan(θ) = 1

Using the expression for tangent above, we get:

a/√(c^2 - a^2) = 1

Squaring both sides and simplifying, we get:

a^2 = c^2 - a^2

Solving for a/c, we get:

a/c = √(2)/2

Since a/c is the sine of the angle θ, we have:

sin(θ) = a/c = √(2)/2

Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition. Alternatively, we can note that the angle whose tangent is equal to 1 is 45 degrees.

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Answer:

y = -13

Step-by-step explanation:

-22 = y - 9

y = -22 + 9

y = -13

Hope this helps!

Answer:

y= -13

Step-by-step explanation:

Isolate the y by adding 9 on each side: -13 = y

Answer: y = -13

I hope this helped, please mark Brainliest, thank you!

Answer:

164.64

Step-by-step explanation:

you just have to multiply

8.4 x 3.5= 29.4 then you do 29.4 x 5.6 = 164.64

Step-by-step explanation:

1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.

2:open the brackets and put signs accordingly.

3: cancel (-1) and (+1).

4: remaining is your answer.

Answer:

the answer would be 2.70 dollars I hope this helps you :)

Step-by-step explanation:

Given the expression:

To factor the given expression, we need two numbers the product of them = 100 and the sum of them = 20

We will factor the number 100

100 = 1 x 100 ⇒ 1 + 100 = 101

100 = 2 x 50 ⇒ 2 + 50 = 52

100 = 4 x 25 ⇒ 4 + 25 = 29

100 = 5 x 20 ⇒ 5 + 20 = 25

100 = 10 x 10 ⇒ 10 + 10 = 20

So, the suitable numbers are 10, 10

so, the factorization will be as follows:

The given expression is a complete square.

So, the answer will be (u+10)(u+10)

Or can be written as (u+10)²

The number of participants that would be needed for a within-subjects experiment is 80.

An experiment simply means a research that's conducted in order to get information about a particular thing.

In this case, we want to know the number of participants that will be neeed within-subjects experiment comparing four different treatment conditions with a total of 20 scores in each treatment.

This will be:

= Number of scores × Number of treatment

= 20 × 4

= 80

The participants needed are 80.

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Answer:

The second one the amount of monthly sales

Step-by-step explanation:

The 2000 is the total

Answer:

B, Irrational number

Step-by-step explanation:

Irrational number because

\(\pi\)

is Irrational number

Answer:

66550000000 in.²

Step-by-step explanation:

22³in x 10⁴in x 5⁴in = 66550000000 in

Answer:

31.2 inches

Step-by-step explanation:

Draw a line representing the height of the triangle, and divide it into 2 triangles.

Apply Pythagoras Theorem on one of the smaller triangles first.

\(h = \sqrt{ {36}^{2} - {(36 \div 2)}^{2} } \\ h = \sqrt{ {36}^{2} - {18}^{2} } \\ h = \sqrt{972} \\ h = 31.17691...\)

h = 31.2 inches (rounded to the nearest tenth)

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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Answer:

10/21

Step-by-step explanation:

The fact that k≥4≥1 is used in the base case of the inductive proof, not in the inductive step.

In the base case, we need to show that the statement holds for k=4. Since 4≥1, this satisfies the condition. The inductive step assumes that the statement holds for some arbitrary k≥4 and then shows that it holds for k+1. The inductive step of an inductive proof aims to show that if a statement holds true for a certain value, it also holds true for the next value. In the given problem, we need to demonstrate that for k≥4, if 2k≥3k, then 2(k+1)≥3(k+1). The fact that k≥4≥1 is utilized in the base case step of the proof. The base case ensures that the initial condition (k=4) satisfies the given inequality. By showing that the inequality holds true for k=4, we establish a starting point for the inductive step. This allows us to apply the inductive step and generalize the result to all values of k greater than or equal to 4.

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The least expensive C.A.R.S. that can be built to those specifications has dimensions of approximately 4.3088 m x 2.1544 m x 1.7321 m and will cost about $265.47 to build.

Let's start by looking at the dimensions of the base. We know that the length of the base is twice its width. Let's represent the width of the base as "x." This means that the length of the base is "2x." The area of the base is simply the product of the length and the width, which is 2x * x = 2x².

Next, let's look at the dimensions of the sides. The height of the box is going to be represented by "h." The length of each side is going to be equal to the length of the base, which we already know is 2x. The width of each side is going to be equal to the width of the base, which is just x. So the area of each side is simply 2hx.

Now we can use the formula for the volume of a rectangular prism to find the value of "h" in terms of "x." The volume of the box is given as 10 m^3, so:

V = lwh = (2x)(x)(h) = 10

Simplifying this equation, we get:

2x²h = 10

Solving for "h," we get:

h = 5/x²

Now that we have an expression for "h" in terms of "x," we can use it to find the total surface area of the box, which is the sum of the area of the base and the area of the four sides. We can then use this expression to find the minimum cost for a given volume of the box.

The total surface area of the box is given by:

A = 2x² + 4(2hx)

Substituting the expression we found for "h" into this equation, we get:

A = 2x² + 4(2x)(5/x²)

Simplifying this equation, we get:

A = 2x² + 40/x

Now we can take the derivative of this expression with respect to "x" and set it equal to zero to find the value of "x" that will minimize the cost of the box. Differentiating and setting equal to zero, we get:

dA/dx = 4x - 40/x² = 0

Solving for "x," we get:

x^3 = 10

Taking the cube root of both sides, we get:

x ≈ 2.1544

Now we can use this value of "x" to find the dimensions of the least expensive C.A.R.S. that can be built to those specifications. The length of the base is twice the width, so:

Length = 2x ≈ 4.3088

Width = x ≈ 2.1544

Height = 5/x² ≈ 1.7321

So the dimensions of the least expensive C.A.R.S. that can be built to those specifications are approximately: Length = 4.3088 m Width = 2.1544 m Height = 1.7321 m

These dimensions will allow us to build a C.A.R.S. with a volume of 10 m^3, while using the least amount of material possible, which means that the cost will be minimized. We can verify this by calculating the total surface area of the box and the cost of the materials needed.

The total surface area of the box can be calculated by substituting the values we found for "x" and "h" into the expression we derived earlier:

A = 2(2.1544)² + 4(2)(5)/(2.1544)² ≈ 28.2742 m²

Now we can calculate the cost of the materials needed to build the box:

Cost = (Area of base)(Cost per square meter for base) + (Area of sides)(Cost per square meter for sides)

Cost = (2.1544²)(10) + (28.2742 - 2(2.1544²))(6) ≈ $265.47

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The joint density function f(x, y) \(= \frac{(6 - x + y)}{64}\) describes the probability density of the random variables x and y within the range -1 < x < 1. Outside this range, the joint density function is zero, indicating no probability density.

The given joint density function is represented as:

f(x, y) = \(\frac{(6 - x + y)}{64}\)

This function describes the probability density of two random variables, x and y, within a specified region.

The function is defined over the range -1 < x < 1,

The density is normalized such that its integral over the entire range is equal to 1.

For any given pair of values (x, y) within the specified range,

plugging them into the function will give the probability density at that point.

The function value is obtained by substituting the values of x and y into the expression

\(\frac{(6 - x + y)}{64}\).

However, the function is not defined outside the range

-1 < x < 1,

As the density is specified only for this interval.

For any values of x outside this range,

the joint density function is equal to zero

(f(x, y) = 0).

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Reducing the variation of a process will increase the width of a given confidence interval relative to that process.

Option C is correct .

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as a confidence interval. By employing the dimensions of values used in the computation of the intervals, it is simple to establish the link between components of two confidence intervals. The width is a fundamental component in these range estimates, which are affected by sample size, etc.

Hence, reducing the variation of a process will increase the width of a given confidence interval relative to that process is false.

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Answer:

254 cm² (to 3 s.f.)

Step-by-step explanation:

Area of shaded region

= area of large circle -area of smaller circle

\(\boxed{area \: of \: circle = \pi {r}^{2} }\)

Radius of large circle= 15cm

Radius of smaller circle= 12cm

Area of shaded region

= π(15²) -π(12²)

= 225π -144π

= 81π

= 81(3.14)

= 254.34

= 254 cm² (3 s.f.)

Explanation

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

From the given question

Also

Therefore, the answer is Reflexive Property; Given

The number of ways 4 people each choose a piece of cake from 7 total is 840.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, 4 people each choose a piece of cake from 7.

We know that, P(n,r) = n!/(n-r)!

Here, P(7, 4) =7!/(7-4)!

= (7×6×5×4×3!)/3!

= 7×6×5×4

= 840

Therefore, the number of ways 4 people each choose a piece of cake from 7 total is 840.

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Answer:

Step-by-step explanation:

The line is a vertical line with an equation of x = 1

y can be anything.

Draw (on graph paper) a dot at x = 1. Go down to - 3 and keep on going down to - 9. Then go up from x = 1. That's what this problem should give you.

Answer:

supplemental

Step-by-step explanation:

adjacent, or consecutive, angles are equal to 180 degrees

This is an example of exponential growth.

Since the population doubles in size every 29 hours,

and the initial population is 30000,

then in 29 hours,

the population = 30000 x 2 = 60000

and in

another 29 hours (total of 58 hours from the start),

the population = 60000 x 2 = 120000

Hence the population after 58 hours is 120000 bacteria.

Answer:

Step-by-step explanation:

210 - (0.45 * 210) = 116.5

Answer:  (x, y) = ( -2, -3 )

=============================================

Work Shown:

2x+y = -7

2( x ) + y = -7

2( 4+2y ) + y = -7 .... plug in x = 4+2y

2*4 + 2*2y + y = -7

8 + 4y + y = -7

5y+8 = -7

5y = -7-8 .... subtract 8 from both sides

5y = -15

y = -15/5 ... divide both sides by 5

y = -3

This y value pairs with...

x = 4 + 2y

x = 4 + 2(-3)

x = 4 - 6

x = -2

So we have (x, y) = (-2, -3) as the solution to the system.

Answer:

(-2,-3)

Step-by-step explanation:

this is the ordered pair when we do (x,y).