Work out the missing number in this sum:
6.802 6 + 0.8+___

To compute the cumulative frequencies, we need to add the frequency values as follows:

Score Cumulative Frequency

50 - 59 4

50 - 69 6 = 4 + 2

50 - 79 13 = 6 + 7

50 - 89 23 = 10 + 13

50 - 59 30 =23 + 7

The linear equation parallel to y = -12x - 72 that passes through (-2, 0) is:

y = -12x - 24

A general linear equation is written as:

y = m*x + b

Where m is the slope, and b is the y-intercept.

And two lines are parallel only if the lines have the same slope and a different y-intercept.

So, if we want to find a line parallel to:

y = -12x - 72

Then the slope of our line must be -12, then our line is something like:

y = -12x + b

Now we know that the line must pass through (-2, 0), replacing that in our line we get:

0 = -12*-2 + b

0 = 24 + b

-24 = b

The linear equation is:

y = -12x - 24

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Answer:

The answer is

A. 4

Step-by-step explanation:

Input data

Procedure

The graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down

An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

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Answer:83.3

Step-by-step explanation:

Answer:

17. 25 \(in^2\)

18. 53 \(m^2\)

19. 21.6 \(cm^2\)

20. 20.8 \(km^2\)

Step-by-step explanation:

The area of a parallelogram is simply the base multiplied by the height.

17.

Base = 5 in

Height = 5 in

Area = Base * Height

Area = 5 * 5

Area = 25 \(in^2\)

18.

Base = 10 m

Height = 5.3 m

Area = Base * Height

Area = 10 * 5.3

Area = 53 \(m^2\)

19.

Base = 5.4 cm

Height = 4 cm

Area = Base * Height

Area = 5.4 * 4

Area = 21.6 \(cm^2\)

20.

Base = 5.2 km

Height = 4 km

Area = Base * Height

Area = 5.2 * 4

Area = 20.8 \(km^2\)

Answer:

Below in bold.

Step-by-step explanation:

x + y = 33      where x = 10 cent coin and y = 20 cent coin

10x + 20y = 460

Multiply first equation by 10:

10x + 10y = 330

Subtract this from the second equation:

10y = 130

y = 13

So there are 13 20c coins

and 33 - 13 = 20 10c coins.

Answer:

Verified below

Step-by-step explanation:

We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)

In trigonometric identities;

Cot θ = cos θ/sin θ

Thus;

(cot θ - 1)/(cot θ + 1) gives;

((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)

Simplifying numerator and denominator gives;

((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)

This reduces to;

>> (cos θ - sin θ)/(cos θ + sin θ)

Multiply top and bottom by ((cos θ + sin θ) to get;

>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)

In trigonometric identities, we know that;

cos 2θ = (cos² θ - sin²θ)

cos²θ + sin²θ = 1

sin 2θ = 2sinθcosθ

Thus;

(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:

>> cos 2θ/(1 + sin 2θ)

This is equal to the left hand side.

Thus, it is verified.

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer:

\(\dfrac{dy}{dx}=\cot x+\dfrac{1}{x}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6 cm}\underline{Product\:Rule}\\\\$\dfrac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)$\\\\\\\underline{Chain\:Rule}\\\\$\dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}$\\\end{minipage}}\)

\(\textsf{Given}:y=\log (x \sin x)\)

\(\textsf{Let }u=x \sin x \implies y=\log(u)\)

Using the product rule, differentiate y with respect to \(u\):

\(\textsf{If }y=\log(u) \implies \dfrac{dy}{du}=\dfrac{1}{u}\implies \dfrac{dy}{du}=\dfrac{1}{x \sin x}\)

----------------------------------------------------------------------------------------

Differentiate \(u=x \sin x\) with respect to x using the product rule:

\(\implies \textsf{Let }f(x)=x \implies f'(x)=1\)

\(\implies \textsf{Let }g(x)=\sin x \implies g'(x)=\cos x\)

\(\implies \dfrac{du}{dx}=x \cos x + \sin x\)

----------------------------------------------------------------------------------------

Use the chain rule to differentiate y with respect to x:

\(\implies \dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}\)

\(\implies \dfrac{dy}{dx}=\dfrac{1}{x \sin x} \times (x \cos x + \sin x)\)

\(\implies \dfrac{dy}{dx}=\dfrac{x \cos x + \sin x}{x \sin x}\)

\(\implies \dfrac{dy}{dx}=\dfrac{x \cos x}{x \sin x}+\dfrac{\sin x}{x \sin x}\)

\(\implies \dfrac{dy}{dx}=\cot x+\dfrac{1}{x}\)

Answer:

\(\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}\)

Step-by-step explanation:

Given:

\(\displaystyle \large{y=\log (x\sin x)}\)

Recall the (common) logarithmic differentiation & chain rules:

\(\displaystyle \large{\dfrac{d}{dx}[\log (u)] = \dfrac{u'}{u\ln 10}}\)

Let \(\displaystyle \large{u=x\sin x}\) then:

\(\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{(x\sin x)'}{x\sin x \ln 10}}\)

Recall product rules:

\(\displaystyle \large{[f(x)g(x)]' = f'(x)g(x)+f(x)g'(x)}\)

Hence:

\(\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{(x)'\sin x + x(\sin x)'}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{\sin x + x\cos x}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{\sin x}{x \sin x \ln 10} + \dfrac{x \cos x}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}\)

From above, recall that:

\(\displaystyle \large{\dfrac{d}{dx}(\sin x) = \cos x}\\\\\displaystyle \large{\dfrac{A\pm B}{C} = \dfrac{A}{C} \pm \dfrac{B}{C}}\\\\\displaystyle \large{\dfrac{\cos x}{\sin x} =\cot x}\)

Hence, the answer is:

\(\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}\)

Answer:

5=x

Step-by-step explanation:

Q=2(2x-5)=3x+x-2x

SOLUTION:

4x-10=4x-2x

-10=2x-4x

-10= -2x

(-+-=+ so 10 and 2 are positive now)

10/2=x

5=x

Answer:

There are no questions....

Are they on your prev one?

Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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Answer:

{0, 1, 2}

Step-by-step explanation:

4x<8x+2

-4x<2

x<-1/2

Only {0, 1, 2} meets all critera

Answer:

84

59

Step-by-step explanation:

In other to have the same number of chayes in both rows and columns ;

If the Number of chairs per row = x ; then number of chairs per column = x

Then the total number of chairs needed = x * x = x²

Hence, if there are 5100 chairs ;

Number of chairs needed more ;

Take the square root of 5100 ;the round to the next whole number :

B.) For number of chairs to be removed ;

Take the square root of 5100 and round down to the whole number.

Hence,

A.) = √5100 = 71.414 = 72

72² - 5100 = 84

B.) 5100 = 71.414 = 71

5100 - 71² =

Answer is 3 2/5. ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer:

3\(\frac{2}{5}\)

Step-by-step explanation:

5 × 3 = 15

2 remains

The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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Answer:

Original price= $150

Step-by-step explanation:

Giving the following information:

Sales pirce= $97.5

Sales discount= 35% decrease

To calculate the original price, we need to use the following formula:

Original price= sales price / (1 - discount)

Original price= 97.5 / 0.65

Original price= $150

hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((

1. The type of function which is best represented by the data in the table is; Quadratic.

2. The statement which is true is; The second differences are constant.

3. The type of function which is best represented by the given table is; Linear equation.

It is evident from the task content that the functions which correctly represents each data table is required to be determined.

Since linear functions are functions in which case, the first differences are constant while quadratic functions are functions in which the second differences are constant.

On this note, the first table correctly represents a quadratic function while the second represents a linear function.

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Answer:

The center is =(3,−2) = 3

Step-by-step explanation:

Factorise(x−3)2+(y+2)2=32

The center is =(3,−2) and the radius is =3

graph{(x^2+y^2-6x+4y+4)=0 [-14.08, 8.11, -5.51, 5.58]}

The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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9514 1404 393

Answer:

  62°

Step-by-step explanation:

If x is the largest angle, the sum of angles in the triangle is ...

  x + (x -3) +(x -3) = 180

  3x -6 = 180 . . . . . simplify

  x -2 = 60 . . . . . . . divide by 3

  x = 62 . . . . . . . . . .add 2

The largest angle is 62°.

Answer:

g^-1(x)=x/2+3/2

Step-by-step explanation:

Answer:

C 18 feet:D

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Hope you have a fantastic day, and do well on your test!!!!!!!!!!!!!!