Find k such that the vertical line x=k divides the area enclosed by y=vi, y y=0 and x=5 into equal parts. 2.50 7.94 O 3.15 None of the Choices O 3.54

Answer:

C

Step-by-step explanation:

As y is zero, y/x will be zero

Answer:

17) Congruent because two sides are congruent and so is the 90 degree vertical angle.

18) Congruent because they have a congruent leg and congruent angle, and they share a side which is congruent to itself. (SAS)

19) Congruent because all three sides are congruent (SSS)

20) congruent, all three sides are the same (SSS)

Answer:

63 i think

Step-by-step explanation:

Therefore, the balance on 15 March will be £686.00.

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.

Here,

a) The total income is the sum of all the "Money in" entries, which are:

Sales from 22-28 February: £35.00

Sales from 1-7 March: £200.00

Online bulk order: £30.00

Total income = £35.00 + £200.00 + £30.00

= £265.00

b) The total expenditure is the sum of all the "Money out" entries, which are:

Wages - overtime: £15.00

Stall hire fee: £120.00

Supplies - tea and coffee: £50.00

Sales - extra weekend opening: £4.00

Materials - trade purchase: £200.00

Total expenditure = £15.00 + £120.00 + £50.00 + £4.00 + £200.00

= £389.00

c) The balance on 15 March can be found by subtracting the total expenditure from the balance carried forward on 1 March, and then adding the total income.

Balance on 15 March = Balance carried forward - Total expenditure + Total income

Balance on 15 March = £810.00 - £389.00 + £265.00

= £686.00

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Answer:

x = 7

2x - 4 = 50/5

2x - 4 = 10

2x =10+4

2x=14

x=14/2

x=7

Answer:

A

Step-by-step explanation:

Answer:

4 in first number is in tenth place, so its 40

4 in second number is in unit place, its 4 only

a) The standard error of the mean value is 890.

b) 0.5 is the probability that the sample mean will be more than $27,175.

c)  \(11%\) of the population means being within \($1,000\) of the sample mean.

d) The population mean is \(71%.\) .

(a) The formula for calculating the standard error of the mean (SE) is as follows:\(SE = / sq rt(n),\) where n is the sample size and is the population standard-deviation.

Inputting the values provided yields:

\(SE = 7,400 sq/69 890\)

The standard error of the mean, rounded to the closest whole number, is \(890.\)

\(= 890\)

(b) We must standardize the sample mean using the following method in order to determine the likelihood that the sample mean will exceed \($27,175:\)

z is equal to\((x - ) / ( / sort(n)).\)

where n is the sample size, x is the sample mean, is the population standard deviation, and is the population mean (which is assumed to be equal to the sample mean because it is not provided).

We obtain the following by substituting the above values: \(z = (27,175 - 27,175) / (7,400 / sqrt(69)) = 0.\)

Obtaining a z-score of \(0\) or above has a \(0.5\) percent chance. As a result, there is a \(0.5\) percent chance that the sample mean will be higher than \($27,175.\)

\(= 0.5%\)

(c) To determine the likelihood that the sample-mean will be within \($1,000\) of the population mean, we must determine the z-scores for the interval's upper and lower boundaries, which are:

\(Z1\) is equal to\((27,175 - 27,175) / (7,400 / sqrt(69)) = 0 Z2\)is equal to \((27,175 + 1,000 - 27,175) / (7,400 / sqrt(69)) 0.14\) \(Z3\) is equal to\((27,175 - 1,000 - 27,175) / (7,400 / sqrt(69)) -0.14\)

The area under the curve between\(z2\) and \(z3\) can be calculated or found using a basic normal distribution table or calculator:

\(P(z2 z3 z2) = P(-0.14 z 0.14) 0.1096\)

Therefore,\(0.1096\), or about \(11%\), of the population means being within \($1,000\) of the sample mean.

\(= 11%\)

(d) If the sample-size were raised to \(100\), we would need to recalculate the standard error of the mean to determine the likelihood that the sample mean will be within \($1,000\) of the population mean:

\(SE = 7,400/7,400/sqrt(100) = 740.\)

We determine the z-scores for the upper and lower boundaries of the interval using the same technique as in (c)

\(z2 = (27,175 + 1,000 - 27,175) / (740) ≈ 1.35\)

\(z3 = (27,175 - 1,000 - 27,175) / (740) ≈ -1.35\)

Once more, we can calculate or use a conventional normal distribution table to get the area under the curve between\(z2\)and\(z3\):

\(P(z2+z+z3) = P(-1.35+z+1.35) = 0.7146\)

Therefore, if the sample size were increased to 100, the likelihood that the sample mean will be within\($1,000\) of the population mean is\(0.7146,\)or roughly \(71%.\)

\(= 71%\)

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Complete Question:

(a) What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)

(b) What is the probability that the sample mean will be more than $27,175?

(c)What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)

(d) What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)

The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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Answer:

wrong

Step-by-step explanation:

Answer:

She's wrong

Step-by-step explanation:

Donna is wrong because all of the 10 bricks weigh more than 7kg :)

Answer:

3x^4

Step-by-step explanation:

3x • 3x • 3x • 3x = 3x^4

said like “3x to the 4th power”

Answer:

\((3x)^4}\)

Step-by-step explanation:

further it can represent as \(3^{4} x^{4}\)

The congruent segments, \( SC \cong HR \) and \( HR \cong AB\), according to the substitution property of equality, gives; \( SC \cong AB \)

The given parameters are;

Required;

To prove;

\( SC \cong AB\)

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

\( SC \cong AB \) (Inverse of the definition of congruency)

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Answer:

Brainliest???

Step-by-step explanation:

Reflection over the y axis

Answer:

y=-5x+4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-16-(-6))/(4-2)

m=(-16+6)/2

m=-10/2

m=-5

y-y1=m(x-x1)

y-(-6)=-5(x-2)

y+6=-5(x-2)

y+6=-5x+10

y=-5x+10-6

y=-5x+4

The radius of the cone whose volume is 3π is approximately 2.121 as per the concept of cone.

To find the radius of a cone whose volume is 3π, we can equate the given volume to the volume formula of a cone and solve for the radius.

The volume formula of a cone is given as:

\(V = \frac{1}{3} \pi}r^{2}h\)

Given:

V = 3π

h = 2

Substituting these values into the volume formula, we have:

\(3\pi = \frac{1}{3} \pi}r^2(2)\)

Simplifying the equation, we get:

\(3 = \frac{1}{3} r^2(2)\)

Multiplying both sides by 3 to eliminate the fraction, we have:

\(9 = 2r^2\)

Dividing both sides by 2, we get:

\(4.5 = r^2\)

Taking the square root of both sides, we have:

r = √4.5

Using a calculator to evaluate the square root of 4.5, we find:

r ≈ 2.121

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The complete question:

The volume of a cone of height 2 and radius r is \(V = \frac{3}{2} \pi}r^{2}h\). What is the radius of such a cone whose volume is 3π ? r= help (numbers)

Answer:

F(7) = 11

Step-by-step explanation:

F(7) = 2(7) -3

      = 14 - 3

      = 11

Answer:

f(7)=2/7t+-3/7

Step-by-step explanation:

you just have to plug 7 in and put an = sign which makes F(7)=2t-3 then solve

Answer:

Step-by-step explanation:

The scale number can be interpreted as (1cm/3,000,000 km), a conversion factor.  Since it is a conversion factor, we can invert it to the form:

(3,000,000 km/1cm)

A measure of 12cm on the map would correspond to:

(12cm)*((3,000,000 km/1cm) = 42,000,000 km

Wow - a long trek, if you need water.

Note that inverting the conversion factor isn't totally necessary, since we could use the original form and divide:  

    12 cm/(1cm/(3,000,000km)) = 42,000,000 km

But I dislike division, so I always invert a conversion factor if it makes the calculation more convenient, for me.

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:

133.3333333333333333%

Step-by-step explanation:

never ending 3

Answer:133.3%

Step-by-step explanation:

The probability of both sample information and a particular state of nature occurring simultaneously is known as joint probability. Then the correct option is D.

Given two random variables that are defined on the same probability space, the joint probability is a statical measure that calculates the likelihood of two events occurring together and at that same point in time.

In the given question it is said that the probability of both sample information and a particular state of nature occurring simultaneously.

So, when the state of nature of the sample remains unchanged it will not affect the sample nor does the output.

Hence, when without affecting the nature of the sample information remains intact. If the nature of the sample is changed the required out will also change.

Since both the measure are occurring simultaneously without changing the nature of the sample.

Hence, in the given condition the correct answer is d which is joint.

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The simplified form of R(x) is \(R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}\)

From the question, we are to simplify the expression

From the given information,

\(f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}\)

and

\(g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}\)

Also,

\(R(x) = f(x) \div g(x)\)

∴ \(R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}\)

\(R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}\)

Factoring each of the quadratics

\(R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}\)

\(R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}\)

\(R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}\)

Simplifying

\(R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}\)

\(R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}\)

\(R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}\)

\(R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}\)

Hence, the simplified form of R(x) is \(R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}\)

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a. the point estimate of the true driver cell phone use rate is 0.3 or 30%.

b. the 90% confidence interval for the true driver cell phone use rate is approximately (21.5%, 38.5%).

c. The practical interpretation of the confidence interval is that we are 90% confident that the true driver cell phone use rate falls within the range of 21.5% to 38.5%

a. The point estimate of the true driver cell phone use rate (population proportion) can be calculated by dividing the number of drivers using their cell phone by the total sample size. In this case, the sample size is 100, and 30 drivers were using their cell phone.

Point estimate = Number of drivers using their cell phone / Total sample size

Point estimate = 30/100 = 0.3 (or 30%)

Therefore, the point estimate of the true driver cell phone use rate is 0.3 or 30%.

b. To compute a 90% confidence interval for the true driver cell phone use rate, we can use the formula for a confidence interval for a proportion. The formula is:

Confidence interval = Point estimate ± (Critical value × Standard error)

The critical value depends on the desired level of confidence. For a 90% confidence interval, the critical value is typically obtained from the standard normal distribution and is approximately 1.645.

The standard error can be calculated using the formula:

Standard error = sqrt((point estimate * (1 - point estimate)) / sample size)

In this case, the point estimate is 0.3, and the sample size is 100.

Standard error = sqrt((0.3 * (1 - 0.3)) / 100) ≈ 0.048

Plugging in the values, we can calculate the confidence interval:

Confidence interval = 0.3 ± (1.645 * 0.048)

Confidence interval = (0.215, 0.385)

Therefore, the 90% confidence interval for the true driver cell phone use rate is approximately (21.5%, 38.5%).

c. The practical interpretation of the confidence interval is that we are 90% confident that the true driver cell phone use rate falls within the range of 21.5% to 38.5%. This means that based on the sample data, we can estimate with 90% confidence that the proportion of drivers using their cell phone while driving in the entire population lies between these two percentages. It provides a range of likely values for the true population proportion.

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63.64% is the percentage of the area of the square.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

The radius of the circle r =  1 in.

The area of the circle = π r² = π (1)² = π = 22/7 inch.

Also the area of square = 1/2 x (diameter)²

The diameter of the square = 2r = 2

Area = 1/2(2)² = 2 square in.

The required percentage = (2 / (22/7)) x 100 = (7 / 11) x 100 = 700 / 11 = 63.6363.

The percentage of the area of the square is 63.64%.

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The equation of the line L in point-slope form is y - y1 = (-1/2)(x - x1).

The equation of the line L in slope-intercept form is y = (-1/2)x + b, where b is y1 + (1/2)x1.

Point-slope form of the equation of a line: The point-slope form is defined as;

y - y1 = m(x - x1)

The equation of a line L in point-slope form that is perpendicular to y = 2x is:

y - y1 = m(x - x1)

where m is the slope of the line L.

To determine the slope of a line perpendicular to another line, we use the formula,

m = -1/m1,

where m1 is the slope of the other line y = 2x.

Therefore, the slope of the line L is m = -1/2.

The equation of the line L is, therefore,

y - y1 = m(x - x1)

y - y1 = (-1/2)(x - x1)

This is the equation of the line L in point-slope form.

Slope-intercept form of the equation of a line: The slope-intercept form is defined as y = mx + b, where m is the slope of the line and b is the y-intercept.

The equation of the line L in slope-intercept form can be obtained by simplifying the equation obtained in point-slope form. The equation is:

y - y1 = (-1/2)(x - x1)

y - y1 = (-1/2)x + (1/2)x1 + b,

where b = y1 + (1/2)x1.

The equation of the line L in slope-intercept form is:

y = (-1/2)x + b

The conclusion is, the equation of the line L in point-slope form is,

y - y1 = (-1/2)(x - x1)

The equation of the line L in slope-intercept form is y = (-1/2)x + b, where b is y1 + (1/2)x1.

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The distance from the point (2, 1) is double it's distance from (1, 2)​ is 2.8

The distance between two points in a 2D Cartesian coordinate system is the length of the path connecting them. The shortest path distance is a straight line. The Pythagorean theorem states that the distance between points (X1, Y1) and (X2, Y2) is given by the formula [(x2 x1)2 + (y2 y1)2], where (x1, y1) and (x2, y2) are two points on the coordinate plane.

Distance = √(y₁-y₂)² + (x₁-x₂)²

distance = √(2-1)² + (1-2)²

the distance = √1+1

The distance = √2 = 1.4 = 2*1.4 = 2.8

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The width of the rectangle is;

Here, we want to get the width of the rectangle

To do this, we need a pictorial representation

We have this as;

As we can see, the rectangle is divided into two equal right-triangles

We have represented the width by w

We can use Pythagoras' theorem to get the width

The square of the diagonal (the hypotenuse) is equal the sum of the squares of the two other sides

Thus, we have;

Using substitution method of simultaneous linear equation the results are x = -1 and y = 3

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here,

Substitution method of simultaneous linear equation is used

y = -2x + 1

-9x - 2y =3

Putting the value of y in the second equation

-9x - 2(-2x + 1) = 3

-9x +4x -2 = 3

-5x = 3 + 2

-5x = 5

\(x = -\frac{5}{5}\\x = -1\)

Putting the value of x in the first equation,

\(y = -2 \times -1+1\\y = 3\)

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Answer:

16

Step-by-step explanation:

(9+V-4) - (5+V-16)

= 9 + V - 4 - 5 - V + 16

= V - V + 9 + 16 - 4 - 5

= 16

Hope this helped!