Harley’s house has a value of £160 000 correct to 2 significant figures.

Write down the greatest possible value of the house

Answer:

The number of students who scored within 2 standard deviations of the mean is 380.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

The number of students who scored within 2  standard deviations of the mean is approximately

By the Empirical Rule, 95% of the students scored within 2 standard deviations of the mean

Out of 400

0.95*400 = 380

The number of students who scored within 2 standard deviations of the mean is 380.

Answer: 380

Step-by-step explanation: 95% of 400 is 380

Answer:

Step-by-step explanation:

Hello

Please what’s the explanation to get the answer (2+2) ² (2+3)³

we use PEMDAS

Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

(2 + 2)² + (2 + 3)³ =

4² + 5³ =

16 + 125 =

141

9514 1404 393

Answer:

  6.75 square units

Step-by-step explanation:

The formula for the area of a rectangle of base 'b' and height 'h' is ...

  A = bh

The formula for the area of a triangle of base 'b' and height 'h' is ...

  A = (1/2)bh

That is, the area of a triangle is half the area of a rectangle with the same base and height. Here, the area of the triangle is ...

  (1/2)(13.5 square units) = 6.75 square units

Answer: x = 2.

Step-by-step explanation:

By an online search, i found that the question is:

"Given that x satisfies the inequality 20*x > 33,  find the smallest value of x if x is a prime number."

To find the smallest value of x we need to input different possible values of x (where we have the condition that x must be a prime number) and see which one is the first one that makes the inequality true.

The prime numbers are:

2, 3, 5, ....

Let's start with the smaller one, x = 2

So we input it in the inequality and get:

20*2 > 33

40 > 33

this is true.

Then we can have x = 2, which is the smaller prime number that satisfies the inequality.

Answer:

(0,8)

Step-by-step explanation:

The slope intercept formula is set up as y=mx+b, where b is the y-intercept value. In the equation y=3x+8, we can see that 8 is the y-intercept. So we plug 8 for y in a coordinate, and 0 for x. The answer is (0,8)

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:the first one

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

3=5x2-6=3x2-2

5x2-6=4

3x2-2=4

Answer:

A and B

Step-by-step explanation:

1) Distance to the focus

From (x,y) to the focus(2,-4) {using distance formula}

=√(x-2)²+(y+4)²

2) Distance to the directrix

Is, y+p where P here is (-6)

So

d2 = y+p

= y+(-6)

= y-6

Answer:

\(\frac{x2}{a} - \frac{y2}{b2} = 1\)

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

\(\frac{X2}{16} - \frac{b}{4} = 1\)

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

I don't feel like explaining so...

a. = 4

The foci c is at +/-2√5, using c² = a² + b²:

B = 2

Substituting the value of a and b to get the equation of the hyperbola:

\(\frac{x2}{a2} - \frac{y2}{b2} = 1\)  

\(\frac{x2}{16} - \frac{b2}{4} = 1\)

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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Answer:

-3/8, -3/16, 7/4

Answer:

Step-by-step explanation:

The first friend would get $60,000

The second friend would get $15,000

The third friend would get $30,000

Answer:

10-4x

Step-by-step explanation:

4×2-4x+2

8-4x+2 =10-4x

Answer:

44.71 kilometers

Step-by-step explanation:

Answer:

I would say 44.71 kilometers

Step-by-step explanation:

When you add all those values together you get 44.71.

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

150 gallons = 4 * 150 = 600 quarts.

You then put 24 of these quarts into a shipping box.

600 / 24 = 25

That means you can get 25 full cases from 150 gallons.

A(0,8); B(16,16) and C(-4,16) are the vertices of triangle ABC with a scale factor of 4.

Given,

Coordinates of triangle ABC are A(0,2), B(4,4) and C(-1,4)

scale factor=4

if scale factor is 'k' then the coordinates (x,y) of any figure are scaled to (kx,ky).

Formula:

Dimension of scaled figure= Dimension of original figure * scale factor.

Let,

k=4

vertices of scaled triangle ABC be A(kx,ky), B(kx,ky) and C(kx,ky).

From formula,

\(A(kx,ky)= A(4*0,4*2) =A(0,8)\\ B(kx,ky)= B(4*4,4*4) =B(16,16)\\ C(kx,ky)= C(4*(-1),4*4) =C(-4,16)\)

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Answer: 13

Step-by-step explanation:

cost for 3 hours: 7+2(3)=13

cost for t hours: 7+2t

Answer:

13

Step-by-step explanation:

Answer:

Undefined.

Step-by-step explanation:

g(-2) = -2 + 2 = 0

So (f/g)(-2) = ( (-2)^2 - 24 - 21)/0  which is undefined.

The percentage of scores below 112 is equal to 78.81.

Let X represent a test's score. X is regularly distributed, hence

P(X < 112)

= P[(X - 100)/15 < (112 - 100)/15]

= P[ SNV < 0.8] .8]

SNV stands for Standard Normal Variable,

A normal distribution with a mean of 0 and a standard deviation of 1 is the standard normal distribution. When referring to a random variable that has this typical normal distribution, the letter Z is frequently employed.

z = (X – μ) / σ

If X is a normal random variable, represents its mean, and represents its standard deviation. The normal distribution formula is also available here.

and the value is 0.7881.

Thus, the percentage of scores below 112 is equal to 78.81.

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The full question

If the scores for a test have a mean of 100 and a standard deviation of 15, what is the percentage of scores that will fall below 112? Assuming a normal distribution

On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. The interest rate on the loan is known as this percentage.

here,

we have

P = 1360;

R = 5.4 ;

T = 12

so, we get,

SI = 1360 X 5.4 X 12 /100

SI =88128/100

= 881.28

Hence, On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

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Answer: 1.32 units

Step-by-step explanation:

The required value of x is  135° in the given polygon. which is the correct answer would be an option (A).

A polygon is given in the figure

According to the given question, the required solution would be as:

Number of sides = 8

The required value of x is the equal to measure of one Interior angle in the given polygon.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 8

Sum of Interior angles = (8 - 2) × 180

Sum of Interior angles = (6) × 180

Sum of Interior angles = 1080°

the measure of one Interior angle = 180°/8

the measure of one Interior angle = 135°

Thus, the required value of x is  135°.

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Point  (4.5, 14) lies on the following equation y = 2x + 5, y = 4x + 4 and  y = 5x + 8.5. Options A, C, and D are correct.

The equation is the relationship between variables and is represented as  y = ax +c is an example of a polynomial equation.

Since, if the point lies on the equation it must satisfy the equation and must given the given y for given x. (4.5, 14) = (x , y)

For A)
y = 2x + 5
y = 2 * 4.5 + 5
y = 9 + 5
y = 15

Similarly
the procedure can be repeated for the other option,
From the calculation, it is found that Point lies on the equation given in Options A, C, and D.

Thus, (4.5, 14) lies on the following equation y = 2x + 5, y = 4x + 4 and  y = 5x + 8.5. Options A, C, and D are correct.

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The question seems to be incomplete, the option can be given as
A) y = 2x + 5
B) y = 3x + 1.5
C) y = 4x + 4
D) y = 5x + 8.5
E = 1/2x + 10

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Answer:

Step-by-step explanation:

We assume your intended attendance equation is ...

  A = -1.95x^3 +70.1x^2 -188x +2150

a. For x=0 (corresponding to 1985), the first three terms are 0, so we have ...

  A = 2150 . . . . the initial value of the function

__

b. For x=13 (corresponding to 1985) we have ...

  A = ((-1.95(13) +70.1)(13) -188)(13) +2150 = (44.75(13) -188)(13) +2150

  = 393.75(13) +2150 = 7268.75

Attendance in the year 1998 is modeled to be about 7269.