11/ 42 Marks
34%
ABC is a straight line and angle CBD = 116°
a) Work out the value of x.
C
+
B
b) P is a point on the minor arc AD.
Explain why angle APD = 116°
+
A
Р

Answer:

D. 569.39 m^3

Step-by-step explanation:

First, we can split up the solid into two shapes: a cone and a cylinder.

Then we can find the volume of the cone

The formula is v= pi r^2 h/3

We know the radius is four and so is the height.

Plug it in and we get 67.02 m^3

Next is the cylinder

Formula is pi r^2 h

We know that the radius is 4 and the height is 10

Plus it in and we get 502.65 m^3

We add 67.02 and 502.65 together to get the total volume.

Answer is D. 569.39 m^3

Mine is a bit higher than D since I used a pi button instead of 3.14

Answer:

Hey there! The answer to your question will be below

Step-by-step explanation:

The answer to your question is -1/2

-1/2x + 1/4

= -1/2

Hope that helps

By:xBrainly

Answer:

Graph is attached.

Step-by-step explanation:

We are to graph the following inequalities:

y > 2x + 4 ... (i)

x + y ≤ 6 ... (ii)

We can graph these inequalities on an online graphing calculator but its recommended that you graph them on your physical graph book.

Your graph is attached below. The shaded region is the required part.

The graph of a system of inequalities represents the solution of the inequalities

The solution to the system of inequalities is [tex]\mathbf{y > \frac 23}[/tex] and [tex]\mathbf{x \le \frac{16}3}[/tex]

The system of inequalities is given as:

[tex]\mathbf{y > 2x + 4}[/tex]

[tex]\mathbf{x + y \le 6 }[/tex]

See attachment for the graphs of [tex]\mathbf{y > 2x + 4}[/tex] and [tex]\mathbf{x + y \le 6 }[/tex]

From the graph, we have:

[tex]\mathbf{y > \frac 23}[/tex]

[tex]\mathbf{x \le \frac{16}3}[/tex]

Read more about system of inequalities at:

https://brainly.com/question/19526736

Answer:

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Step-by-step explanation:

Step(i):-

Given random sample of size 'n' =17

Given mean of the sample 'x⁻' = 56

Given standard deviation of sample 's' = 10

95% confidence intervals about the population mean is determined by

[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]

Degrees of freedom

ν = n-1 = 17-1 =16

t₀.₀₅ = 1.7459  (from t-table)

Step(ii):-

95% confidence intervals about the population mean is determined by

[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]

[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]

( 56 - 4.2344 , 56 + 4.2344)

(51.7656 , 60.2344)

Conclusion:-

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Answer:

True

Step-by-step explanation:

Coefficient of realism called alpha which is a decimal number between 0 and 1. This number provides the optimistic view. The number 1 - [tex]\alpha[/tex] is amount of emphasis that is placed in pessimistic outcome. If the coefficient of realism alpha is 1 then criterion of realism will yield same result as maxi max criterion.

Answer:

Look at the numbers on the sides. If they are not spaced out very far, it's centimeters. If they are spaced out very far, it's inches

Step-by-step explanation:

this is how you read a ruler

Answer:

Start at 0

Step-by-step explanation:

Start at 0, then see how far the object goes.

Answer:

A

The  test statistics is  [tex]t = -1.7[/tex]

B

The  Null and  Alternative hypothesis are

      [tex]H_o : \mu = 47.2[/tex]   and  [tex]H_a : \mu \ne 47.2[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 47.2 miles/gallon(MPG)[/tex]

    The sample size is  [tex]n = 250 \ van[/tex]

     The  sample mean is  [tex]\= x = 47.0[/tex]

      The sample  standard deviation is  [tex]\sigma = 1.9[/tex]

      The level of significance is  [tex]\alpha = 0.02[/tex]

Given that the value which the manufacturer gave the automobile is  47.2 and  it is believed that this is not correct, then  

The  Null Hypothesis is  

        [tex]H_o : \mu = 47.2[/tex]

The alternative Hypothesis  is  

        [tex]H_a : \mu \ne 47.2[/tex]

The test statistics can be mathematically evaluated as  

        [tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

        [tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]

       [tex]t = -1.7[/tex]

Answer:

The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]

The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).

Slope = 3, y intercept = 2

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

Work Shown:

Find the slope of the line through (x1,y1) = (-2,-4) and (x2,y2) = (1,5)

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

m = (5 - (-4))/(1 - (-2))

m = (5 + 4)/(1 + 2)

m = 9/3

m = 3  is the slope

Plug m = 3 and (x1,y1) = (-2,-4) into the point slope formula. Solve for y.

y - y1 = m(x - x1)

y - (-4) = 3(x - (-2))

y + 4 = 3(x + 2)

y + 4 = 3*x + 3*2 ... distribute

y + 4 = 3x + 6

y + 4 - 4 = 3x + 6 - 4  ... subtracting 4 from both sides

y = 3x + 2  is the slope intercept equation

Answer:

length of side BC = 11.9cm

The complete question found on brainly (ID: 14303570 ) is stated below:

Find the length of side BC.

Give your answer to 1 decimal place.

∠A = 58°

AC = 14cm

Find attached the diagram of the triangle.

Step-by-step explanation:

From the diagram

∠A = 58°

∠B = 90°

AC = 14cm

The triangle is a right angled triangle

To get the length side of BC, we would

apply trigonometry SOHCAHTOA.

In this question the sine ratio would be appropriate since we know the hypotenuse but we are looking for the opposite side (BC).

Sine ratio: Sin58° = opposite/hypotenuse

Sin58° = BC/AC

Sin58° = BC/14

BC = 14sin58°

BC = 14 × 0.8480

BC = 11.9cm

length of side BC = 11.9cm (1 decimal place)

Answer:

4

  [tex]P(X \ge 219 ) = 0.093[/tex]

5

 [tex]P(X \ge 219 ) = 0.1038[/tex]

Step-by-step explanation:

From the question we are told that  

    The percentage of hair dryers that are defective is p=2%  [tex]= 0.02[/tex]

      The  sample size is  [tex]n =10000[/tex]

       The  random number is  x = 219

The mean of this data set is evaluated as

     [tex]\mu = n* p[/tex]

substituting values

     [tex]\mu = 10000 * 0.02[/tex]

    [tex]\mu =200[/tex]

The standard deviation is evaluated as

      [tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]

substituting values  

      [tex]\sigma = \sqrt{[200 (1 -0.02)]}[/tex]

     [tex]\sigma = 14[/tex]

Since it is  a one tail test the degree of freedom is  

      df =  0.5

So  

   [tex]x_l = x- 0.5[/tex]

   [tex]x = 219 - 0.5[/tex]

    [tex]x = 218.05[/tex]

Now applying normal approximation

    [tex]P(X \ge 219 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]

substituting values  

    [tex]P(X \ge 219 ) = P(z > \frac{218.5 - 200}{14} )[/tex]

    [tex]P(X \ge 219 ) = P(z > 1.32} )[/tex]

From the z-table  

    [tex]P(X \ge 219 ) = 0.093[/tex]

Considering Question 5  

The  random number is  x = 90

      The mean is  [tex]\mu = n * p[/tex]

Where  n = 100

   and  p  =  0.85

So  

     [tex]\mu = 0.85 *100[/tex]    

     [tex]\mu = 85[/tex]

The standard deviation is  evaluated as

     [tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]

substituting values  

      [tex]\sigma = \sqrt{[85 (1 -0.85)]}[/tex]        

     [tex]\sigma = 3.5707[/tex]      

Since it is  a one tail test the degree of freedom is  

      df =  0.5

Now applying normal approximation

    [tex]P(X \ge 90 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]

   substituting values  

    [tex]P(X \ge 219 ) = P(z > \frac{89.5 - 85}{3.5707} )[/tex]

    [tex]P(X \ge 219 ) = P(z > 1.2603} )[/tex]

From the z-table  

   [tex]P(X \ge 219 ) = 0.1038[/tex]

Answer:

a) Discrete random variable

b) Continous random variable.

Step-by-step explanation:

a) As the number of people can take only integer values, from 0 to n (0, 1, 15, 256, for example, but not 5.6) and not decimals values, we can say that it is a discrete variable.

b) In this case, the weight of a Upper T dash bone steak is a physical variable and can take decimals positive values (0.645 lbs for example).

Then, this variable is a continous variable.

Answer:

A. positive

Step-by-step explanation:

A line that goes up from down has a positive slope.

Answer:

17

Step-by-step explanation:

The closest perfect cube (to 360) is 343 (7^3) .

360-343 = 17

Subtract 17.

Answer:

You should subtract 17 from 360 to make a perfect cube

Step-by-step explanation:

Answer:

( 2,1) is the center of dilation and 4 is the scale factor

Step-by-step explanation:

A' = k( x-a) +a, k( y-b)+b  where ( a,b) is the center of dilation and k is the scale factor

3,1 becomes 6,1

6,1 = k( 3-a) +a, k( 1-b)+b

6 = 3k -ka+a

1 = k -kb +b

4,1 becomes 10,1

10,1 = k( 4-a) +a, k( 1-b)+b

10 = 4k -ka+a

1 = k -kb +b

Using these two equations

6 = 3k -ka+a

10 = 4k -ka+a

Subtracting the top from the bottom

10 = 4k -ka+a

-6 = -3k +ka-a

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

4 = k

Now solving for a

6 = 3k -ka+a

6 = 3(4) -4a+a

6 =12 -3a

Subtract 12

6-12 = -3a

-6 = -3a

Divide by -3

-6/-3 = -3a/-3

2 =a

Now finding b

1 = k -kb +b

1 = 4 - 4b+b

1 =4 -3b

Subtract 4

-3 = -3b

Divide by -3

1 = b

Answer:

Dilation factor: 4.  

Center of dilation: (2, 1).  

Step-by-step explanation:

The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.  

Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.  

In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.  

10 = 4(4 – a) + a

10 = 16 – 4a + a

10 = 16 – 3a

-3a + 16 = 10

-3a = -6

a = 2

1 = 4(1 – b) + b

1 = 4 – 4b + b

1 = 4 – 3b

-3b + 4 = 1

-3b = -3

b = 1

And so, your center of dilation will be (2, 1).  

Hope this helps!  

Answer:

  x + y + z = 14

Step-by-step explanation:

If the points are designated A, B, C, then ...

  AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).

That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...

  (1, 1, 1)·(x, y, z) = (1, 1, 1)·A

  x + y + z = 14

Answer:

-17/72

Step-by-step explanation:

-4/9 + 7/12 + (-3/8) =

We need a common denominator. The least common multiple of 9, 12, and 8 is 72.

= -4/9 * 8/8 + 7/12 * 6/6 + (-3/8) * 9/9

= -32/72 + 42/72 - 27/72

= 10/72 - 27/72

= -17/72

Answer:

Your correct answer is 17/72

Answer:

cos∅ = 16√481/481

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

cos∅ = adjacent/hypotenuse

tan∅ = opposite/adjacent

Step 1: Find hypotenuse

15² + 16² = c²

c = √481

Step 2: Find cos∅

cos∅ = 16/√481

cos∅ = 16√481/481

Answer:

y <= (2/5)x - 3/2

Step-by-step explanation:

y-intercept is -3/2

slope = 2/5

shading is below the line

Answer: y <= (2/5)x - 3/2

Answer:

  B.  zero

Step-by-step explanation:

The slope of a line can be computed as ...

  slope = rise/run

When the line is horizontal, the "rise" is zero over any "run", so the slope is zero.

Answer:

a) The student cannot receive an A in the class.

b) The student must score 119 in the third exams to make an A.  This is clearly not possible, since he cannot make 119 in a 100-points exam.

c) The student can make a B but he must score at least 84 in the third exam.

Step-by-step explanation:

To make an A, the student must score 315 (350 x 90%) in both home and the three exams.

The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.

To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.

B ≥ 280 and < 315.

Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.

Answer:

16%

Step-by-step explanation:

Find the z-score.

z = (x − μ) / σ

z = (93 − 85) / 8

z = 1

This means 93 is one standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations.  So 32% is either less than -1 or greater than +1 standard deviations.  Normal curves are symmetrical, so 16% is greater than +1 standard deviations.

Answer:

A. converse

Step-by-step explanation:

Let's first define some concepts:

Statement             If p , then q

Converse        If q , then p  

Inverse                If not p , then not q  

Contrapositive If not q , then not p

From the statement we have:

a ⇒b

b ⇒a

if you look at the definitions then:

The second statement is the converse of the first

Answer:

Converse

Step-by-step explanation:

Got Correct On ASSIST.

Answer:

c

Step-by-step explanation:

next

Answer:

For the Square

Base length is 6 units

Height is 4 units

Volume is 48 cubic units

Volume of 4 square pyramids is 192 cubic units

(Rectangular)

Base length is 12 units

Base width is 8 units

Height is 6 units

Volume is 192 cubic units

Step-by-step explanation:

Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.

Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex  form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.

Answer:

BC ≈ 10.94

Step-by-step explanation:

Base on the triangle we were given 2 sides and an angle. We were also asked to find the last length BC.

we can use cosine rule to find the side BC.

Base on cosine rule

a² = b² + c² - 2bc cos A

a = BC

b = AC = 14

c = AB = 10

a² = 14² + 10² - 2 × 14 × 10 cos 51°

a² = 196  + 100 - 280  cos 51°

a² = 296 - 280 × 0.62932039105

a² = 296 - 176.209709494

a² = 119.790290506

square root both sides

a = √119.790290506

a = 10.9448750795

BC ≈ 10.94

Answer:

BC = 10.94

Step-by-step explanation:

its a las of cosines

a² = b² + c² - 2bc cos A

AB = 10

AC = 14

angle A = 51°

BC² = 10² + 14² - (2 * 10 * 14 cos 51°)

BC = sqrt 119.8

BC = 10.94

Step-by-step explanation:

Using the trigonometric identity

sin(a - b) = sin a cos b - cos a sin b

So sin 79° cos 19° - cos 79° sin 19° can be written as

sin ( 79 - 19) = sin 60

And

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

Hope this helps you

Answer:

Step-by-step explanation:

As always, put the given information into the equation and solve for the unknown variable.

First ordered pair

  x -2(-3) = 2

  x +6 = 2 . . . . simplify

  x = -4 . . . . . . subtract 4

  (x, y) = (-4, -3)

Second ordered pair

  8 -2y = 2

  -2y = -6 . . . . . subtract 8

  y = 3 . . . . . . . divide by -2

  (x, y) = (8, 3)

Answer: -7/12

Step-by-step explanation: an number multiplied by 1 is itself