A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 mark

Answer:

2.6 miles

Step-by-step explanation:

1 hour 26 minutes= 86 minutes

86-34=52 total walk time

52 minutes= 5*1/2 miles

=2.5 miles walked

and 2 minutes.

so we need to find 1/5 of 1/2

(1/2)/5=0.1 mile

2.5+0.1=2.6 miles

Answer:Yes, because all integers have decimals. No, because integers do not have decimals. No, because integers cannot be negative. Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern.

Step-by-step explanation:

Answer:

x = -8

I hope this helps!

Answer:

  x ≥ -4/5

Step-by-step explanation:

Maybe you want to solve ...

  4x+4 ≤ 9x +8

  0 ≤ 5x +4 . . . . . subtract 4x+4

  0 ≤ x +4/5 . . . . . divide by 5

  -4/5 ≤ x . . . . . . . subtract 4/5

Answer:

x ≥−4/5

Step-by-step explanation:

Answer:

£23.96

Step-by-step explanation:

Area to be painted:

3.6 m * 8.3 m = 29.88 m^2

The area to be painted is 29.88 m^2.

A tin of paint covers 8 m^2. We divide to find the number of tins needed.

29.88/8 = 3.735

Since full tins must be bought, the smallest number of tins needed is 4.

Now we find the price of 4 tins. 1 tin costs £5.99, so 4 tins cost:

4 * £5.99 = £23.96

Answer:

$402

Step-by-step explanation:

Hello!

If you made 3.80 an hour and worked 40 we can multiply these to find the total amount you earned.

3.80 * 40 = 152

You also made 250 in tips so we add that to the total

152+250 = 402

The answer is $402

Hope this helps!

Answer:

  y = (x -1)² -3

Step-by-step explanation:

A quadratic with a vertex at (h, k) will have an equation of the form ...

 y = a(x -h)² +k

You have (h, k) = (1, -3), and a vertical scale factor* of 1. So, the equation of the graphed curve is ...

  y = (x -1)² -3

_____

* One way to determine the value of "a" in the form shown is to look at the vertical difference between the vertex and the points 1 unit right or left of the vertex. Here, those points are 1 unit above the vertex, so the vertical scale factor "a" is 1.

Answer:

Step-by-step explanation:

Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA

Starting with the expression

4sinB= 3sin(2A+B)

Let us re write angle B = (A + B) - A

and 2A + B = (A + B) + A

Substituting the derived expression back into the original expression ww will have;

4Sin{(A + B) - A } = 3Sin{(A + B)+ A}

From trigonometry identity;

Sin(D+E) = SinDcosE + CosDSinE

Sin(D-E) = SinDcosE - CosDSinE

Applying this in the expression above;

4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}

Open the bracket

4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA

Collecting like terms

4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA

Sin(A+B)CosA = 7Cos(A+B)sinA

Divide both sides by sinA

Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA

Since cosA/sinA = cotA, the expression becomes;

Sin(A+B)cotA = 7Cos(A+B)

Finally, divide both sides of the resulting equation by sin(A+B)

Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)

CotA = 7cot(A+B) Proved!

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

Answer:

6

Step-by-step explanation:

To calculate x+10, we first need to find x. To do this, we can use the first equation.

We are given the equation:

[tex]x^2-8x=48[/tex]

To solve for x, turn one side of the equation into 0 and solve. Therefore:

[tex]x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12[/tex]

So, the possible values for x are -4 and 12.

However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.

So:

[tex]x+10\\(-4)+10\\=6[/tex]

Answer:

Add a zero to the remainder and a decimal point in the quotient. Then we can continue to divide decimals. We divide 64 by 5 and obtain 12 as a quotient and 4 as a remainder. Since the remainder is not zero, we can continue to get a decimal answer by adding a decimal point in the quotient and a zero to the remainder

Step-by-step explanation:

frustum of a cone is: = pi * l(R + r)

(l) = slant height of the frustum.

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°

Answer:

7 8 9

Step-by-step explanation:

Answer:

x = 150 feets

Step-by-step explanation:

Given that,

The height of a building model is 2% of its actual height.

The building model is 3 feet tall, h = 3 feet

We need to find the height of the actual building. Let it is x.

According to question,

h = 2% of x

We have, h = 3 feet

So,

[tex]x=\dfrac{h}{2\%}\\\\x=\dfrac{3}{2/100}\\\\x=150\ \text{feet}[/tex]

So, the actual height of the building is 150 feets.

Answer:

Given the information above, the area of the square is 361 cm²

Step-by-step explanation:

A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.

The perimeter of the square is 76. So, let's divide 76 by 4.

76 ÷ 4 = 19

So, the lengths of each sides in the square is 19cm.

In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.

19 × 19 = 361

So, the area of the square is 361 cm²

Answer:

361 cm^2

Step-by-step explanation:

The area of a square can be found by squaring the side length.

[tex]A=s^2[/tex]

A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.

[tex]s=\frac{p}{4}[/tex]

The perimeter is 76 centimeters.

[tex]s=\frac{76 cm}{4}[/tex]

Divide 76 by 4.

[tex]s=19 cm[/tex]

The side length is 19 centimeters.

Now we know the side length and can plug it into the area formula.

[tex]A=s^2\\s=19cm[/tex]

[tex]A= (19 cm)^2[/tex]

Evaluate the exponent.

(19cm)^2= 19 cm* 19cm=361 cm^2

[tex]A= 361 cm^2[/tex]

The area of the square is 361 square centimeters.

Answer:

(–81, 9), (–36, 6), (–1, 1) are the correct three points.

Step-by-step explanation:

Given the function:

[tex]f(x) =\sqrt x[/tex]

Please refer to the attached image.

The green line shows the graph of actual function.

It is reflected over y axis.

The reflected graph is shown in black color in attached image.

When reflected over y axis, the sign of variable [tex]x[/tex] changes from Positive to Negative.

So, the resultant function becomes:

[tex]f(x)=\sqrt{-x}[/tex]

i.e. we will have to give the values of x as negative now.

so, the options in which value of x is negative are the possible answers only.

The possible answers are:

(–81, 9), (–36, 6), (–1, 1) and

(–49, 7), (–18, 9), (–1, 1)

Now, we will check the square root function condition.

In the 2nd option, (–18, 9) does not satisfy the condition.

So, the correct answer is:

(–81, 9), (–36, 6), (–1, 1)

Answer:

A on E2020

Step-by-step explanation:

:)

Answer:

−5 < x < 10

Step-by-step explanation:

−6 < x − 1 < 9

Add 1 to all sides

−6+1 < x − 1+1 < 9+1

−5 < x < 10

Answer:

B

Step-by-step explanation:

Add one to everything

-5 < x < 10

Best of Luck!

Answer:

164

Step-by-step explanation:

B for brackets

O for of

D for division

M for multiplication

A for addition

S for subtraction

You first start with the brackets (20) and multiply with 4 which is equal to 80 and then add it to 84 which makes 164

I hope this helps

a)

X + Y = 5

2X - Y = 9      

X + 2X + Y - Y = 5 + 9

3X = 14

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:

X+ Y = 5

14/3 + Y = 5

Y = 5 - 14/3

.........................

b)

3X - Y = 10

X + Y = 18        

3X + X - Y + Y = 10 + 18

4X = 28

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:

X + Y = 18

7 + Y = 18

Y = 18 - 7

Answer:

11 adults and 16 children

Step-by-step explanation:

a + c = 27 and 4a + c = 60

3a = 60 - 27 = 33

a= 11  

so c = 16

The correct answer is D. ​No because the permutations rule would be used to determine the total number of combinations.

Explanation:

The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.

Answer:

y = 1/3x + 4/7

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Formula: y = mx + b

Step 1: Find slope m

m = (1 - 2)/(-3 - 4)

m = -1/-7

m = 1/7

y = 1/7x + b

Step 2: Find y-intercept b

1 = 1/7(3) + b

1 = 3/7 + b

b = 4/7

Step 3: Write linear equation

y = 1/3x + 4/7

Answer:

(-2, 4, 2)

Where x = -2, y = 4, and z = 2.

Step-by-step explanation:

We are given the system of three equations:

[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]

And we want to find the value of each variable.

Note that both the second and third equations have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.

Solve the second equation for z:

[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]

Likewise, solve the third equation for y:

[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]

Substitute the above equations into the first:

[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]

Hence, x = -2.

Find z and y using their respective equations:

Second equation:

[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]

Third equation:

[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]

In conclusion, the solution is (-2, 4, -2)

Answer:

x = -2

y =4

z=-2

Step-by-step explanation:

4x−y−2z=−8

−2x+4z=−4

x+2y=6

Solve the second equation for x

x = 6 -2y

Substitute into the first two equations

4x−y−2z=−8

4(6-2y) -y -2 = 8  

24 -8y-y -2z = 8

-9y -2z = -32

−2(6-2y)+4z=−4

-12 +4y +4z = -4

4y+4z = 8

Divide by 4

y+z = 2

z =2-y

Substitute this into -9y -2z = -32

-9y -2(2-y) = -32

-9y -4 +2y = -32

-7y -4 = -32

-7y =-28

y =4

Now find z

z = 2-y

z = 2-4

z = -2

Now find x

x = 6 -2y

x = 6 -2(4)

x =6-8

x = -2

Answer:

[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Step-by-step explanation:

The total number of ways in which 5 specimens can be selected from the  dish at random is given as C(40, 5).

Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).

3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).

Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Answer:

Step-by-step explanation:

When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:

[tex]sin(x)=\frac{32}{45}[/tex] and

sin(x) = .711111111

Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:

[tex]sin^{-1}([/tex]  

and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325 so

Angle of depression = 44.67 or 44.7 degrees.

Answer:

Its 45.3!!!

Step-by-step explanation:

[tex](-3+5,10-7)=(2,3)[/tex]

Answer:

The equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Step-by-step explanation:

To find the equation for the circle 12 seconds when the radius of the ripple increases at a rate of 50 cm/s, the circle radius will be;

50 * 12 = 600 cm

Then place the equation inform of Pythagoras equation which is;

x^2 + y^2 = r^2

Where r is the radius

x^2 + y^2 = 600^2

x^2 + y^2 = 360,000

Then, the equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Answer:

A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.

Step-by-step explanation:

Answer:

C.) A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.

Step-by-step explanation:

Answer:

We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Step-by-step explanation:

We are given that a researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Let [tex]\mu[/tex] = mean weight of cereal in its 18-ounce boxes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 18       {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 18      {mean that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces}

Also, it is given that the P-value is 0.01 and the level of significance is 0.05.

The decision rule based on the P-value is given by;

Here, clearly our P-value is less than the level of significance as 0.01 < 0.05, so we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.

Therefore, we conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.