Mark is making concrete. Concrete is made by mixing cement, sand and gravel in the ratio 1:2:3. Mark wants to make 600kg of concrete. How much sand does Mark need

Answer:

vertex = (4, 5 )

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 4)² + 5 ← is in vertex form

with vertex = (4, 5 )

Answer: 8

Evaluating the function for x = -1

[tex]f(x)=x^2+7\\f(-1)= (-1)^2+7\\f(-1)=8[/tex]

Answer:

1,45 cubic units

Step-by-step explanation:

The method of cylindrical shells demands that the volume of the solid is given by:

[tex]V=2\pi\int_a^b xf(x)dx[/tex]       (1)

In this case you have that f(x) is:

[tex]f(x)=cos(\frac{\pi}{2}x)[/tex]

a = 0

b = 1

First, you solve the integral, by parts:

[tex]\int xf(x)dx=\int xcos(\frac{\pi}{2}x)dx=x(\frac{2}{\pi})sin(\frac{\pi}{2}x)-\int (\frac{2}{\pi})sin(\frac{\pi}{2}x)dx\\\\=(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)+C[/tex]

Next, you calculate the volume of the solid, by replacing the solution to the integral in the equation (1):

[tex]V=2\pi[(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)]_0^1\\\\V=2\pi[(\frac{2}{\pi})-(\frac{2}{\pi})^2]=1,45u^3[/tex]

hence, the volume of the solid generated is 1,45 cubic units

Answer: Finding the number of equal-sized parts into which a number can be split

Step-by-step explanation:

Hi, a division expression is the division of 2 numbers that results in a quotient.

The quotient is the number of times that the second number in the division is contained in the first number.

For example 20 ÷ 2 = 10

Number 2 is contained 10 times in the number 10, or in other words, 20 can be split into ten equal-sized parts.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

A

Step-by-step explanation:

for edge

Answer:

15 days

Step-by-step explanation:

5 x 21 = 105

105/7 = 15

Answer:

15 days

Step-by-step explanation:

As the number of people in that family increases the time taken reduces, so the time is in inverse proportion to the number of people in that family.

Let the number of days taken by a family of 7 to finish a quantity of food be x.

⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{1}{\frac{7}{5} }[/tex]

⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{5}{7}[/tex]

⇒ x = [tex]\frac{21 * 5}{7}[/tex]

x = 15

∴ It would take a family of 7 15 days to finish a quantity of food.

Hope this helps!!!

Answer:

b => base  => 40 cm

h => altitude => 30 cm

A = h*b/2

h=b-10

600=(b-10)b/2

600 = (b^2-10b)/2

1200=b^2-10b

b^2-10b-1200=0

(b-40)(b+30)=0

b=40 cm

h=b-10 = 40-10=30

Answer:

Almost about 4500 mm

Step-by-step explanation:

Measure the pennies width and estimate. Multilpy by 2000 and there you go!

Answer:

25

Step-by-step explanation:

The ratio of cranberry to blueberry muffins sold was 2/3.

This means that for every 3 blueberry muffins, 2 cranberry muffins were sold.

The ratio of blueberry to cinnamon muffins sold was 4/1.

This means that for every cinnamon muffin, 4 blueberry muffins were sold.

In other words, the ratio of cinnamon muffins to blueberry was 1/4.

60 blueberry muffins were sold on Monday.

This means that the number of cranberry muffins sold was:

2/3 * 60 = 40 cranberry muffins

This also means that the number of cinnamon muffins sold was:

1/4 * 60 = 15 cinnamon muffins

To find how many more cranberry muffins were sold than cinnamon muffins:

40 - 15 = 25 muffins

25 more cranberry muffins were sold.

Answer:

25

Step-by-step explanation:

Answer:

The vertical angles theorem

Step-by-step explanation:

The Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.

Angles ∠JKN and ∠MKL fit the criteria of the vertical angles theorem, meaning they are congruent.

Answer:

-8

Step-by-step explanation:

f(1) = -2

g(4)= 6

-8 *(-2) -4 * 6 = 16 -24 = -8

Work Shown:

Circumference = pi*diameter

Circumference = 3.14*7

Circumference = 21.98 inches approximately

This is approximate since pi = 3.14 is approximate.

Answer:

[tex]Slope:\frac{3}{2}\\y-intercept:2[/tex]

Step-by-step explanation:

Answer:

{-12,12}

Step-by-step explanation:

-|-x| = -12 multiply both sides by -1

|-x| = 12 apply rule for solving absolute value equations

-x = 12 and -x = -12 solve

x = -12 and x =12

Answer:

210 KM

Step-by-step explanation:

first 20minutes is 1/3 of an hour

20/60=1/3 hour

how far does the car drive =time *speed

=2 1/3 hour *90= 210 km

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Answer:

x=0.333

Step-by-step explanation:

12(3x)=12

36x=12

/36 on both sides

x=0.333

Answer:

1:6

Step-by-step explanation:

3x/8 = 9y/4

Multiply by 8

3x = 9y/4 *8

3x = 18 y

Divide by 3

x = 18y/3

x = 6y

The ratio is of x to y is

1:6

Answer:

Step-by-step explanation:

3x/8=9y/4

3x/2=9y

1.5x=9y

1.5x:9y

Answer:

a. 0.17

b. 0.95

Step-by-step explanation:

The key to answering both questions is that we should understand that the probability of an event happening = 1 - the probability of the event not happening

Firstly, we want to calculate the probability of less than four

Probability of less than four = 1 - probability of four or more heads

that is 1 - 0.83 = 0.17

Probability of less than 8 = 1 - probability of 8 or more = 1-0.05 = 0.95

Answer:

34.5% probability that the jury returns a guilty verdict

Step-by-step explanation:

We have these following probabilities:

If the police can discredit the police department, 15% probability of a guilty verdict.

70% probability of the police department being discredited by the defense.

If the police can discredit the police department, 80% probability of a guilty verdict.

100 - 70 = 30% probability of the defense not discrediting the police.

What is the probability that the jury returns a guilty verdict?

15% of 70% and 80% of 30%. So

p = 0.15*0.7 + 0.8*0.3 = 0.345

34.5% probability that the jury returns a guilty verdict

Answer:

y = 6

Step-by-step explanation:

-3x + 9y = 18

-3(6) +6y = 18

-18 +6y = 18

Add 18 to each side

-18+18 +6y =18+18

6y = 36

Divide each side by 6

6y/6 = 36/6

y = 6

Answer:

3:1

Step-by-step explanation:

Since there are 3 times more blue favorite kids, the ratio is

3:1

The ratio of the number of students who said blue to the number of students who said green is 3 : 1.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Mark asked each student in a class to name their favorite color.

For this class,

the number of students who said blue is three times the number of students who said green.

Let n be the number of students who said green.

Then, 3n, the number of students who said blue.

The ratio of the number of students who said blue to the number of students who said green.

= 3n/ n

= 3/1

= 3: 1.

Therefore, the ratio is 3 : 1.

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Answer:

let f(x)= y

y = 4x+8

x= 4y + 8

4y = x - 8

y = (x - 8)/4

Hope this helps.

Answer:

x/4 - 2 = y

Step-by-step explanation:

soo switch x and f(x)

x=4y+8

then bring it back to like how it was before

x-8=4y

then

(x-8)/4=y

then simplify

x/4 - 8/4 = y

which can then be simplified to

x/4 - 2 = y

Answer:

Options B, C and D

Step-by-step explanation:

Linear pair of angles means sum of the angles of the pair is 180° which are formed at a point of a line.

In other words, pair of supplementary angles is the linear pair.

From the figure attached,

Pair of the linear angles are,

1). ∠BAC and ∠CAD

2). ∠BAE and ∠EAD

3). ∠EAD and ∠DAC

Therefore, Options B, C and D are correct.

Answer:

B, C, and D

Step-by-step explanation:

Answer:

so the answer is the second one. Hope this working helps

3.142*4.5²=63.6255

Answer=63.63

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

x = 5, y = 9.

Step-by-step explanation:

8^x / 2^y = 64

3^4x * (1/9)^(y -1) = 81

From the first equation

2^3x / 2^y = 2^6

2^(3x-y) = 2^6

So 3x - y = 6  ..........(1)

From the second equation:

3^4x * 9^(-(y-1)) =  3^4

3^4x * 3^2(-(y-1)) = 3^4

3^(4x+ 2(1 - y)) = 3^4

So 4x + 2(1 - y) = 4

4x - 2y = 2

2x - y = 1   .............(2)

Subtract: (1) - (2):

x = 5.

and  2(5) - y = 1

so y = 9.

Solving the simultaneous equations we get x is 5  and y is 9 .

Simultaneous equations in algebra are those that concurrently involve two or more variables, such as x and y. Even though they are solved simultaneously, the equations are known as simultaneous equations. Just these equations alone have innumerable answers.

A system of equations, often known as an equation system, is a collection of finite equations for which common solutions are sought.

The two given equations can be simplified as:

[tex]8^x \div 2^y = 64\\\\or,\frac{2^{3x}}{2^y} =2^6\\\\or, 2^{3x-y}=2^6\\\\or, 3x-y = 6[/tex]

And :

[tex]3^{4x} \times (\frac{1}{9})^{y-1}=81\\\\or, 3^{4x} \times 3^{-2(y-1)}=3^4\\\\or, 3^{4x+2-2y}=3^4\\\\or, 4x-2y = 2\\\\or,2x-y=1[/tex]

Now we can solve the two simultaneous equations :

3x - y = 6 and 2x - y = 1

Subtracting the equations we get:

x = 5

and

y = 9

Solving the simultaneous equations we get the value of x as 5 and the value of y as 9 .

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Answer:

x < 6

Step-by-step explanation:

There is an open circle ( no equals) at 6   and the line goes to the left

This means that it is less than 6

x < 6

Answer:

-3/8 +4x -9z

Step-by-step explanation:

this should be the translated answer, the variables don't need a multiplication sign because they aren't written as numbers

Answer:

First space: 15

Second space: 20

Third space: 0

Fourth space: 20

Step-by-step explanation:

If the florist decrease x times the value of the bouquet by 1, the number of bouquets sold is 30 plus 3 times x, so we have that:

P(x) = (20 - x)*(30+3x)

P(x) = 600 +30x - 3x2

The vertical axis of the graph represents the profit P(x) of the florist.

So observing the graph, we can see that the maximum profit is 675, and occurs when the value of x is 5, that is, the price of the bouquet is 20 - 5*1 = $15

Looking again to the graph, we see that when x = 20 her profit is zero (the price of each bouquet will be 20 - 20*1 = 0)

The interval of x for which the florist have a positive profit (P(x) > 0) is between x = -10 and x = 20, but the florist cannot make a negative number of one-dollar decrease, so the lower number in the interval should be 0.

Answer:

675

20

(0,20)

Step-by-step explanation:

Answer:

You can also represent it as  [tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

[tex](\sqrt[3]{2})^{3} =2\\2^{\frac{1}{3} } =2[/tex]