Workers in an office of 60 staff were asked their favourite type of take-away.
The results are summarised in the table.

Take-away Frequency Angle
Pizza 7
a
Curry 19
b
Fish & chips 4
c
Kebab 5
d
Other 25
e
Work out the size of each angle to draw a pie chart.

Answer:

B) [tex]f(x)=3e^x^+^6-4[/tex]

D) [tex]f(x)=3(x+6)^2-4[/tex]

Step-by-step explanation:

I did what the other person said and I got 1/2.

The correct functions have the same transformations are,

⇒ f (x) = 3eˣ⁺⁶ - 4

And, f(x) = 3(x+6)² - 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 3 csc (x + 6) - 4

Now, In the given function;

⇒ f (x) is a translation of g(x) = 3csc x of 6 units to the left and 4 units down.

By options;

⇒ f (x) = 3eˣ⁺⁶ - 4

And, f(x) = 3(x+6)² - 4

Both function is a translation of 6 units to the left and 4 units down.

Thus, The correct functions have the same transformations are,

⇒ f (x) = 3eˣ⁺⁶ - 4

And, f(x) = 3(x+6)² - 4

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The number 77.31 x 10^4 in scientific notation is 7.731 x 10 ^ 5. To achieve this, the decimal place was moved to the left and the power of 10 increased accordingly.

To express the number 77.31 x 10^4 in scientific notation, we need to adjust it to fit the format 'a x 10^n', where 1 ≤ |a| < 10 and n is an integer. So, the main step is to transfer the decimal place in '77.31' to after the first digit, followed by multiplying by an appropriate power of 10.

Firstly, rewrite 77.31 as 7.731 by moving the decimal place one place to the left. Now, since our original number was multiplied by 10^4, this needs to be amended by 1 place for the movement of the decimal point. This results in 10^5, since you are now multiplying by 10 one more time than before.

Combining these, the given number is represented in scientific notation as 7.731 x 10 ^ 5.

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Answer:

w: 100w = 80 x 35 = 2800/100 = 28  strands in one pom pom

b: 100b = 80 x 25= 2000/100 = 20   strands in one pom pom

r: 100r = 40 x 80 = 3200/100 = 32  strands in one pom pom

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

0.0009) is 9x10^-4

Step-by-step explanation:

Answer:

y = 56

Step-by-step explanation:

the two angles are equal to 180

y - 24 +3y - 20 = 180

4y - 44 = 180

4y = 224

y = 56

Total cost of the chicken wings is $12.71

Step-by-step explanation:

⇒ Total Cost = 3.91 × 3.25

⇒ Total cost = $12.71

Final answer:

To find the total cost of chicken wings, add the weights of both packages (1.28 pounds + 2.63 pounds = 3.91 pounds) and multiply by the price per pound ($3.25), yielding a total cost of $12.71.

Explanation:

The problem provided describes a scenario where Raman buys two packages of chicken wings weighing 1.28 pounds and 2.63 pounds. To calculate the total cost of the chicken wings at a price of $3.25 per pound, first, we need to determine the total weight of the chicken wings by adding the weight of both packages together. Next, we multiply the combined weight by the price per pound.

Here is the step-by-step calculation:

Add the weights of the two packages: 1.28 pounds + 2.63 pounds = 3.91 pounds.

Multiply the total weight by the price per pound: 3.91 pounds *$3.25 per pound.

Calculate the overall cost: 3.91 * $3.25 = $12.71.

Therefore, the total cost of the chicken wings is $12.71.

Answer:

[tex]width \: of \: the \: rectangle \\ = \frac{area \: of \: rectangle}{length \: of \: rectangle} \\ \\ = \frac{45 {x}^{8} \times {x}^{9} }{5 {x}^{3} \times {x}^{4} } \\ \\ = \frac{45 {x}^{8 + 9} }{5 {x}^{3 + 4} } \\ \\ = \frac{45 {x}^{17} }{5 {x}^{7} } \\ \\ = 9 {x}^{17 - 7} \\ \\ = 9 {x}^{10} \: yards \\ \\ \therefore \: width \: of \: the \: rectangle \\ \: \: \: \: \: \: = 9 {x}^{10} \: yards \\ [/tex]

Step-by-step explanation:

[tex] \because \: ( {a}^{m} )^{n} = {a}^{m \times n} \\ \\ \therefore ( {9}^{3} )^{3} = {9}^{3 \times 3} = {9}^{9} \\ [/tex]

If he drives 125 miles in 2 1/2 hours, he will drive 125 ÷ 2 1/2 miles per hour.

125 ÷ 2 1/2 = 50 miles

answer: 50 miles per hour

Answer:

Step-by-step explanation:

as the temp t increases the number of cricket chirps also increases.

1: The complete table is according to the given function :

t  :    40   50   60   70   80   90   100

c :     10   50   90  130  170  210  250

2: It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.

The given function is,

c = 4t - 180

Here t represents the temperature

c represents the cricket chirps per minutes

Now plug in each temperature value and solve for c:

When t = 40:

c = 4(40) - 150

c = 160 - 150

c = 10

When t = 50:

c = 4(50) - 150

c = 200 - 150

c = 50

When t = 60:

c = 4(60) - 150

c = 240 - 150

c = 90

When t = 70:

c = 4(70) - 150

c = 280 - 150

c = 130

When t = 80:

c = 4(80) - 150

c = 320 - 150

c = 170

When t = 90:

c = 4(90) - 150

c = 360 - 150

c = 210

When t = 100:

c = 4(100) - 150

c = 400 - 150

c = 250

Therefore, the complete table is:

t  :    40   50   60   70   80   90   100

c :     10   50   90  130  170  210  250

When the value of t is 60, the value of c is 90.

It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.

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Answer: 38.47cmsqr

Step-by-step explanation:

Answer:

c = [tex]\frac{5-b}{3ab}[/tex]

Step-by-step explanation:

Given

3abc + b = 5 ( isolate the term in c by subtracting b from both sides )

3abc = 5 - b ( divide both sides by 3ab )

c = [tex]\frac{5-b}{3ab}[/tex]

Answer: -b-5/3ab

Step-by-step explanation:

3abc + b = 5

3abc + b - b = 5 - b

3abc = 5 - b

3abc / 3ab = (5 - b) / 3ab

c = (5 - b) / 3ab

Answer:

8

Step-by-step explanation:

Set up an equation:

x+ (3/4)x = 14

Solve for x:

Combine like terms:

(7/4)x = 14

Divide both sides by 7/4

x = 8

Answer:

77 laptops and 65 desktops

Step-by-step explanation:

142/2=71

71+6=77

71-6+65

Answer:

74 Labtops

Step-by-step explanation:

you first have to subtract 6 from 142

142-6= 136

divide 136 by two.... for the labtops and the computers.

136 ÷ 2 = 68

68 is the number of desktops...to find the number of labtops you just need to add 6 again.

68 + 6 = 74 Labtops

To check your answer you can just add

74+68 and if it equals to what you started with then that's your answer

74 + 68 = 142

Answer:

Cannot simplify the fractions further than that

Step-by-step explanation:

The fractions 5/8 and 3/10 have already been simplified so they do not need to be simplified anymore. If you are wanting to put them in decimal form then that is different. All you have to do is plug it in the calculator.

9514 1404 393

Answer:

  A. They form a linear pair.

  B. They are supplementary.

Step-by-step explanation:

An interior angle and its adjacent exterior angle of a polygon are a linear pair. The angles of any linear pair are supplementary.

Answer:

beggining poit:3   second point (potentially):  1,5

Step-by-step explanation:

in the y intercept 3 is it so which ever has a 3 as the starting point there could be an option

for the 2x part that is the slope otherwise known as rise over run so what you do is that you turn it to a fraction over or under 1 meaning you rise for 2 and go to the right 1

rise 2

      _

run  1

in order to rise 2 you go up 2 from the y intercept(3) and in order to run you go right since its a positive

once you plot those two dots then you draw a line across

Answer:

[tex](x^4)^2=x^8[/tex]

Step-by-step explanation:

Because of the power of a power property, which states that [tex](x^n)^m=x^{n\times{m}}[/tex], where m and n are real numbers, the expression you mentioned can be simplified by applying this property like this: [tex](x^4)^2=x^{4\times2}=x^8[/tex]

Answer:

look at the picture shown

Answer: The speed of the current is 1.5 km/h .

Step-by-step explanation:

Let x = speed of current and y = speed of canoe.

Since  , [tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

As per given , we have

[tex]x+y=\dfrac{12}{2}\\\\ x+y=6......................(1)[/tex]

[tex]y-x=\dfrac{12}{4}\\ y-x=3...............(2)[/tex]

Adding (1) and (2) , we get

[tex]2y=9\\\Rightarrow\ y=\dfrac{9}{2}=4.5[/tex]

Put value of y in (1) , we get

[tex]x+4.5=6\\\Rightarrow\ x=1.5[/tex]

Hence, the speed of the current is 1.5 km/h .

To find the speed of the current, we can use the concept of relative velocity and set up equations for the downstream and upstream journeys.

In order to find the speed of the current, we can use the concept of relative velocity. Let's assume the speed of the canoeist in still water is 'v' km/h and the speed of the current is 'c' km/h.

Downstream journey: The effective speed of the canoeist is 'v + c' km/h. Given that the canoeist took 2 hours to travel 12 km downstream, we can set up the equation:

(v + c) * 2 = 12

Upstream journey: The effective speed of the canoeist is 'v - c' km/h. Given that the canoeist took 4 hours to travel 12 km upstream, we can set up the equation:

(v - c) * 4 = 12

Solving these two equations simultaneously will give us the values of 'v' and 'c', and the value of 'c' will represent the speed of the current.

Answer:

The slope is up 5 over 1

Step-by-step explanation:

Rise over run Which is 5/1

To get the answer you need to follow the x axis and then the y axis or find a point and subtract with an another point on a graph

Or rise over run if u don’t want a graph

Answer:

   a system of linear equations with solution (x, y) = (1, -1)

Step-by-step explanation:

The two given linear equations in x and y are consistent and independent, so will have one solution. That solution is easily found using a graphing calculator. It is (x, y) = (1, -1).

_____

"What is ..." is a pretty open question with lots of different answers that won't be helpful. If you're seeking a specific answer, it would be nice to see the question say what answer you seek.

To find the number of each type of shot, we can create a system of equations based on the given information and solve it. The equations are x + y = 56 and x + 2y = 95.

To solve this problem, we can create a system of equations based on the given information. Let's assume that the team made x 1-point shots and y 2-point shots. We know that the team made 56 successful shots in total, so the first equation is x + y = 56. We also know that the team scored 95 points in total, and since each 1-point shot contributes 1 point and each 2-point shot contributes 2 points, the second equation is x + 2y = 95.

Now we can solve this system of equations:

x + y = 56

x + 2y = 95

By solving these equations, we can find the values of x and y, which represent the number of 1-point and 2-point shots respectively.

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Team made 17 1-point shots and 39 2-point shots.

Let's define variables to set up the system of equations:

x: the number of 1-point shots

y: the number of 2-point shots

We know from the problem statement that:

The total number of shots is 56.

The total points scored is 95.

We can represent these conditions with the following system of equations:

Equation 1: x + y = 56

Equation 2: x + 2y = 95

Now, let's solve this system step-by-step:

Step 1: Solve Equation 1 for x:

x = 56 - y

Step 2: Substitute this expression into Equation 2:

56 - y + 2y = 95

Step 3: Simplify and solve for y:

56 + y = 95

y = 39

Step 4: Substitute y back into Equation 1 to find x:

x + 39 = 56

x = 17

Thus, the team made 17 1-point shots and 39 2-point shots.

Answer:

0.08333333333

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

4[z+3(z-1)]=36

z+3(z-1)=36/4

z+3z-3=9

4z-3=9

4z=9+3

4z=12

z=12/4

z=3

Answer:

4z+2(square)2z=2(square)6

Step-by-step explanation:

4((z+3(z-1)))=36

4(z^2-z+3((z-3)))=36

4(z^2-z+3z-3)=36

4((z^2+(-z+3z)-3))=36

4(z^2+2z-3)=36

4z^2+8z-12=36

4z^2+8z=24

((4(square)z^2))+(square)8z=(square)24

4z+2(square)2z=2(square)6

Answer:

f(4) =[tex]\frac{1}{2}[/tex]

x = 8

Step-by-step explanation:

f(4) =[tex]\frac{1}{2}[/tex]     [ image of 4 is  [tex]\frac{1}{2}[/tex]]

f(x) = 4

then x = 8  [ the preimage of 4 is 8]

Answer:

when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]

Step-by-step explanation:

Considering the expression

[tex]f(x) = 5[/tex]

Rewrite the function as an equation

[tex]y = 5[/tex]

Comparing with slop-intercept form

[tex]y=mx+b[/tex]

So,

[tex]m=0[/tex]

[tex]\mathrm{Axis\:interception\:points\:of}\:5:\quad \mathrm{Y\:Intercepts}:\:\left(0,\:5\right)[/tex]

Therefore, when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]

The graph for  [tex]f(x) = 5[/tex] is also attached below.

Keywords: graph, function

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Answer:

16

Step-by-step explanation:

64÷4=16

Answer:

the answer would be 8

Step-by-step explanation:

64 is the area squared so you need to find the square root of 64 because that would be the opposite.

Answer:

I have bought 4 shirts and 6 pants.

Step-by-step explanation:

Let I have bought x number of shirts and y number of pants.

So, the two equation that we can write from the given conditions are

x + y = 10 ............. (1) and

24x + 32y = 288 ...... (2)

Now, solving equations (1) and (2) we get

24x + 32(10 - x) = 288

⇒ 8x = 320 - 288 = 32

⇒ x = 4

And y = (10 - 4) = 6

Therefore, I have bought 4 shirts and 6 pants. (Answer)

Answer:

42.0

Step-by-step explanation: