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 14
a
Curry 6
b
Fish & chips 4
c
Kebab 14
d
Other 22
e
Work out the size of each angle to draw a pie chart.
a
=

b
=

c
=

d
=

e
=

When the highest and lowest scores are removed, the new mean becomes 84. if the highest of the 12 scores is 98, The lowest score is 46.

We are given that the arithmetic mean of 12 scores is 82. This means that the sum of the 12 scores is 12 * 82 = 984.

We are also given that when the highest and lowest scores are removed, the new mean becomes 84. Let's denote the lowest score as "L" and the highest score as 98. So, the sum of the remaining 10 scores is (984 - L - 98).

We can set up the equation for the new mean as follows:

(984 - L - 98) / 10 = 84

Simplifying the equation, we have:

(886 - L) / 10 = 84

886 - L = 840

-L = 840 - 886

-L = -46

L = 46

Therefore, the lowest score is 46.

The lowest score among the 12 scores is 46.

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The  transformation of \(\(y= \frac{x^{4} }{6x+6}\)\) graph is compressed by a factor of 2.

The function is a rational function in which the numerator is a degree 4 polynomial, and the denominator is a degree 1 polynomial.

Rational functions are in the form of \(\(f(x) = \frac{p(x)}{q(x)}\)\), where p(x) and q(x) are polynomial functions and the degree of p(x) is less than the degree of q(x).

To transform a graph of a function, one can translate, stretch, or reflect it.

Here are some of the transformations of the function \(\(y= \frac{x^{4} }{6x+6}\)\)

Vertical Shift: To get the new graph, we add or subtract a constant from the function.

When f(x) is replaced with f(x) + k, we get a graph that is k units above the graph of f(x). In this case, if we subtract 2 from the equation, we get the following equation:

\(y = (x^4) / (6x+6) - 2\)

This means that the graph of the function is shifted 2 units downwards.

Horizontal Shift: To get the new graph, we add or subtract a constant to the variable.

When f(x+c) is replaced with f(x), the graph is shifted c units to the left.

When f(x-c) is replaced with f(x), the graph is shifted c units to the right.

In this case, we can shift the graph by substituting x-2 for x in the function.

The new function is: \(y = ((x-2)^4) / (6(x-2)+6)\)

This means that the graph is shifted 2 units to the right.

Vertical Stretch/Compression: When a constant is multiplied to the function, the graph is vertically stretched or compressed.

In this case, if the function is multiplied by 2, we get the following function:

\(y = 2(x^4) / (6x+6)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by dividing the function by a constant.

Horizontal Stretch/Compression:

When a constant is multiplied to the variable of the function, the graph is horizontally stretched or compressed. In this case, if the variable is divided by 2, we get the following function:

\(y = (x^4) / (3x+3)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by multiplying the variable by a constant.

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Answer:

1 =125

2=55

3=95

...........

The inequality 54x/64 ≥ 49x/59 simplifies to x ≥ 0. Thus, the solution for x is greater than or equal to zero.

To solve the inequality 54x/64 ≥ 49x/59, we can begin by cross-multiplying:

(54x)(59) ≥ (49x)(64)

3186x ≥ 3136x

Next, we can subtract 3136x from both sides:

3186x - 3136x ≥ 0

50x ≥ 0

Finally, we divide both sides by 50:

x ≥ 0/50

x ≥ 0

Therefore, the solution to the inequality is x ≥ 0.

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Value of P(5) is 0.058 by probability.

What is a math illustration of probability?

Given that ,

p = 1 / 4 = 0.25

1 - p = 1 - 0.25 = 0.75

n = 10

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

(a) x = 5

P(X = 5) = ((10! / 5! (10 - 5)!) * 0.255 * (0.75)10 - 5

              =  ((10! / 5! (5)!) * 0.255 * (0.75)5

              =  0.058

P(5) = 0.058

(b)

P(X > 3) = 1 - P(X \leq 3)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= 1 - 0.776

= 0.224

P(ore than 3) = 0.224

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The complete question is-

Take another guess: A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)

1. Interest rate, as a percent, rounded to 2 decimal places = 4.00% .2. Exact length of time, t = 34.66 years, rounded to 2 decimal places = 34.66 years.3. Exact length of time, t = 5.58 years, rounded to 2 decimal places = 5.58 years.

Principal amount = $15,000, Interest rate = 4%Compounding semiannually Cousin's principal amount = $15,000Compounded continuously.

To get the same return: Let the interest rate be 'r'. Then, Number of times compounded in a year, n = ∞The formula used is: A = Pe^(rt)Where, P is the principal amount, t is the time period in years A is the final amount after t years.

e is a mathematical constant and its value is approximately equal to 2.71828Substituting the values of P, r and t in the above formula, we get:15000e^(r*∞) = 15000 * e^(0.04*1)

Hence, e^(r*∞) = e^(0.04)

Taking natural logarithm on both sides, we get: r*∞ = 0.04ln e = 1.0So,r = 0.04 / ∞Interest rate, as a percent, rounded to 2 decimal places = 4.00%.

Part 2: It takes for an investment earning interest at a rate of 2% compounded continuously to quadruple in value.

The formula used is: A = Pe^(rt)Where, P is the principal amount , t is the time period in years , e is a mathematical constant and its value is approximately equal to 2.71828

Substituting the values of P, r and A in the above formula, we get:4P = Pe^(0.02t) => 4 = e^(0.02t)

Taking natural logarithm on both sides, we get:ln4 = 0.02tln e = 1.0So,t = ln4/0.02Exact length of time, t = 34.66 years, rounded to 2 decimal places = 34.66 years.

Part 3: It will take for $4,000 to grow to $7,000 if the investment earns an interest rate of 4% per year compounded continuously.

The formula used is: A = Pe^(rt)

Where,P is the principal amountt is the time period in yearse is a mathematical constant and its value is approximately equal to 2.71828Substituting the values of P, r and A in the above formula, we get:7000 = 4000e^(0.04t)

Taking natural logarithm on both sides, we get:ln(7000/4000) = 0.04tln e = 1.0So,t = ln(7/4)/0.04Exact length of time, t = 24.97 years, rounded to 2 decimal places = 24.97 years.

Part 4: It takes for an investment earning interest at a rate of 13% compounded quarterly (i.e., 4 times a year) to triple in value.

The formula used is:A = Pe^(rt) Where,P is the principal amountt is the time period in years, e is a mathematical constant and its value is approximately equal to 2.71828

Substituting the values of P, r and A in the above formula, we get:3P = P(1+(0.13/4))^(4t)Taking natural logarithm on both sides, we get:ln3 = 4tln(1+(0.13/4))ln e = 1.0So,t = ln3 / (4ln(1+(0.13/4)))

Exact length of time, t = 5.58 years, rounded to 2 decimal places = 5.58 years.

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Answer:

c

Step-by-step explanation:

an expression is the sum.... difference or product of a value and a variable

Answer:

c

Step-by-step explanation:

Answer:

What do you need help with?

Step-by-step explanation:

What do you need help with-?

Answer:

15&25

Step-by-step explanation:

umm 5,10,15,20,25

25*2=50???

not for sure on it but maybe?

Answer:

Because it goes by 5 each time, I presume the numbers 15 and 25 are the answers. Then 25 is multiplied by two, yielding 50.

Step-by-step explanation:

So, there are the answers, I believe. There was not a lot of information on the problem here.

Answer: 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.

Let's find 25% of 50.

Explanation:

25% of 50 can be written as 25% × 50

= 25/100 × 50

= 25/2 = 12½ = 12.5

Thus, 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.

1 1/10 Should be right because you have to make the denominators match and it's pretty simple from there just subtract and add

Therefore , the solution of the given problem of unitary method comes out to be Amy creates the sand masterpiece by using 8 cups of sand.

To complete the assignment, use the tried-and-true straightforward methodology, the real variables, and any pertinent details from the preliminary and specialised questions. In response, customers might be given another opportunity to range sample the products. In the absence of such changes, major advances in our knowledge of programmes will be lost.

Here,

If Amy fills 16 bottles with 1/2 cup of each colour of sand, the total amount of sand she uses may be calculated by multiplying the total number of bottles by the amount of sand in each container.

The total quantity of sand utilised is thus:

=> 16 x 1/2 = 8 cups

Amy creates the sand masterpiece by using 8 cups of sand.

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Answer:

explanation below

Step-by-step explanation:

if sum of any 2 sides length is greater than the third side and not take rotation transformation into account, only 1 triangle can be formed.

Answer:

Step-by-step explanation:

ODYSSEY

Answer: $63.40

Step-by-step explanation:

She starts out with $317  but she will only get 80%  which means she will lose 20%

100%-80%=20%

take 20% of 317

.2 x 317    convert 20% to decimal by moving decimal twice and multiply

=63.4

She will lose $63.40

Reason:

If she withdraws early, she can only withdraw 80% of what she put in. She takes a 20% penalty.

20% of 317 = 0.20*317 = 63.40 dollars is how much she loses.

Put another way:

She is able to withdraw 0.80*317 = 253.60 dollars if doing so early. She lost 317-253.60 = 63.40 dollars

Answer:

the surface area of a rectangle box of 5cm long, 3cm wide and 4cm wide is 94cm²

Answer:

D

Step-by-step explanation:

3.19 become 3.20 . 1.69 becomes 1.70. Then 3.20 plus 1.70 is 4.90 or 4.9.

Answer:

D. 4.9

3.19 -> 3.2

1.69 -> 1.7

3.2 + 1.7 = 4.9

The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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The explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1)

We can easily determine the value of any term in the sequence using the formula once you have those values.

where:

The sequence's nth word is a n.

The first term in the series is a 1.

The frequency of successive terms is expressed as r.

The sequence's length, n, is given.

The values of a 1, r, and n must be known in order to use this algorithm as a geometric sequence calculator. You can easily determine the value of any term in the sequence using the formula once you have those values.

Therefore, the explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1).

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Answer:

50,20

Step-by-step explanation:

let the two numbers be x and y respectively.

According to the question,

y=2/5 times of x

Or,

y= 2x/5 ..........(1)

Again,

or, x+y=70

or, x+2x/5=70

or, (5x+2x)/5=70

or, 7x=350

therefore x=50

putting the value of y in equation (1)

y=2x/5

y= (2×50)/5

therefore, y=20

Answer:

x = 175

Step-by-step explanation:

given:

A number is 2 /5 times another number. Their sum is 70.

find: the numbers (coefficient)

solution:

cross multiply

2 ( x ) = 70

5

2 (x) = 70 (5)

2 (x) = 350

x = 350

       2

x = 175

check:

2 ( x ) = 70

5

2 ( 175 ) = 70

5

350 = 70

 5

70 = 70

Functions

The total cost of Zacaria's kayaks store is made of a fixed cost and a variable cost. The fixed cost must be paid even if no kayaks are sold, and the variable cost depends on the number of kayaks sold per year (called x in the rest of this answer).

a. We know each kayak is sold for $425, thus for x kayaks, the total income (or revenue) function is:

R(x) = 425x

b. As mentioned above, the total cost is the sum of the fixed and the variable cost. Each kayak cost $315, thus:

C(x) = 315x + 15,600

c. The break-even point occurs when the cost and the revenue are balanced (no loss-no profit). Equating both functions:

315x + 15,600 = 425x

Subtracting 315x:

15,600 = 425x - 315x

Simplifying:

15,600 = 110x

Solving for x:

x = 15,600 / 110

x = 141.8

Thus, 142 kayaks approximately must be sold to be in break-even condition.

d. Since the earnings are proportional to the number of kayaks sold:

R(x) = 425x

There is no limit for the value of x that maximizes this function, i.e., the greater the value of x, the greater the earnings. There is no maximum point in this function.

In case the earnings function is referring to the profit function, then:

E(x) = R(x) - C(x)

E(x)= 425x - (15,600 + 315x)

E(x) = 110x - 15,600

This function doesn't have a maximum point because it's a linear equation, so there is not a theoretical maximum value for x

Answer:

Step-by-step explanation:

this a educatated gues and i wanna say B or C bc the line is positive so im leaning towards c more but you can choose ?

As per the coordinates of the labeled point, the point-slope equation of the line is y + 5 =  2(x+ 2).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

To find the equation of a line passing through two given points, we can use the point-slope form of the equation of a line:

First, let's find the slope of the line:

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

m = (5 - (-5)) / (3 - (-2))

m = 10 / 5

m = 2

Next, we can choose one of the given points to use in the point-slope form. Let's use (-2, -5):

y - (-5) = 2(x - (-2))

y + 5 = 2(x + 2)

Therefore, the equation is y + 5 = 2(x + 2).

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13.

Then, the zeros are x=-5 and x=4.

14.

Then, the zeros are x=-6 and x=10.

15.

Then the zeros are x=5 and x=10.

16.

Then the zeros are x=-8 and x=7.

17.

Then the zeros are x=-8 and x=6.

18.

Then there is only one zero at x=6.

19.

Then the zeros are x=-30 and x=-2.

20.

Then the zeros are x=-4 and x=25.

The value of the function a, b, c, d, e, f, g, and h are -1, -10, -100, -1000, 1000, 100, 10, and 1 respectively.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The given function is f(x).    

\(\rm f(x) = \dfrac{1}{x}\)

The values of f(x) at a given point will be shown in the table.

    x                       f(x)

   -1                        -1

 -0.1                      -10

-0.01                   -100

-0.001                -1000

0.001                 1000

 0.01                    100

  0.1                      10

   1                         1

Thus, the value of the function a, b, c, d, e, f, g, and h are -1, -10, -100, -1000, 1000, 100, 10, and 1 respectively.

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Answer:

a = -1
b = -10
c = -100
d = -1000
e = 1000
f = 100
g = 10
h = 1

☆

EDGE2022; Good Luck!!! :D

Answer:

Step-by-step explanation:

15) x should +ve

16) x should be -ve

Positive integers between 100 and 999.

1) Are divisible by 7 = 128

2) Are odd = 450

3) Have the same three decimal digits = 9

4) Are not divisible by 4 = 675

Positive integers between 100 and 999 is 900

1) Number divisible by 7 = 105,112,119.......994

a = 105 , d = 7 , l = 994

l = a + (n-1)d

994 = 105 + (n-1)7

n = 128

2) Are odd half number will  be odd = 900/2

odd number = 450

3) Have same three decimal digit

111,222,333,444,555,666,777,888,999

Total = 9

4)Not divisible by 4

Divisible by 4 = 100,108,112,........996

a = 100, d = 4, l =996

l = a + (n-1)d

996 = 100 + (n-1)4

n = 225

Not divisible by 4 = 900 - 225

Not divisible by 4 = 675

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Answer:

Fact

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

6/2=3 and 48/3=16

The y coordinate of the point L that partitions the segment in the given ratio is -21.5

The given parameters are:

J = (-25, 10)

K = (5, -20)

Ratio = m : n = 7 : 3

Remove the x coordinates of points J and K

So, we have

J = 10

K = 20

The y coordinate of the point L that partitions the segment in the given ratio is calculated as:

L = 1/Ratios * (mKy + nJy)

So, we have

L = 1/(7 +3)* (7 * -20 + 3 * -25)

Evaluate the expression

So, we have

L = -21.5

Hence, the y coordinate of the point L that partitions the segment in the given ratio is -21.5

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Answer:

4ab-2a+8

Step-by-step explanation:

(9ab-2a+7)-(5ab-1)

9ab-2a+7-5ab+1

9ab-5ab-2a+7+1

4ab-2a+8