a group of people were given a spelling test. the table shows their marks. work out the range of the marks. how many students are in the group. work out the mean mark of the group.

The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3

linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.

if f(0) = -3, it means at x = 0, f(x) = -3

and if f(7) = 11, it means at x = 7, f(x) = 11

So the Linear equation that will yield these results is f(x) = 2x - 3

In conclusion, the Linear function is f(x) = 2x - 3

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Answer:777

Step-by-step explanation: I do not care

There are 333 pages are in my book.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are more than 200 pages but fewer than 800 in my book.

And, All the digits of my number are the same and the number is divisible by 9.

Now,

Let a number with three same digit = xxx

So, We get;

200 < xxx < 800

Since, the number is divisible by 9.

So, By the rule of the number divide by 9, we get;

x + x + x = 9k

3x = 9k

for k = 1;

x = 3

Thus, Number of pages = 333

Therefore,  

There are 333 pages are in my book.

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Step-by-step explanation:

There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.

a. Find the percentage of marbles that are not blue.

100% - 40% = 60%

b. Find the number of marbles that are not blue​.

60% = 0.6

0.6 * 185 = 111 marbles

Answer:

2xy(8x + 5)

Step-by-step explanation:

16x²y + 10xy ← factor out 2xy from each term

= 2xy(8x + 5)

The graph is attached and the table of value of the graph is as follows

x     y

-4   12

0    4

5    -6

The function y = −2x + 4 is a linear function and will have a straight line graph

The table of values is gotten form the equation y = −2x + 4

solving for x = -4,

y = −2 * -4 + 4 = 12

solving for x = 0

y = −2 * 0 + 4 = 4

solving for x = 5,

y = −2 * 5 + 4 = -6

x     y

-4   12

0    4

5    -6

The graph is plotted by finding the points in the table in the Cartesian plane and joining the points together

Other values are solved for in similar step

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Answer:Here is your answer

Step-by-step explanation:

Answer:

Domain = { -2 , 0 , 2 , 4 }

Range = { 3 }

Step-by-step explanation:

Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values

Since the x-values for the Function attached are -2 , 0 , 2 , 4

and the y-values for the Function is 3

Then the Domain = { -2 , 0 , 2 , 4 }

and the Range = { 3 }

Glad to Help

Answer:

Neither of them are solutions unless you had a typo in the question.

Step-by-step explanation:

1) plug in the known values into both of the equations

First Coordinate:

y-x[tex]\leq[/tex]-5
(1)-(0)[tex]\leq[/tex]-5
1[tex]\leq[/tex]-5 which is not true.
In this case, we do not need to plug in (0,1) into both of the equations because the coordinate cannot be a solution unless the coordinate works in BOTH of the equations.

Second Coordinate:

1)  y-x[tex]\leq[/tex]-5
(-6)-(-1)[tex]\leq[/tex]-5

(-6)+1[tex]\leq[/tex]-5 -->    It becomes a +1 because two negatives make a positive

-5 [tex]\leq[/tex]-5 - -> which means this is true because -5 is less than or equal to -5

2) y-2x>-5
(-6)-2(-1)>-5

-6(2)>-5
-12>-5 NOT TRUE

ANSWER: Neither of them are solutions unless you had a typo in the question.

Answer:

Step-by-step explanation:

A and D are the answers that I would pick

Answer:

B and C

Step-by-step explanation:

- 1 / -3 = 1/3, we know negative divide by a negative number = positive

- -1/3 = 1/3, we know negative times negative = positive

We have coordinates (-2, -3) and (1, 1)

To find: Slope of a line that passes through these two coordinates

Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)

We will use the formula of Slope :

m = y₂ - y₁ / x₂ - x₁

Where 'm' stands for slope

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

m = 1 + 3 /  1 + 2

m = 4 / 3

The slope of the line is  4/3

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The expression that shows the distance you would drive from the gym to the office along this road is b.|-6|+|4|

Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance is defined as an object's total movement without regard for direction. The distance can be defined as how much ground an object has covered regardless of its starting or ending point.

To find the distance between two points in a number line we do the absolute value of the points subtracted. That is if we need to find the distance between point a and point b in a number line we do |a-b|.

Now, the Gym is at point -6 in the number line and the office is at point 4 in the number line, then the distance from -6 to 4 is |-6-4| = |-10| = 10.

Now, option a is |-6+4| ≠ |-6-4|.

The option b is |-6|+|4| = 6+4 = 10 =|-6-4|. Then, option b is correct.

Option c is -6+4 ≠ |-6-4|.

The option d is -|6|+|4| = -6+4 ≠ |-6-4|.

Then, the correct answer is b.

The complete question is given below.

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Complete question

Which expression shows the distance you would drive from the gym to the office along this road?

a.|-6 + 4|

b.|-6|+|4|

c.-6+4

d.-|6|+|4|

Answer:

2x^2 -x -10 is the answer as a product

3x-3 as a sum

Step-by-step explanation:

Assuming (2x-5)(x+2)=0

Let's distribute.

(2x^2+4x)(-5x-10)=0

Then combine like terms

2x^2 -x -10 is the answer as a product

3x-3 as a sum

The dimension of the box will be (40 inch × 40 inch × 10 inch).

How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.

Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).

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The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.

From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.

In this case, Omar bought 3.5k of onions are 8.90 per kilo.

The amount that Omar will pay for the onions will be:

= Number of kilograms × Cost per kg

= 3.5 × 8.90

= $31.15

In conclusion, the amount is $31.15.

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The final answer of the given quadratic equation is 2x - 3y + 7= 0.

What is the quadratic equation?

Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

We have,

                 2x = 3y - 7

Converting the given equation in the form of ax + by + c = 0, we get

                 2x - 3y + 7= 0

Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.

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An equation relating W to T is given by W = 700 + 25T. Also, a graph of this linear equation is shown in the image attached below.

In order to write an equation relating W to T, we would define the variables that represents the amount of water in the pond (in liters) and the number of minutes this water has been added as follows:

The initial volume of water is given by:

700

The volume of water added to this pool would be given by:

25T

Therefore, the total volume of water added to this pool is given by:

W = 700 + 25T

Next, we would determine the points for the graph of this equation:

At T = 0, we have:

W = 700 + 25(0)

W = 700   ⇒ (0, 700)

At T = 1, we have:

W = 700 + 25(1)

W = 725   ⇒ (1, 725)

At T = 2, we have:

W = 700 + 25(2)

W = 750   ⇒ (2, 750)

At T = 3, we have:

W = 700 + 25(3)

W = 775   ⇒ (3, 775)

At T = 4, we have:

W = 700 + 25(4)

W = 800   ⇒ (4, 800)

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The total sum of money is 77 dollars .

Let the total sum of money be x .

⇒ Aziz's share = 4x / 11

   Ahmad's share = 7x / 11

Given : Aziz received 21 dollars less than Ahmad

⇒ 4x / 11 = ( 7x / 11 ) - 21

Solving the above linear equation in one variable ,

( 7x - 4x ) / 11 = 21                      ( taking like terms together )

3x = 21 * 11

x = 7 * 11

x = 77

Aziz's share = ( 4 / 11 ) * 77 = 28

Ahmad's share = ( 7 / 11 ) * 77 = 49

Total Sum of money = 28 + 49 = 77 dollars .

Hence , the total sum of money = 77 dollars .

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Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). Each double will occur once with the probability of 1/36

The sample space for the event of  rolling 2 fair six-sided  dice is  :

S={ (1, 1),(1, 2),(1,3),(1,4),(1,5),(1,6),(2,1)........., (6,5),(6,6) } , So in total for the outcome, we get a total of 36 pairs, with the probability of getting an event as 1/36, now the situation given to us is the vent of getting a double.So the event space for getting a double while  rolling 2  dice  is E = { (1, 1),(2, 2),(3,3),(4,4),(5,5),(6,6) } , the outcome will be 6 pairs, so the probability for each double pair to  come out when we roll the  2 dice is:  1/36  and the probability of getting the least double from  the 6 pairs of double is: 1/6

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Answer:

[tex]\textsf{Quotient}: \quad 2i^3+4i^2-5i+6[/tex]

[tex]\textsf{Simplified Quotient}: \quad 2-7i[/tex]

Step-by-step explanation:

Long division method

Given rational expression:

[tex]\dfrac{2i^4-6i^3-25i^2 +31i-30}{i -5}[/tex]

Solve using long division:

[tex]\large \begin{array}{r}2i^3+4i^2-5i+6\phantom{)}\\i-5{\overline{\smash{\big)}\,2i^4-6i^3-25i^2 +31i-30\phantom{)}}}\\{-~\phantom{(}\underline{(2i^4-10i^3)\phantom{-b00000000000.)}}\\4i^3-25i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(4i^3-20i^2)\phantom{))))))))))))}}\\-5i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(-5i^2+25i)\phantom{........}}\\6i-30\phantom{)}\\-~\phantom{()}\underline{(6i-30)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Therefore, the quotient is:

[tex]2i^3+4i^2-5i+6[/tex]

Imaginary number rule

[tex]i^2=-1[/tex]

Simplify the quotient:

[tex]\implies 2i^3+4i^2-5i+6[/tex]

[tex]\implies 2i^3+4(-1)-5i+6[/tex]

[tex]\implies 2i^3-4-5i+6[/tex]

[tex]\implies 2i^3-5i-4+6[/tex]

[tex]\implies i(2i^2-5)+2[/tex]

[tex]\implies i(2(-1)-5)+2[/tex]

[tex]\implies-7i+2[/tex]

[tex]\implies 2-7i[/tex]

Answer:

length = 13 cm , width = 14 cm

Step-by-step explanation:

let the length be n , then the width is n + 1

the perimeter (P) of a rectangle is calculated as

P = 2(l + w) ← l is the length and w the width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

so, length = 13 cm and width = 14 cm

The missing parts of the table for the function are 49, 1 and 49 respectively

An exponential function is a type of function which involves exponents. A simple exponential function is of the form y = bˣ

Given:  the exponential function y = (1/7)ˣ

In order to find the missing parts, we have to substitute the relevant values into the function. Thus:

For x = -2:

y = (1/7)ˣ

Substitute x = -2 into the function:

y = (1/7)⁻² = 49

For x = 0:

y = (1/7)ˣ

Substitute x = 0 into the function:

y = (1/7)⁰ = 1

For x = 2:

y = (1/7)ˣ

Substitute x = 2 into the function:

y = (1/7)² = 1/49

The missing part is 49

Therefore, the missing parts of the table are 49, 1 and 49 respectively

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Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.

The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.

We have  Margin of error(E)=0.02,

Significance level([tex]\alpha[/tex])=0.01

Proportion(p)=0.13

Therefore, q is defined by =1-p

                =>  q =1-0.13

                =>q=0.87

So, the Z-score is 2.582

Now, we know that sample size(S) is given by

                =>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]

               =>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]

               =>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000

               =>S=([885.01] / [1+1885.01]) × 1000

                =>S=(0.200351)×1000

                =>S=2003.51=2004 (approx)

Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of  sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.

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Answer:

£250

Step-by-step explanation:

Divide $405 by $1.62 which is 250.

Multiply that by £1 which is £250.

Answer:

sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1

The required answers for given similar triangles are DF= 3, EF= 2.25, and scale factor 4/3 respectively.

In geometry, two geometrical triangle are similar if they have the same shape, and corresponding sides are equate by some factor. More accurately, one can be obtained from the other by uniformly scaling.

For length of side DF, ratio of corresponding sides is equal.

⇒  [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]

⇒  [tex]\frac{2}{1.5}=\frac{4}{DF}[/tex]

⇒  DF = 3

Similarly for EF,

 [tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]

⇒[tex]\frac{2}{1.5}=\frac{3}{EF}[/tex]

⇒ EF = 2.25

At last, by using same concept of similarity scale factor is

 [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]

⇒ [tex]\frac{AB}{DE} =\frac{4}{3}[/tex]

This is our scale factor for both triangle.

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Total amount that Mikaela spent on the paddleboard is 578.5065.

According to given data,

original price = 899$ and 40% off.

state tax rate is 7.25%.

Solution:-

Applying formula,

⇒ 899 × (7.25% + 1) × (1 - 40%)

⇒ 899 × 1.0725 × 0.6

⇒ 578.5065.

Total amount that Mikaela spent on the paddleboard is 578.5065.

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The probability that he is a male civilian employee is 0.13362.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that 66% of full-time law enforcement employees are sworn officers, 34% of them are civilian employees (100 - 66).

Given that 60.7% of civilian employees are women. Therefore, the percentage of men is (100 - 60.7)% or 39.3%.

Therefore, the likelihood that he works as a male civilian is 39.3% of 34%, which equals 0.393 * 0.34, = 0.13362.

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The number of terms in the expression 5x - 2 is 2

The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be

The terms can be like terms or unlike terms

The two terms given is separated by the subtraction operator and are both unlike terms

The first term 5x consist of

The second term is just a constant which is 2

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