Solve the discriminant

Answer:

If 11 people use all three facilities, this means:

22 − 11 or 11 are using the gym and the pool but no the track,

29 − 11 or 18 are using the pool and the track but no the gym,

25 − 11 or 14 are using the gym and the track but no the pool.

How many people use the gym only?

130 − (14 + 11 + 11) = 94

How many people use the pool only?

62 − (18 + 11 + 11) = 22

How many people use the track only?

58 − (14 + 11 + 18) = 15

How many people go in for sports?

94 + 22 + 15 + 11 + 14 + 18 + 11 = 185

How many people use exactly one of the facilities?

94 + 22 + 15 = 131

What is the probability that the person uses exactly one of the facilities?

= 131/185 ≈ 0.7081

Step-by-step explanation:

its a bit confusing

Hope It Helps !!!!

Answer:

Inverse variation here gives out a function [tex]xy=(-32)[/tex].

Step-by-step explanation:

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.

An inverse variation can be represented by the equation

[tex]xy=k \\or \\y=kx[/tex]. That is, y varies inversely as x if there is some nonzero constant k.

Here, the product is given by

[tex]xy=(-4)[/tex]×[tex]8[/tex]

[tex]xy=(-32)[/tex]

We will be plotting the graph of the function [tex]xy=(-32)[/tex]

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Answer:

3rd option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-2)}{4-0}[/tex] = [tex]\frac{-1+2}{4}[/tex] = [tex]\frac{1}{4}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{4}[/tex] x - 2 ← equation of line

The surface area of the composite figure is 714 sq. in.

Let, a be the edge of the cube.

Then, surface area of the cube = 6a² square unit

Let, length of the cuboid = l unit

Width of the cuboid = w unit

Height of the cuboid = h unit

Then, surface area of the cuboid = 2(lw+lh+hw) square unit

Given, edge of cube = 4 in.

∴ Surface area of cube = (6×4²) sq. in. = 96 sq. in.

Now, given, length of cuboid = 15 in.

Width of the cuboid = 10 in. & height of the cuboid = 7 in.

∴ Surface area of the cuboid = 2{(15×10)+(15×7)+(10×7)} sq. in.

                                                = 2{150+105+70} sq. in.

                                                = 2{325} sq. in. = 650 sq. in.

Here, we have to find the surface area of the composite figure.

We have to subtract the surface area from both of cube & cuboid, where they are attached.In that case, we have to subtract (4×4) from both.

So, we have to subtract 2(4×4) sq. in. = 32 sq. in.

∴ The surface area of the composite figure = (650+96-32) sq. in.

                                                                        = 714 sq. in.

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The value of f(x) = 3x² - 2x at x = 4 is 40.

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.

Here, the given function;

    f(x) = 3x² - 2x

put the value of x = 4, we get

     f(4) = 3 X 4² - 2 X 4

     f(4) = 3 X 16 - 8

      f(4) = 48 - 8

     f(4) = 40

Thus, the value of f(x) = 3x² - 2x at x = 4 is 40.

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the equations that will have only one solution are:

An equation of the form:

a*x + b = c*x + d

Has one solution only if a ≠ c.

With that in mind, we can see that the equations that will have only one solution are:

19x - 18 = -19x + 18  (option c)

19x + 18 = -19x + 18  (option d)

In the other two cases, the slopes of the linear equations are equal, so these equations have no solutions or infinite solutions.

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Answer:

Mark will use 1.25 pounds of pork.

Step-by-step explanation:

Let b represent the number of pounds of pork and p represent the number of pounds of beef. Since the ratio of beef to pork is 3 to 1, we have b/p = 3/1, which then becomes b = 3p. From this:

[tex]3p + p = 7[/tex]

[tex]4p = 7[/tex]

[tex]p = 1.75[/tex]

[tex]b = 3 \times 1.75 = 5.25[/tex]

Answer:

the answer is d........

The inequality 4(x – 3) + 4 < 10 + 6x is solved as x > -9. Then the variable x is greater than the negative 9. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign.

The inequality equation is given below.

4(x – 3) + 4 < 10 + 6x

Then the steps of solving are given below.

1. The distributive property: 4x – 12 + 4 < 10 + 6x

2. Combine like terms: 4x – 8 < 10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: –2x < 18

5. The division property of inequality: x > –9

Then x is greater than the negative 9.

Then the correct option is B.

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The value of an expression will be equal to -1.

The complete question is given below:-

If the value of w is -5 then find the value of the expression w² + 3w -11.

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

The given expression will be solved as follows:-

E = w² + 3w -11.

E = ( -5 )²  + ( 3 x -5 ) -11

E = 25 - -15 - 11

E = 25 - 26

E = -1

Therefore the value of an expression will be equal to -1.

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Answer:

45/32 or 1.40

Step-by-step explanation:

Answer:

3 9/32 or 105/32

Step-by-step explanation:

2 1/2 = 5/2, 1 3/4 = 7/4

5/2 * 7/4 = 35/8

35/8 * 3/4 = 105/32

105/32 = 3 9/32

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The height of domino number 10 is 56.9 inches.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

The exponential function:-An exponential function is given by:

y = abˣ

where a is the initial value of y at x = 0, y, x are variables and b is the multiplication factor

Let y represent the height of the number x domino

Since the height of the smallest domino no 0 is 3 inches, hence a = 5. b = 100% + 19% = 1.19

y = 10(1.19)ˣ

For x = 10:

y = 10(1.19)¹⁰= 56.9 inches

Therefore the height of domino number 10 is 56.9 inches.

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Answer:

The value of x is 4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

11−2x+6x+5=32

11+−2x+6x+5=32

(−2x+6x)+(11+5)=32

4x+16=32

4x+16=32

Step 2: Subtract 16 from both sides.

4x+16−16=32−16

4x=16

Step 3: Divide both sides by 4.

((4x)/4) = (16/4)

x = 4

Answer:

11-2x+6x=32-5

-2x+6x=27-11

-2x+6x=16

4x÷4=16÷4

x=4

Answer:

D

Step-by-step explanation:

The vertex is at (-2,4), so substituting into vertex form, only C and D match.

Also, the graph opens down, so the coefficient of x² is negative.

This eliminates C, leaving us with D

Step-by-step explanation:

1. let n=2, then, n+2= 2+2=4 so 2^2= 4 and 4^2=16 then 16-4=12 which is an even number

2. let n=4, the. n+3=4+3=7, and 4^2=16 and 7^2=49 then 49-16 =33 which is an odd number

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Answer:

Step-by-step explanation:

A pack of sugar costs £1.25 for 500g. How much for 1kg?

500g = 1/2Kg or 0.5 Kg

so 1.25£ is 0.5Kg (1/2)

1.25 * 2 = 2.50£ is your answer

Answer:

2.5

Step-by-step explanation:

Change 500g into kg

500g=500/1000kg

        =0.5kg

If                  0.5kg cost 1.25

what about 1kg

   = (1*1.25)/0.5

   = 1.25/0.5

   =2.5

The LCM of the given numbers have been determined.

LCM stands for Least Common Multiple .

For two numbers , LCM is the number that is the smallest number of which they both are a factor.

It is asked to determine

LCM of 6 and 9

6 = { 6 , 12 , 18 , 24 , 30 , 36 , 42 .....}

9 = { 9 , 18 ,27 .....}

The LCM of 6 , 9 is 18

LCM of 8 and 12

8 = { 8,16,24,32....}

12 = {12 , 24 ,36....}

The LCM of 8 and 12 is 24

LCM of 4 , 6 and 8

4 = {4 , 8 , 12 , 16 , 20,24,28 ....}

6 = { 6 ,12 ,18,24......}

8 = {8 , 16,24 .....}

The LCM of 4,6 and 8  is 24

The LCM of 6 and 15 is 30  

The LCM of 20 and 30 is  60

The LCM of 25,30 and 75 is 150

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Answer:

(10+4/2, 6+9/2)

(7, 7.5)

The Midpoint is (7, 7.5)

Step-by-step explanation:

I just added the x values and divided them by 2 and then the same for the y values.

Answer:

(7,7.5)

Step-by-step explanation:

midpoint formula:

(X1,X2) divided by two and (Y1,Y2) also divided by two.
so you get

10+4/2 and 6+9/2

Add it all up you get

14/2 and 15/2

divide it:

(7,7.5)

Answer:

if you're supposed to be solving for x then the top one is x=-y+3 and the bottom is x=-y+5

Answer:

y = (5/3)x + 4

Step-by-step explanation:

The general equation for slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. Since you have been given both of these values, you can plug them into the formula to find your answer.

slope (m) = 5/3

y-intercept (b) = 4

y = mx + b

y = (5/3)x + 4

Answer:

No

Step-by-step explanation:

The constant of proportionality is k = y/x. In this case, k is 5. When you multiply k which is 5 with the x value you should get the y value. You will see that 2 X 5  = 10, 3 X 5 = 15, and 5 X 5  = 25 but 4X 5 is not equal to 24. This means the ordered pair (4, 24) does not lie on the straight line that is formed where all the other ordered pairs (2,10), (3,15), and (5,25) lie.

For a proportional relationship in a table, the k is constant for all the ordered pair x and y values. All the ordered pairs in the table should also lie on the same straight line.

So the answer is no.

-2/3.

That is the slope because this equation is written in slope-intercept form (y=mx+b) where...

m= slope

b = y-intercept

Answer:

4762

Step-by-step explanation:

0.21g x 10,000= 2100

0.21 x 5,000= 1050

0.21 x 4,000= 840

0.21 x 4700 =  987

0.21 x 4760 = 999.6

0.21 x 4762= 1000.02

( how much it's made from x the quantity = the grams or kg)

Answer:

$24

Step-by-step explanation:

Cranberries needed: 1 pound

Cost of 1 pound = $4

Almonds needed: 4 pound

Cost of 1 pound = $5

4 x 5 = $20

20 + 4 = $24

Answer:

4.80

Step-by-step explanation:

The equivalent expression to 7^13/7^7 would be 7^6.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We have given an expression as  7^13/7^7

The equivalent expression;

[tex]\dfrac{7^{13}}{7^7} \\\\7^{13-7}\\\\7^6[/tex]

Hence, The equivalent expression to 7^13/7^7 would be 7^6.

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Answer:

-3

Step-by-step explanation:

The points (3,-4) and (1,2) lie on the line.

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

Using the continuity concept, as the value of the function has to be equal to the limit, it is found that the value of k is of k = -4.

A function is said to be continuous at x = a if, and only if:

[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex]

In this problem, we have to check at x = -2, hence:

[tex]\lim_{x \rightarrow -2} f(x) = f(-2)[/tex]

[tex]k = \lim_{x \rightarrow -2} f(x)[/tex]

For the limit, we have to check the lateral conditions, hence:

[tex]\lim_{x \rightarrow -2} f(x) = \lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x - 2)(x + 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 -2 = -4[/tex]

Hence, from the continuity condition, k = -4.

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Step-by-step explanation:

Hi there!

According to the question;

The gradient of line is 1/2 and passes through the point (4,-2).

Since, It has one point and gradient we use one point formula to find the equation of the line.

Note:

One point formula: (y-y1) = m (x-x1)

(4,-2) = (x1,y1)

So, using this formula we get;

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

Multiply both sides by 2.

2(y+2) = (1/2)*2(x-4)

2y+4 = x-4

Take 2y+4 in right side

0 = x-4 - (2y+4)

Therefore, x-2y-8 = 0 is the required equation.

Hope it helps!

Hi there!

We're given the following information:

With this information, we can go ahead and plug the data into the point slope equation: y - y₁ = m(x - x₁).

Plug in 1/2 for m, and (4,2) for x1 and y1:

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

[tex]\sf{y-(-2)=\dfrac{1}{2}(x-4)}[/tex]

[tex]\sf{y+2=\dfrac{1}{2}(x-4)}[/tex]

[tex]\sf{y+2=\dfrac{1}{2}x-2}\\\sf{y=\dfrac{1}{2}x-2-2}\\\\\sf{y=\dfrac{1}{2}x-4}[/tex]

Hence, y = 1/2x - 4.

I hope that helps! :)

If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)

Binary operators are operators that involves two functions, there are four binary operators: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division. First, we determine the domains of the functions f(x) and g(x):

f(x):

Domain - [-3, 3]

g(x):

Domain - (- ∞, + ∞)

If we divide f(x) by g(x), then we must take g(x) = 0 into account, since it leads to indetermination. In this case, x = 1/3. Then, the domain of the resulting function:

(f/g)(x):

Domain - [-3, 1/3) ∪ (1/3, 3]

If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)

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