Constant of Proportionality PROPORTIONALITY OF EACH GRAPH. NOT ALL CHOICES WU BE USED. 1/2 3 4 1 I 2 2. 1/4

The probability that you win a prize is 0.00003797372

From the question, we have the following parameters:

Sample Space = 1 to 22

This means that

Sample size, n = 22 i.e. the count of numbers from 1 to 22

The count of numbers to be drawn is 5

So, the individual probabilities are

P(1) = 5/22

P(2) = 4/21

P(3) = 3/20

P(4) = 2/19

P(5) = 1/18

The probability of winning is the product of the above

So, we have

p = 5/22 * 4/21 * 3/20 * 2/19 * 1/18

Evaluate

p = 0.00003797372

Hence, the probability is 0.00003797372

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The answer for 2+22+222+2222+22222 is 24690

Answer:

22222222222

Step-by-step explanation:

222+22+2222+22²22

it's 2.84

step by step:

Start by setting it up with the divisor 33 on the left side and the dividend 94 on the right side.

The divisor 33 goes into the first digit of the dividend 9, 0 time(s). Therefore, put 0 on top.

Multiply the divisor by the result in the previous step (33 x 0 = 0) and write that answer below the dividend.

Subtract the result in the previous step from the first digit of the dividend (9 - 0 = 9) and write the answer below.

Move down the 2nd digit of the dividend 4

The divisor 33 goes into the bottom number 94, 2 time(s). Therefore, put 2 on top.

Multiply the divisor by the result in the previous step (33 x 2 = 66) and write that answer at the bottom.

Subtract the result in the previous step from the number written above it. (94 - 66 = 28) and write the answer at the bottom.

it's a repeating decimal so make sure to add a line on top of the last to digits to represent that it is repeating.

Answer:

a)62

b)6 months

Step-by-step explanation:

a) if he pays $6 every month then you would times $6 by 5 to find out how much he paid off which is 30 so you would add that to the current amount therefore $30+$32=$62

b) You would do $32 divided by 6 to find out how much hit would take to pay off which is 5 but there is 2 remaining so he can pay that off the next month, so it takes 6 months

Equation of the line through the given pair of points.(-7,-1) and (-2,-8) is

5y ++7x = -54

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line. Any line's equation can be used to determine whether a given point is on the line or not. A linear equation with a degree of one is the equation for a line.

general equation of line is

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

here [tex]x_{1} is -7 \\ y_{1} is -1[/tex]

y +1= [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex](x+7)

y +1= [tex]\frac{-7 }{5 }[/tex](x+7)

5y +5 = -7x -49

5y ++7x = -54

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a. The rate of change in length of baby grace is 0.75.

b. The linear equation for Baby Grace growth rate in point slope form is y - 20 = 0.75(x - 4)

a. The slope of the line for baby Claire growth is 0.8.

b. Baby girl Claire growth rate is faster than baby girl Grace growth rate.

Let's solve for the growth chart of baby grace.

Therefore,

a.

The rate of change in length of baby Grace can be found as follows:

rate of change = y₂ - y₁ / x₂ - x₁

Hence, using (4, 20)(6, 21.5)

rate of change = 21.5 - 20 / 6 - 4

rate of change = 1.5 / 2

rate of change = 0.75

b . The linear equation in point slope form can be found as follows;

y - y₁ = m (x - x₁)

where

Therefore,

y - 20 = 0.75(x - 4)

Let's tackle the growth chart for baby Claire,

a.

slope of the line = y₂ - y₁ / x₂ - x₁

Using (4, 22)(14, 30)

slope of the line = 30 - 22 / 14 - 4

slope of the line = 8 / 10

slope of the line = 4 / 5 = 0.8

b.

Therefore, Baby Claire growth rate is faster than baby Grace.

This is because bay Claire growth rate is 0.8 and baby Grace is 0.75.

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The characteristics that describe the following data-set are given as follows:

Categorical and bivariate.

First, we classify the variable as either numerical or categorical, as follows:

In the context of this problem, the variables are as follows:

Thus the variable is categorical.

Additionally, there are two variables in this problem, the ones stated above, the type of service and the age, hence the data set is classified as bivariate.

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The principal with the given simple interest, rate of interest and time period is $4550.

Given that, interest = $637, rate of interest = 7% and time period = 2 years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

We know that, simple interest = (P×R×T)/100

Put simple interest = $637, R=7% and T=2 years, we get

637 = (P × 7 × 2)/100

⇒ 14P=63700

⇒ P=63700/14

⇒ P= $4550

Therefore, the principal with the given simple interest, rate of interest and time period is $4550.

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Answer: 51

Step-by-step explanation:

8.50 x 6 = 51

Answer:

$51

Step-by-step explanation:

Since it's $8.50 per hour. Their asking you how many per 6 hours.

You multiply 8.50 x 6.

8.50 x 6= 51.

Answer:

here,

2x=76 (because of adjacent angle)

76/2=x

x=38

again,

x+y=180(because of straight angle)

y=180-38

y=142

We have that the Decrease of £16870 by 3%  is mathematically given as

P=168193.9=>168193.90 2dp

Arithmetic

Question Parameters:

Decrease £16870 by 3% Give your answer rounded to 2 DP.

Generally the equation for the 3%  of 16870  is mathematically given as

X=0.03*16870

X=506.1

Therefore Decrease £16870 by 3% we have

16870  - 506.1

P=168193.9

Answer:

= £16363.9

Step-by-step explanation:

- Decrease is a reduction and can be done only by subtraction in two ways;

[tex] = (100 - 3)\% \\ = 97\%[/tex]

- Then multiply the result to the value being decreased;

[tex] = \frac{97}{100} \times 16870 \\ \\ = 16363.9 \: \: euros[/tex]

[tex] = \frac{3}{100} \times 16870 \\ \\ = 506.1 [/tex]

- Then reduce the original by the result:

[tex] = 16870 - 506.1 \\ = 16363.9 \: euros[/tex]

Answer: 72 degrees

Step-by-step explanation: We know that angle DHG and angle EHF are congruent due to the vertical angles theorem. Since these two angle measures are congruent, this also means that the expression 6(x-2) is congruent to 3x+30. To find the angle measure of DHG, we need to find x. We can set these two expressions equal to each other and solve for x.

6(x-2) = 3x+30

6x-12 = 3x + 30

-3x -3x

3x-12=30

+12 +12

3x=42

~divide by 3 on both sides~

x = 14

Now that we know our x variable, we can substitute 14 into the expression for angle DHG.

6(14-2)

6(12)

72.

Answer:

∠DHG = 72°

Step-by-step explanation:

As ∠DHG and ∠EHF are vertical angles, they are congruent.

What are vertical angles?

Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).

Equation:

∠DHG = ∠EHF

[6(x - 2)] = (3x + 30)

Step 1: Distribute 6 through the parentheses.

[tex]\implies 6(x) + 6(-2) = 3x + 30[/tex]

[tex]\implies 6x - 12 = 3x + 30[/tex]

Step 2: Subtract 3x from both sides.

[tex]\implies 6x - 3x - 12 = 30[/tex]

[tex]\implies 3x - 12 = 30[/tex]

Step 3: Add 12 to both sides.

[tex]\implies 3x - 12 + 12 = 30 + 12[/tex]

[tex]\implies 3x = 42[/tex]

Step 4: Divide both sides by 3.

[tex]\implies \dfrac{3x}{3} = \dfrac{42}{3}[/tex]

[tex]\implies \boxed{x = 14}[/tex]

Step 5: Substitute the value of x into ∠DHG to find its measure.

[tex]\implies \angle DHG = 6(14 - 2)[/tex]

[tex]\implies \angle DHG = 6(12)[/tex]

[tex]\implies \angle DHG = \boxed{72^\circ}[/tex]

Therefore, the measure of ∠DHG is 72°.

Corresponding parts of congruent triangles are congruent.

What do you mean by congruency?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid movements like translation, rotation, and reflection. This indicates that one item may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a sheet of paper, they are congruent. The paper may be turned over.

Corresponding parts of congruent triangles are congruent.

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Answer:

The correct option is B.

The value of the function n(x) = -1 -x + 4 when x = -2,0, and 5 are  respectively.

Function:

A function is defined as a relationship between a set of inputs having one output each.

It can be represented as f(x).

Given,

Here we have the function

n(x) = -1 -x + 4

And we need to find the value of the function when x takes the values -2, 0 and 5.

To solve this one, then we have to put the value of x on the function and then we have to simplify it in order to get the value of the function.

For that first we have to put the value of x = -2, then we get,

n(-2) = -1 - (-2) + 4

n(-2) = -1 + 2 + 4

n(-2) = -1 +6

n(-2) = 5

Now we have to apply the value of x as 0, then we get the value of function as,

n(0) = -1 - 0 + 4

n(0) = -1 + 4

n(0) = 3

Finally we gave to apply the value of x as 5, then we get the value of n(5) as,

n(5) = -1 - 5 + 4

n(5) = -6 + 4

n(5) = -2

Therefore, the resulting values are 5, 3 and -2.

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Answer:

1) 5x-8

2) 2x(4x+3)  

Step-by-step explanation:

The given inequality is true as the value on the right side of the inequality is less than the value on the left side.

What is an equality?

Inequality is a relation which makes a comparison which is non-equal between two numbers or other mathematical .

We are given an inequality 15-700<1000

The left hand side of the inequality on solving becomes,

15-700= -685

Hence the inequality becomes -685<1000

as  a negative value is always less than that of a positive values

Hence 15-700<1000

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Step-by-step explanation:

remember, when 2 signs collide (like a mathematical operation and the sign of an operand of that operation), the following is always true (for additions/subtractions and multiplications/divisions) :

+ + = +

+ - = -

- + = -

- - = +

and don't forget : when a number or term is positive, we usually don't write the sign. only the mathematical operation.

1. 2 - 3 = -1

2. 11 - 10 = 1

3. 3 - 5 = -2

4. 22 - 21 = 1

5. -8 + 44 = 36

6. -12 + 6 + 3 = -3

7. 16 + 12 = 28

8. -36 + 36 = 0

9. -4 × 10 = -40

10. -1 × -1 = 1

11. 7 × -7 = -49

12. -4 / 4 = -1

13. -7 × -5 = 35

14. -10 × 8 = -80

15. -2 × -7 = 14

The plan that cannot be used to prove that the two triangles are congruent based in the given information is: b. ASA.

The following theorems can be used to prove that two triangles are congruent to each other:

The two triangles only have a pair of corresponding congruent angles, while all three corresponding sides are shown to be congruent to each other.

This means that ASA which requires two pairs of congruent angles, cannot be used to prove that both triangles are congruent.

The answer is: b. ASA.

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From the equation 3x + 59 = 120, the unit cost of the shirts is $20.33.

An equation is a mathematical statement used to equate two mathematical expressions.

To demonstrate equality, equations use the equation symbol (=).

The total amount spent on new clothes = $120

The number of shirts bought = 3

The cost of the pair of pants bought = $59

Equation of the situation is 3x + 59 = 120,where x = the unit cost of the shirts.

3x + 59 = 120

Subtract 59 from both sides:

= 3x + 59 - 59 = 120 - 59

Simplify both equations:

3x = 61

Divide both sides by 3:

3x/3 = 61/3

x = 20.33

Thus, we can conclude that the equation for the new clothes Jennifer bought at the mall shows that each shirt costs $20.33.

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The time taken to complete 5 questions is (option b) 22 minutes, 30 seconds

Given,

The number of questions = 2

Time taken to complete 2 questions = 9 minutes

Now,

The number of questions = 5

We have to find the time taken to complete 5 questions:

We can consider ratio here:

That is,

Number of questions : Time taken to complete

So,

2 : 9 and 5 : x

Lets equate:

2 : 9 = 5 : x

That is,

2x = 5 × 9

Now, divide 2 on both sides:

2x/2 = (5 × 9) / 2

Here,

x = 45/2

Then,

x = 22.5

Converting this into minutes, we get 22 minutes, 30 seconds.

That is,

The time taken to complete 5 questions is (option b) 22 minutes, 30 seconds

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The order of the scale from smallest to the largest is:

The smallest = 1 inch to 3 yards

The middle : 1 inch to 1.1 yards

The largest : 1 inch to 1 yard

A scale drawing is either a larger or smaller version of a diagram.  A scale factor provides information on the unit of conversion between the original image and the scale drawing.   A scale factor is the ratio of the length of the scale drawing to the length of the actual drawing.

The first step is to convert the given scale factors to the same units of measurement.

All of the measurements would be converted to yards

1 feet = 3 yards

1 inch to 3 yards

1.1 yards = 1 meter

1 inch to 1.1 yards

1 inch to 1 yard

The smallest = 1 inch to 3 yards

The next : 1 inch to 1.1 yards

The largest : 1 inch to 1 yard

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The slope of the given line a is found as 4.

For the given question;

The graph of the given line a is given.

Select any two points from the graph lying on the line.

(x, y) = (1, 1)

(x, y) = (2,5)

Thus, the slope will be;

Slope = m = (y - y)/(x - x)

m = (5 - 1)/(2 - 1)

m = 4/1

m = 4

Thus, the slope of the given line a is found as 4.

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Answer:I think you should multiply by who many

Step-by-step explanation:

so 2.19x and 2.99x

THE GCF IN THE EXPRESSION IS 5 MEANING WE ARE GOING TO DIVIDE EACH AND EVERY TERM BY 5 .

[tex] = 5(3w + 13)[/tex]

ATTACHED IS THE SOLUTION

There are two lines a and b, Which are parallel lines and a line that cut the parallel lines a and b is transversal t.

1. Angle 8 is 86°

2. Angle 9 is 94° and

3. Angle 10 is 86°.

Given that,

There are two lines a and b, Which are parallel lines and a line that cut the parallel lines a and b is transversal t.

The interior angles are 7,8,9 and 10.

The angle 7 and 8 are consecutive angles and angle 7= 94°.

The angle 8 and 10 are alternative angles.

We have to find the angles 8,9 and 10.

We take,

The angle 7 and 8 are consecutive angles and angle 7= 94°.

Consecutive angles condition is Sum of the pair of consecutive angles is equal to 180°.

Now,

∠7+∠8=180°

94°+∠8=180°

∠8=180°-94°

∠8=86°

We got angle 8 as 86°.

Now, we take

The angle 8 and 10 are alternative angles.

Alternative angles condition is The pair of alternative angles are always equal if the two lines are parallel lines.

Now,

∠8=∠10

86°=∠10

∠10=86°

We got angle 10 as 86°.

Then we can say that the angle 7 and 9 are alternative angles.

Then,

∠7=∠9

94°=∠9

∠9=94°

We got angle 9 as 94°.

Therefore, The angle 7 is 94°, ∠8 is 86°, ∠9 is 94° and ∠10 is 86°.

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The length of the sides (8in, 15 in, z) into the Pythagorean Theorem. Then, find the length of the missing side z.

z = 17

This is further explained below.

Generally, In the field of mathematics, the Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic connection in Euclidean geometry among three sides of a right triangle.

Pythagoras is credited with developing this theorem. It indicates that the total of the areas of the squares on the other two sides is equal to the area of the square whose side is the hypotenuse.

This signifies that the size of the square whose side is the hypotenuse is equal to that amount.

In conclusion,

a² + b² = c²

8² + 15² = z²

64 + 225 = 289

z² = 289

z = 17

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