Given the formula for the nth term, state the first 5 terms of each sequence.t1= 800, tn= -0.25tn-1

The point that best represents 1/3 is point M .

The number line ranges from 0 to 0.5 with 10 divi

The slope of the given equation is 0.075 and  y-intercept is 0.125

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

First writing the given equation in standard slope intercept form :

y = mx + c.........(1)

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function

8y = 0.2(3x - 5)

8y = 0.6x - 1

y = 0.6/8x - 1/8

y = 0.075x - 0.125

Now, comparing it with equation (1) we get :

m = 0.075 and c = - 0.125

hence the slope of the given equation is 0.075 and  y-intercept is 0.125

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To find z, consider the right-angled triangle at the botton in the diagram showm

Let the common base of both triangles be m

To find y:

To find x:

Input data

75% = 0.75

format

y = kx

Procedure

The k factor would be equal to 0.25

The answer would be

Problem

Solution

Let x = age, W= weight the two variables of interest

We have the following probabilities given:

P(x<37) =0.142

P(W< 2500) = 0.051

P(x <37 AND W<2500)= 0.031

And we want the following probability and we can use the total probability rule:

P(x < 37 OR W< 2500) = P(x<37) +P(W< 2500) -P(x<37 AND W<2500)

If we replace we got:

P(x < 37 OR W< 2500)= 0.142+ 0.051- 0.031= 0.162

The value of the composite function is determined as: (g o f)(5) = 6.

To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.

Given the following:

f(x) = x² - 6x + 2

g(x) = -2x

Therefore:

(g o f)(5) = g(f(5))

Find f(5):

f(5) = (5)² - 6(5) + 2

f(5) = 25 - 30 + 2

f(5) = -3

Find g(f(5)) by substituting x = -3 into g(x) = -2x:

g(f(5)) = -2(-3)

g(f(5)) = 6

Therefore, (g o f)(5) = 6.

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Let be "x" the amount of money (in dollars) you would save with the discount.

By definition, a percent can be converted to a Decimal number by dividing it by 100. Then, since the cake store is having 25% off sale on all cakes, this can be written as:

According to the information given in the exercise, the regular price of the cake you want is $9. Based on this, you can set up the following expression for price of the cake with the discount (in dollars):

Evaluating, you get:

Knowing this value, you can set up that:

Finally, evaluating, you get:

The answer is: You would save $2.25 with the discount.

Sue's total pay for the year given the salary, bonus and share of profit is  £38,110.

Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.

Salary for the year = monthly salary x number of months in a year

£1410 x 12 = £16,920

The next step is to determine the profit last year

Profit = total revenue - total cost

£549,000 - £473,500 = £75,500

Now determine the share of profit that Sue would earn.

Share of profit = 26% x  £75,500

0.26 x  £75,500 = £19,630

Now determine the total bonus she would earn : 4 x £390 = £1560

Total salary = £1560 +  £19,630 +  £16,920 = £38,110

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0.12

Probability is the likelihood or chance that an event will occur. It ca be expressed as:

where:

n(E) is the expected event

n(S) is the total sample space

If Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B, the percentage amount of egg bought from B will be 25% (100-75)

n(S) = 25%

If 3% of the eggs from B are green, hence n(E) = 3%

Determine the required probability

Pr(egg is from farm B) = n(E)/n(S)

Pr(egg is from farm B) = 3/25 = 0.12

Hence the probability that the egg is from farm B is 0.12

Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as

an = a1 + d(n - 1)

where

a1 is the first term of the sequence

n = number of terms

d = common difference

In this case, n would be t(number of years

From the information given,

a1 = 3

Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24

We have

24 = 3 + d(7 - 1)

24 = 3 + 6d

6d = 24 - 3 = 21

d = 21/6 = 3.5

The linear model would be

an = 3 + 3.5(t - 1)

Substituting H for an, the linear model is

H = 3 + 3.5(t - 1)

At 2020, t = 11

H = 3 + 3.5(11 - 1) = 3 + 35

H = 38

The resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].

Given are the three different matrices as -

A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]

C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]

We can solve the given expressions as follows.

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Therefore, the resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

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Percentage of the wheat crop planted = 128/ 545 x 100

= 12800/545

= 23.4 percent

The distance, x, from one corner to another corner three corners away is 4. 70cm

The distance, y, from one corner to another corner two corners away is 4. 07cm

It is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees

Also note that the have the trigonometric identities;

Using the cosine identity, we have;

sin θ = adjacent/ hypotenuse

substitute the values

cos 60 = 2.35/x

cross multiply

x = 2. 35/cos 60

x = 2. 35/ 0. 5

x = 4. 7 cm

Then, we have,

sin 60 = y/ 4. 7

y = sin 60 × 4.7

y = 0. 8660 × 4. 7

y = 4. 07cm

Hence, the values are 4. 7cm and 4. 07cm

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An envelope is rectangular in shape.

Given the width = 15cm, and diagonal = 17cm

Let h represent the tall length of the envelope

Applying Pythagoras theorem, we have

The envelope is 8cm tall

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

triangle diagram

Step 02:

angles:

we must analyze the diagram to find the solution

angle 1:

angle 1 = 180° - 155° = 25°

angle 2:

angle 2 = angle 1 = 25°

angle 3:

angle 3 = 180° - 25° - 25° = 130°

angle 4:

angle 4 = 155°

angle 5:

angle 5 = 180° - 25° = 155°

That is the full solution.

we have that

Divide $90 by the number of shares

so

90/9=$10

the answer is $10

By solving the equation 5x + 12 = -2, the value of x in is -2.8

Solution

5x = -2-12

5x = -14

We get -14

x = -14 ÷ 5

x = -2.8

Hence, by solving the equation 5x + 12 = -2, the value of x in is -2.8

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The amount for social security for all 3 months will $930 and the contribution for Medicare will be $217.5.

Given that the salary exists paid in US dollars, we can consider that Renae Walters falls under the social security and Medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for Medicare.

Social security contribution = Social security tax rate × Income earned

January for example Social Security = 0.062 × $15,000 = $930    

Medicare contribution = Medicare tax rate × Income earned

January for example Medicare = 0.0145 × $15,000= $217.5

The above method will apply through the months without changes.

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Given the following set of data:

8 12 15 9 10 12 12 18 14 15 10 11 12 9 17

We will find the range of the data.

We need to find the maximum and the minimum

The maximum = 18

The minimum = 8

So, the range = maximum - minimum = 18 - 8 = 10

So, the answer will be The range = 10

Answer:

379,001.

Explanation:

The population of the city grows by 4.25%.

This is a constant factor and models an exponential function.

An exponential population function is of the form:

From the given problem:

This then gives us:

The population after 12 years will be approximately 379,001.

1) Let's sketch this out to better grasp it

2) We can see that there are two legs and two angles (one of them is missing) so let's solve it using the Law of Sines:

The statement that reflects the running rates is Pepe ran 9/8  mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.

Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.

Speed = distance / time

Speed if Paul ran 1/5 mile in 4/15 hour

Speed = 1/5 ÷ 4/15

1/5 x 15/4 = 3/4 miles per hour

Speed if Pepe ran 8/10 mile in 1/4 of an hour

Speed = 8/10 ÷ 1/4

8/10 x 4 = 16/5 = 3 1/5 mile per hour

Difference in speeds =

[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]

Speed if Paul ran 4/15 mile in 1/5 hour

Speed = 4/15 ÷ 1/5

4/15 x 5 = 4/3 = 1 1/3 miles per hour

Speed if Pepe ran 1/4 mile in of 8/10 an hour

Speed = 1/4 ÷ 8/10

1/4 x 10/8 = 5 / 16

Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]

Speed if Paul ran 1/3 mile in 19/24 hour

Speed = 1/3 ÷ 19 / 24

1/3 x 24/19 = 8/19 miles per hour

Speed if Pepe ran 1/2 mile in of 9/8 an hour

Speed = 1/2  ÷ 9/8

1/2 x 8/9 = 4/9 mile per hour

Difference = 4/9 - 8/19 = 4/171

Speed if Pepe ran 9/8  mile in 1/2 hour

Speed = 9/8 ÷ 1/2

9/8 x 2 = 2 1/4  miles per hour

Speed if Paul ran 19 / 24 mile in of 1/3 an hour

Speed =  19 / 24  ÷ 1/3

19 / 24 x 3 = 2 3/8 miles per hour

Difference =

[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]

[tex]\frac{3 - 2}{8}[/tex] =  [tex]\frac{1}{8}[/tex] miles per hour

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Comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :

Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.

Contrast is range is different:

Range = { 3, 5, 7, 9} for domain {1,2,3,4}

Range = set of all real numbers for domain all real numbers.

As given in the question,

Given function for the graphs are:

y =2x+1

Different domains

Domain ={1,2,3,4}

Domain =All real numbers

Compare with y=mx +c

Slope m =2

For y-intercept put x=0

y=2(0) +1

 =1

For x-intercept put y=0

0 =2x+1

⇒x=-1/2

Contrast:

For domain ={1,2,3,4}

Range is :

y = 2(1)+1

  =3

y=2(2)+1

 =5

y=2(3) +1

 =7

y=2(4)+1

 =9

Range ={ 3, 5, 7,9}

For domain= all real numbers

Range = set of all real numbers

Therefore, comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :

Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.

Contrast is range is different:

Range = { 3, 5, 7, 9} for domain {1,2,3,4}

Range = set of all real numbers for domain all real numbers.

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Answer:

-2 and -10

Explanation:

There are two numbers at a distance of 4 units from -6, the number that is 4 units to the right and the number that is 4 units to the left.

So, the number that is 4 units to the right is equal to

-6 + 4 = -2

And the number that is 4 units to the left is equal to

-6 - 4 = -10

Therefore, the numbers are -2 and -10 and they are represented as

∠A + ∠B + ∠C = 180°

reason : Sum of all angle of triangle is 180°

72° + 86° + ∠C = 180°

158° + ∠C = 180°

∠C = 180° - 158°

∠C = 22°

hence the value of ∠3 is 22°

Now ,

∠3 =∠4

reason : Being vertically opposite angle

4 = 22°

hence the value of ∠4 is 22°

Again ,

∠C + ∠D + ∠E = 180°

reason : Sum of all angle of triangle is 180°

22° + ∠D + 70° = 180°

92° + ∠D = 180°

∠D = 180° - 92°

∠D = 88°

hence the value of ∠5 is 88°..

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hope it helps ....☘✨

To prove that p || r, we will complete the data in the given table

ANSWER

Quadrant II

EXPLANATION

• All angles between 0° and 90° are in the first quadrant.

• All angles between 90° and 180° are in the second quadrant.

• All angles between 180° and 270° are in the third quadrant.

• All angles between 270° and 360° are in the fourth quadrant.

115° is an angle measure that is between 90° and 180°. Therefore its terminal end is in the second quadrant.

GIven the table above :

We have that

x y

2 8

4 4

6 0

8 4

The table represents a Non - Linear Function

Reason: It is because there is no constant ratio or proportion between x and y.