5. Find the sum of the first ten terms of each arithmetic series. (2 marks each = 4 marks)
a. 2+8+14+...
b. 45 +39 +33 +...

On solving the provided question, we got by the help of Slope formula - [tex]= 5x - y + 5 = 0[/tex]

A line's slope can be calculated as the ratio of how much y rises when x rises by a specific amount. A line's slope, or how much y increases as x increases, is indicated by the word "slope." Along the straight line, the slope is constant (equal) everywhere.

From the figure we got that,

X1 = 0, Y1 = 5

X2 = -1, Y2 = 0

(0,5) and (-1,0)

By the of slope formula

[tex]\frac{y - y1}{x - x1} = (\frac{y2 - y2}{x2 - x1} )(\frac{x - x1}{y - y1} )[/tex]

[tex]{y - 5} = (\frac{0-5}{-1-0} )({x - 0 )\\\\\\[/tex]

[tex]= > 5x - y + 5 = 0[/tex]

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The area of the given circle is 95 cm².

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, we know that the diameter of the circle is 11 cm.

Radius = Diameter/2

11/2

5.5 cm

Area of circle: πr²

3.14(5.5)²

3.14*30.25

94.985

Rounding off: 95 cm²

Therefore, the area of the given circle is 95 cm².

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Answer:

20:50 or 2:5

Step-by-step explanation:

30 dogs

20 cats

50 total animals

Part to whole relationship:

20:50

Answer:

smaller = 25, bigger = 65

Step-by-step explanation:

x = smaller

y = bigger

2x + 15 + x = 90

3x + 15 = 90

3x = 75

x = 25

y + x = 90

y + 25 = 90

y = 65

Answer:

Your answer is [tex]x = -1[/tex] and [tex]y = -2[/tex]

Step-by-step explanation:

(attached)

The function r ( m ) $12 more than the salary of someone who has worked for m months.

What is function?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x.

If we have S(m) represents salary after m months i.e. y=S(m) will be the graph of salary Corresponding to the number of months m.

So, we have [tex]m+12 \geqslant 12$,[/tex]

[tex]$\Rightarrow S(m+12)$[/tex] will give us the value of Salary after 12 months of the Job.

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The mean weight of 7 grapefruits will be 7 pounds and the standard deviation will be 0.84 pounds.

The mean weight of R will be 3 pounds and the standard deviation will be 0.36 pounds.

The mean weight of Q will be 4 pounds and the standard deviation will be 0.48 pounds.

a. The mean and standard deviation of 7 grapefruits will be 7 times the mean and standard deviation of a single grapefruit, respectively.

b. If G represents the weight of a single grapefruit, then

R = G + G + G

= 3G.

The mean and standard deviation of R will therefore be 3 times the mean and standard deviation of a single grapefruit, respectively.

c. If T represents the total weight of all 7 grapefruits, then

Q = T - R

= 7G - 3G

= 4G.

The mean and standard deviation of Q will be 4 times the mean and standard deviation of a single grapefruit, respectively.

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The number 1.1 * 10⁴ in standard form is 11000

From the question, we have the following parameters that can be used in our computation:

Number = 1.1\times 10^{4}1.1×104

Rewrite the given number properly

So, we have the following representation

Number = 1.1 * 10⁴

Solving further, we need to apply the law of indices to expand the exponents

Using the above as a guide, we have the following:

Number = 1.1 * 10 * 10 * 10 * 10

Evaluate the product of the 10's

So, we have the following representation

Number = 1.1 * 10000

Evaluate the products of the 1.1 and 10's

So, we have the following representation

Number = 11000

Hence, the number is 11000

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Answer:

16

Step-by-step explanation:

AB = 20 - 12 = 8

BC = 8 : 2 = 4

CD = 4 + 12 = 16

Answer:

CD = 16

Step-by-step explanation:

Check the image for the steps

Step-by-step explanation:

always remember Pythagoras for right-angled triangles (90°) :

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.

so, in our case

ramp² = 11² + 60² = 121 + 3600 = 3721

ramp = sqrt(3721) = 61 ft

Answer:

61 feet

Step-by-step explanation:

Because the triangle is a right triangle we can use the Pythagorean theorem to solve for the length of the ramp.

The Pythagorean theorem is a² + b² = c²

Where, a and b = leg lengths and c = hypotenuse (longest side)

Here, the length of the ramp represents the hypotenuse as it is the longest side. We are also given the length of the legs. The lengths being 60 ft and 11 ft.

This means that a and b = 11 and 60

We can plug these lengths in and then solve for c or the length of the ramp

a² + b² = c²

==> plug in a = 11 and b = 60

11² + 60² = c²

==> simplify exponents

121 + 3600 = c²

==> add 121 and 3600

3721 = c²

==> take the square root of both sides

61 = c

So the length of the ramp is 61 feet

Your first step of simplifying is to distribute the "–" or "–1" in front of the second set of parentheses through that second set of parentheses.  The –1 must be distributed to every term in the second set:

    [tex]\begin{aligned}(4x^2-5x)-(4x^2-4x-8)&=(4x^2-5x)\boldsymbol{{}-1}(4x^2-4x-8)\\[0.5em]&=4x^2-5x\boldsymbol{{}-1(4x^2)-1(-4x)-1(-8)}\\[0.5em]&=4x^2-5x\boldsymbol{{}-4x^2+4x+8}\\[0.5em]&=-x+8\\\end{aligned}[/tex]

That's what changes the sign on every term in the second set of parentheses, making that –8 become +8.

The value of the exponent illustrated as 27^1/3 is 3.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this situation, it should be noted that 27^1/3 simply means the cube root of 27. This will give a value of 3.

Check: 3 × 3 × 3 = 27.

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Answer:

The function rule for g(x) can be obtained by performing the transformations described on the function f(x) = -6x.

First, we need to stretch the graph of f(x) vertically by a factor of 7. This means that the y-values of the points on the graph of g(x) will be 7 times the y-values of the points on the graph of f(x). We can achieve this by multiplying the y-values of the function f(x) by 7.

Next, we need to reflect the graph of g(x) in the x-axis. This means that the y-values of the points on the graph of g(x) will be the negative of the y-values of the points on the graph of f(x). We can achieve this by multiplying the y-values of the function f(x) by -1.

Applying these transformations to the function f(x) = -6x, we get the function rule for g(x) as follows:

g(x) = (-1) * (7) * (-6x)

= (-1) * (-42x)

= 42x

Therefore, the function rule for g(x) is g(x) = 42x.

Therefore the solution of this question is ratio length =  every 1 inch of toy car represents 1.5 feet of actual car

In mathematics, a ratio shows how two numbers are multiplied together. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.

Here,

A toy Jeep measures 12 1/2 inches.

Before calculating the ratio, let's first convert each size into the same unit of measure and decimal points:

=>12 ½ = 25/2  

=> 12.5 inches;

=> 18 ¾ = 75/4

=> 18.75 feet .

The actual length of a jeep is 18.75 feet.

The ratio can now be determined by converting feet to inches.

1 inch of a toy car equals 1.5 feet of an actual car because

=> 1 foot = 12 inches

=>  12.5 inches : 225 inches

 => 225 / 12.5

=> 18 inches

Therefore, every 1 inch of toy car represents 1.5 feet of actual car.

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Jamal's estimate of the distance across the gorge is 1424.56 ft

What is Pythagorean Theorem ?

The Pythagorean Theorem is a well-known geometric principle that states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equal the total of the squares on the legs.

First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.

Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:

AC^2 = YA^2 + YC^2

He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:

AC^2 = 500^2 + 327^2

AC^2 = 250000 + 107649

AC^2 = 357659

AC = √357659

AC ≈ 597.56 ft

Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:

distance across gorge = XA + AY

distance across gorge = AC + YA + YC

distance across gorge = 597.56 ft + 500 ft + 327 ft

distance across gorge ≈ 1424.56 ft

This is Jamal's estimate of the distance across the gorge.

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The cost of each small package of cookies is $7 and the cost of each large package of cookies is $11.

What is a variable?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye colour, and vehicle kind.

Given that the total cost of  3 small packages of cookies and 14 large packages of cookies is $203.

The total cost of  11 small packages of cookies and 11 large packages of cookies is $220.

Assume that the cost small packages of cookies is x and large packages of cookies y.

Then the cost of 3 small packages of cookies and 14 large packages of cookies is (3x + 14y).

The cost 11 small packages of cookies and 11 large packages of cookies is (11x + 11y).

The system of linear equation is

3x + 14y = 203  .....(i)

11x + 11y = 220  .....(ii)

Multiply equation (i) by 11 and equation (ii) by 3

33x + 154y = 2233

33x + 33y = 660

______________

        121y = 1573

Divide both sides by 121:

y = 13

Putting y = 13 in equation (i)

3x + 14 × 13 = 203

3x = 21

x = 7

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Answer:

45

Step-by-step explanation:

The five rational numbers between - 4 / 7 and - 3 / 8 by discretizing the set of rational numbers are - 181 / 336, - 85 / 168, - 53 / 112, - 37 / 84, - 137 / 336.

Rational numbers are real numbers of the form m / n, where m and n are integers and n is a non-zero number. In this case, we need to determine five numbers between two given rational numbers: - 4 / 7, - 3 / 8.

Since there is an infinite set of rational numbers, we must create an additional criterion to discretize that set and find the five required numbers more easily. This can be done by means of the following formula:

y = a + (b - a) · [x / (n + 1)]

Where:

If we know that a = - 4 / 7, b = - 3 / 8 and n = 5, then the five rational numbers are:

n = 1

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (1 / 6)

y = - 181 / 336

n = 2

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (2 / 6)

y = - 85 / 168

n = 3

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (3 / 6)

y = - 53 / 112

n = 4

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (4 / 6)

y = - 37 / 84

n = 5

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (5 / 6)

y = - 137 / 336

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Answer:

½

Step-by-step explanation:

The coefficient of x is 1 but the equation is not in the form of y = mx + b

x - 2y = 4

-2y = 4 - x

2y = x - 4

y = ½x - 2

Therefore, the gradient is ½

The value of quotient will be;

⇒ 60

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒   15 ) 900 (

Now,

Solve the expression by dividing, we get;

⇒   15 ) 900 ( 60

          - 90

          --------

            × 0

Thus, The value of quotient will be;

⇒ 60

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The resulting triangle is 7/10 the original triangle.

The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).

Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 7/10,

Then changed triangle is  A'B'C'

So, relation between them is A'B'C' = 7/10(ABC)

Thus, the resulting triangle is 9/5 multiple of triangle ABC.

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The required point at which point is the object accelerating toward the right is Z.

A  force following up on a moving body at a point to the bearing of movement, having a tendency to cause the body to follow a round or ended way. The power of gravity following up on a satellite in circle is an illustration of a centripetal power; the rubbing of the tires of a vehicle making a turn comparatively gives centripetal  force on the vehicle.

The item in the guide is moving by round movement: consequently, there is a force (called centripetal force ) that pulls the item towards the center point of the circle.

As indicated by Newton's law motion,

F = ma

a power on the item relates to a speed increase, and this speed increase (called centripetal speed increase) has a similar course of the power. Thus, since the speed increase is towards the focal point of the circle also, the main place of the direction where the speed increase is towards the right is at point Z.

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To obtain a score of 85% on a test worth 135 points, one needs to get 115 points. By using proportions, we get the required value.

A proportion is defined as an equality between two ratios.

Consider two ratios a:b and c:d. Then, the proportion we can write,

a: b = c : d

Then, the simplification we have for this proportion is

a/b = c/d or ad = bc

It is given that, a certain test is worth 135 points.

One to get 85% on this test, he/she needs to get X number of points.

So, we can write the proportions as

X : 135 = 85 : 100

⇒ X/135 = 85/100

⇒ X = 85/100 × 135

∴ X = 114.75 ≅ 115 points

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Answer:

.5l means that you are going to add 1/2 cups of lemon juice for every bath that you make.  If you made one batch, you would use  1/2 of lemon juice. If you made 2 batches you will add 1 cup of lemon juice and so on.

2s means that you will add 2 cups of sugar for each batch.  If you made one batch, you would add 2 cups of sugar, if you made 2 batches you would add 4 cups nd so on.

Step-by-step explanation:

It is possible to calculate the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

The likelihood that responses to fewer than two of the final six questions were right can be calculated using the procedure below:

There are 6 questions with a total of 4 possible answers, hence the value of p is:

The following formula provides the probability:

The following formula is used to calculate the likelihood that Ira would properly answer exactly 1 of the final 6 questions:

P(X = 1) = 0.35595

P(X = 0) = 0.17797 gives the likelihood that Ira will correctly answer 0 out of the final 6 questions.

 Accordingly, the likelihood that the last 6 questions' answers contain fewer than 2 valid responses is: P = 0.17797 + 0.35595.

P = 0.53392

P = 53.392%

Hence, the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.

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In parallelogram lonm, om is 34.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

First we have OQ =QM,

So 2x+3=3x-4,

x =7.

Hence OM =2(17)=34.

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Answer: D) 34

Step-by-step explanation:

edge 2023

The equations representing the number and value of coins are n + q = 12  and 5n + 25q = 2.20 respectively.

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

The given problem can be solved as follows,

Suppose the number of nickel and quarter coins are n amd q respectively.

Then, the equation for the total number of coins can be written as,

n + q = 12                  (1)

And, the equation for their value is given as,

5n + 25q = 2.20       (2)

Hence, the two equations that can be used to represent the given case are n + q = 12  and 5n + 25q = 2.20 respectively.

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Answer: (-1, 3)

Step-by-step explanation:

Midpoint formula: ((x1 + x2) / 2, (y1+y2) / 2)

((-5+7)/2, (4+2) / 2))

((-2/2), (6/2))

(-1, 3)