the first and last term arithmetic sequence are 9 and 165 respectively.if the sum of all the terms of the arithmetic sequence is 3480,find the number of terms and the common difference of this arithmetic sequence​

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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$0.56 per unit.

$2.24 ÷ 4 = 0.56 per unit

Answer:

0.56

Step-by-step explanation:

2.24/4=0.56

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The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.

We shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:

squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)

a² is common and can be cancel out

square root of (36a⁸/255a²) = square root of (36a⁶/255)

square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}

square root of (36a⁸/255a²) = 6a³/15

square root of (36a⁸/255a²) = 2a³ × 3/5 × 3

we divide through by the common factor 3

square root of (36a⁸/255a²) = 2a³/5

Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.

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The correct options are as follows:

The experiment is rolling the die.

A trail is one rolling of the die.

The outcome is the number that is rolled on the die.

In the given question, we have to identify the experiment, trail, and outcome. In the given example, the experiment is rolling the die. Experiment is a procedure that can be repeated infinitely and has a possible set of outcomes. The trail is the number of times an experiment is repeated. In the given example, the rolling of one die is the trail.

The outcome of the random experiment is the result of the given trail. In the given example, the outcomes can be 1.

Hence the correct options:

The experiment is rolling the die.

A trail is one rolling of the die.

The outcome is the number that is rolled on the die.

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The value of three subsets is \(n(x_{1})=36, n(x_{2})=9, & n\left(x_3\right)=54\).

A set is a collection of objects or elements, grouped in the curly braces, such as {a, b, c, d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.

The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.

If set A has {X, Y} and set B has {X, Y, Z}, then A is the subset of B because elements of A are also present in set B.

Let the number of elements in \($x_2$\) be \($x$\), then

\($$\begin{aligned}& n\left(x_1\right)=4 x \\& n\left(x_2\right)=x \\& n\left(x_3\right)=6 x\end{aligned}$$\)

Given that number of elements in \($x=99$\)

\($$\begin{aligned}\Rightarrow & n\left(x_1\right)+n\left(x_2\right)+n\left(x_3\right)=99 \\\Rightarrow & 4 x+x+6 x=99 \\\Rightarrow & 11 x=99 \\\Rightarrow & x=9 \\\therefore & n\left(x_1\right)=4 x=4 \times 9=36 \\& n\left(x_2\right)=x=9 \\& n\left(x_3\right)=6 x=6 \times 9=54\end{aligned}$$\)

Therefore, the value of  \(& n\left(x_3\right)\)\(=54\).

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The value of the z-score for the number 15  in a data set is 0.93.

Define z-score.

A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.

You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.

                     ∴  z = (x – μ) / σ

Given:

σ = 4.32

x = 15

Data set: 5, 7, 9, 11, 13, 15, 17

So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7

                = 77/7

            μ = 11

z = (x – μ) / σ

  = (15 - 11)/4.32

   = 4/4.32

z  = 0.93

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The number of inches by which each dimension must be increased is 10 inches.

Let length and width be increased by x.

so we get, the length = (10 + x) and breadth = (5 + x)

(10 + x)(5 + x) = 6 × 10 × 5

50 + 10 x + 5x + x² = 300

x² + 15x- 250 = 0

x² + 25x- 10x - 250 = 0

x  (x + 25) - 10 (x + 25) = 0

(x + 25)(x - 10) = 0

x = -25 is not the right choice as length cannot be negative.

so x = 10

so both dimensions should be increased by 10 inches.

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The complete question is -

A rectangular picture frame is 5 inches wide and 10 inches tall. You want to make the area 6 times as large by increasing the length and width by the same amount. Find the number of inches by which each dimension must be increased.

Answer:

x = -3

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable. i really hope this makes sense and helps:)

Step-by-step explanation:

1

Distribute

10−4(6+2)=74

10{\color{#c92786}{-4(6x+2)}}=7410−4(6x+2)=74

10−24−8=74

10{\color{#c92786}{-24x-8}}=7410−24x−8=74

2

Subtract the numbers

10−24−8=74

{\color{#c92786}{10}}-24x{\color{#c92786}{-8}}=7410−24x−8=74

2−24=74

{\color{#c92786}{2}}-24x=742−24x=74

3

Subtract the same term from both sides of the equation

2−24=74

2-24x=742−24x=74

2−24−2=74−2

2-24x{\color{#c92786}{-2}}=74{\color{#c92786}{-2}}2−24x−2=74−2

4

Simplify

Subtract the numbers

Subtract the numbers

again

−24=72

-24x=72−24x=72

5

Divide both sides of the equation by the same term

−24=72

-24x=72−24x=72

−24−24=72−24

\frac{-24x}{{\color{#c92786}{-24}}}=\frac{72}{{\color{#c92786}{-24}}}−24−24x=−2472

6

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

=−3

x=-3x=−3

Solution

x=-3

The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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Answer:

$886.47

Step-by-step explanation:

Answer: D) 1*5=5

Step-by-step explanation: 1.09*5.4=5.5 so the closest number to that is 5.The rest of the answer choices are not possible.

Answer:

(x2-x1)+(y2-y1)

Step-by-step explanation:

X2=0

X1=1

y2=9

y1=6

(0-1)+(9-6)

-1+3

2

The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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Answer: 14, 16, 32 and 45

The term in the AP whose value is 201 / 2 is 71.3.

The first term of an arithmetic progression is 5 and the common difference is - 3/2.

The formula of the arithmetic progression can be described as follows:

nth term = a + (n - 1)d

where

Therefore, using the arithmetic progression formula,

a = 5

d = 3 / 2

nth term = 201 / 2

let's find the term(n)

Therefore,

- 201 / 2 = 5 + (n - 1) - 3 / 2

- 201 / 2 = 5  - 3 / 2 n  + 3 / 2

- 201 / 2  - 3 / 2 - 5 =  - 3 / 2 n

- 107  =  -3 / 2 n

-3n = - 214

n = 214 / 3

n = 71.3

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Answer:

21,656

Step-by-step explanation:

Answer:

formula is 6a²= surface area

but since one side is not being painted it is

5a²= surface area

5(3.2)²

=51.2cm

The approximate probability that no less than 97 out of 146 registered voters will vote in the presidential election is 0.0293, rounded to four decimal places.

The probability that no less than 97 out of 146 registered voters will vote in the presidential election can be approximated by the normal distribution. The probability of a given registered voter voting can be assumed to be 63%, which is equivalent to 0.63. The mean number of people voting can be calculated by multiplying the number of registered voters (146) by the probability of a given person voting (0.63). This gives a mean of 92.38. The standard deviation can also be calculated by multiplying the number of registered voters by the probability of a given person not voting (1-0.63) and then taking the square root. This gives a standard deviation of 5.90.Using the normal distribution, the probability that no less than 97 out of 146 registered voters will vote in the presidential election can be calculated using the formula:P(x ≥ 97) = 1 - P(x < 97)    = 1 - Φ(97; 92.38, 5.90)   = 1 - 0.9707   = 0.0293

Therefore, the approximate probability that no less than 97 out of 146 registered voters will vote in the presidential election is 0.0293, rounded to four decimal places.

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Answer:

800 centimeters

Step-by-step explanation:

1 meter=100 centimeters

So multiply 8 meters times 100 centimeters and you get 800 centimeters.

I hope this helped!!!!!!

Answer:

800 Centimeters

Step-by-step explanation:

You multiply 8 by 100.

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

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In the ΔWXY, with the incenter of the triangle being Z.

1. The measure of m∠WYZ = 43°.

2. The measure of m∠WXY = 66°.

3. The measure of m∠YWX = 28°.

4. The measure of m∠ZWX = 14°.

What is an incenter?

The intersection of the triangle's three interior angle bisectors forms the triangle's incenter. Due to the junction point of the central axis being the centre of the triangle's inscribed circle, this point is equally spaced from the sides of a triangle.

In ΔWXY, the incenter of the triangle is Z.

This means that ∠W, ∠Y and ∠X are equally bisected angles.

It is given that the measurement of ∠WYX = 86° and ∠WXZ = 33°

1. The measure of angle ∠WYZ.

The angle ∠WYX is bisected by the line segment YZ.

It forms two angles ∠WYZ and ∠XYZ.

So, the measurement of ∠WYZ = ∠WYX/2

∠WYZ = 86°/2

∠WYZ = 43°

Therefore, the measurement of ∠WYZ = 43°.

2. The measure of angle ∠WXY.

The angle ∠WXY is bisected by the line segment XZ.

It forms two angles ∠WXZ and ∠ZXY.

The measurement of angle ∠WXZ = 33°.

So,  the measurement of ∠WXY = ∠WXZ × 2

∠WXY = 33° × 2

∠WXY = 66°

Therefore, the measurement of ∠WXY = 66°.

3. The measure of angle ∠YWX.

According to the properties of the triangle, the sum of three angles of triangle is 180°.

So, the equation will be -

∠YWX + ∠WXY + ∠XYW = 180°

∠YWX + 66° + 86° = 180°

∠YWX + 152° = 180°

∠YWX = 180° - 152°

∠YWX = 28°

Therefore, the measurement of ∠YWX = 28°.

4. The measure of angle ∠ZWX.

The angle ∠YWX is bisected by the line segment WZ.

It forms two angles ∠YWZ and ∠ZWX.

So, the measurement of ∠ZWX = ∠YWX/2

∠ZWX = 28°/2

∠ZWX = 14°

Therefore, the measurement of ∠ZWX = 14°.

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Answer:

Circle - A=C

Step-by-step explanation:

The equation is a circle because the ratio of \(x^2 \ and \ y^2\) must be equal,

Given the equation of the circle \(3x^2 + 6x + 3y^2 + 7y + 4 = 0\)

Rearrange the equation

\(3x^2 + 6x + 3y^2 + 7y + 4 = 0\\ 3x^2 + 3y^2 + 6x +7y + 4 = 0\)

The equation is a circle because the ratio of \(x^2 \ and \ y^2\) must be equal,

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Answer:

do the butterfly method if you don't know how to do that comment and I'll show you a screenshot

Answer:5

Step-by-step explanation:

5098

Answer:

I think it B.

Step-by-step explanation:

I think it B.

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Answer:I don’t know this one sorry

Step-by-step explanation:

We have to find the line equation that gives us the value of Y for some value of X

in this case, whe have to find the line equation so that y = 5 when x = 0, y = 7 when x = 1, etc.

the line equation is y = mx + b in general

when x = 0, y = b, so for the first table b = 5 and for the second table b = 0;

the difference between each value of Y is 2 (5, 7, 9, 11) so the m value for the first table is 2

and for the second table, the difference between each Y value is 13, so m = 13 for the second table

Therefore, for the first table the equation is: Y = 2X + 5

and for the second table, te equation is Y = 13X