Find the explicit formula for an arithmetic sequence with a common difference of 8 and whose first term is -2.

Answer: $609

Step-by-step explanation:

2436/4 = 609

Answer: [tex]\$5500, \$14,500[/tex]

Step-by-step explanation:

Given

[tex]\$20,000[/tex]  is invested in two accounts with a 12% and 11% rate of interest.

Total interest after a year is  [tex]\$2255[/tex]

Suppose x amount is invested in first, so the remaining amount is invested in other

Simple interest and Compound interest is the same for a year

[tex]\therefore \text{Interest}=\dfrac{P\times R\times T}{100}[/tex]

For first investment

[tex]I=\dfrac{x\times 12\times 1}{100}\\\\I=0.12x[/tex]

For second investment

[tex]II=\dfrac{\left(20,000-x\right)\times 11\times 1}{100}\\\\II=0.11\left(20,000-x\right)[/tex]

The sum of the two must be [tex]\$2255[/tex]

[tex]\Rightarrow 0.12x+0.11\left (20,000-x\right)=2255\\\Rightarrow 0.01x=2255-2200\\\\\Rightarrow x=\dfrac{55}{0.01}\\\\\Rightarrow x=\$5500[/tex]

Remaining amount is

[tex]\Rightarrow 20,000-5500\\\Rightarrow \$14,500[/tex]

Answer:

109 took physics and 392 took Trigonometry

Step-by-step explanation:

The missing angles and their reasons are as follows;

a) x = 65°; Opposite angles

b)  y = 71°; Alternate angles

c) z = 44°; sum of angles in a triangle

a) In triangles or line geometry, we know that the angles that are directly opposite to each other are known as opposite angles. They are also referred to as as vertical angles or even vertically opposite angles in some cases and are always congruent to each other.

We see that x is an opposite angle to 65 and so;

x = 65°

b) Alternate angles are gotten on the opposite sides of a transversal line they always have the same size. In this problem, we see that y is an alternate angle to 71° and as such;

y = 71°

c) The sum of angles in a triangle is 180° and as such;

x + y + z = 180°

Thus;

65 + 71 + z = 180

z = 180 - 136

z = 44°

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Answer:

D. Angles 4 and 7

Step-by-step explanation:

Answer 1 and 4 are supplementary angles.

Step-by-step explanation:

Supplementary angles are angles adding up to 180, the only angles listed that are supplementary angles is 1 and 4.

Have a good day!

Answer: Municipal Bank will charge him 8% simple interest

Step-by-step explanation:

A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.

The area occupied within an object's three-dimensional bounds is referred to as its volume. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.

given

Calculate the box's volume and provide your answer in units.

Due to the fact that x = 4.28, the remaining sides are 2x + 5 = 2(4.28) + 5 = 13.56

and x - 2 = 4.28 -2 = 2.28.

We are aware that volume is calculated as follows: 13.56 (4.28) ( 2.28 )

=[tex]135.25cm^{3}[/tex]

A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.

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Therefore , the solution of the given problem of slope comes out to be

y = (-1/2)x + 8.

The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line's slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the formula y = 3x - 7.

Here,

Locate the slope first.

These two positions (0, 8) and are in the line, therefore we know that (6,5)

Slope: (y2-y1)/(x2 - x1)

Slope = 8-5 / 0-6

Slope = 3/-6 => Slope = -1/2

The gradient is -1/2. When x = 0, you can find the y-intercept. We also know that the line passes through the point (0,8), and since x = 0, the y-intercept is equal to 8.

using the slope-intercept form, which is

Using the equation y = mx + b, where m denotes the slope and b the y-intercept, we get:

y = (-1/2)x + 8

Therefore , the solution of the given problem of slope comes out to be

y = (-1/2)x + 8.

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sorry i cant help im not there yet im not that high a grade yet

The price that maximize the profit is $10 or $22.

What is maximum profit?

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit.

Given:

f(p) = -50p^2 + 1600p - 11000

Now to find velocity point

[tex]-\frac{b}{2a} = \frac{-1600}{2(-50)} = \frac{1600}{100} = 16[/tex]

So for the price p = 16 that generates maximum profit.

Now

f(16) = -50(16)^2 + 1600(16) - 11000 = 1800

The maximum profit is 1800.

At breakeven, f(p) = 0

So,

[tex]-50p^2 + 1600p - 11000 = 0\\p = \frac{-1600 + -\sqrt{(1600)^2 - 4(-50)(-11000)} }{2(-50)} \\p = \frac{-1600 + - \sqrt{2560000 - 2200000} }{-100} \\p = \frac{-1600+-\sqrt{360000} }{-100} \\p = \frac{-1600+-600}{100}\\ p = 10, 22[/tex]

So p = $10   or  p = $22

Hence, the price that maximize the profit is $10 or $22.

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The value of tan 1 is  45 degree.

tangent is the trigonometric ratio.

we can find out the value of tangent by taking opposite side of the theta angle divided by the adjacent side of the theta angle.

tan Q = perpendicular of triangle /base of triangle.

sine theta divided by cos theta gives the value of tan theta.

tan Q = sin Q/ cos Q.

some formula of the tan Q are as follows,

1- tan Q = sin Q/cos Q

2- tan Q= 1 /cot Q

3-tan^2 Q =sec^2 Q -1

4- tan(90 - Q)=cot Q

5- tan (Q+π)=tan Q

6- tan (π-Q)=-tan Q

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The longer ladder can reach 3 8/7 feet higher than the shorter one.

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'x' is the only variable in the provided polynomial. As a result, the polynomial  4x² - 3x + 7  has one variable.

A polynomial is an expression in mathematics made up of variables (sometimes referred to as indeterminates) and coefficients that only employs the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that combines variables, constants, and exponents utilizing addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

given

'x' is the only variable in the provided polynomial. As a result, the polynomial  4x² - 3x + 7  has one variable.

The following list includes a few examples of polynomials with one variable: x+2. x2+3x+2.

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Answer:

Step-by-step explanation:

Answer:

312.5

Step-by-step explanation:

250+(0.2p)=1p

p=312.5

Answer:

Histograms subdivide data into intervals (bins), and use rectangles (usually columns) to show the frequency (count) of observations in each interval. ... Dot plots include ALL values from the data set, with one dot for each occurrence of an observed value from the set.

Step-by-step explanation:

histogram-Analyzing whether a process can meet the customer's requirements. Analyzing what the output from a supplier's process looks like. Seeing whether a process change has occurred from one time period to another. Determining whether the outputs of two or more processes are different.

Dot plots are used for continuous, quantitative, univariate data. Data points may be labelled if there are few of them. Dot plots are one of the simplest statistical plots, and are suitable for small to moderate sized data sets. They are useful for highlighting clusters and gaps, as well as outliers.

Answer:

Magnitude: 3√10

Direction angle: 71.56°

Step-by-step explanation:

The magnitude ||v|| of a vector <a,b>, would be:

[tex]||v||=\sqrt{a^{2}+b^{2}[/tex]

[tex]||v||=\sqrt{3^{2}+9^{2}[/tex]

[tex]||v||=\sqrt{9+81}[/tex]

[tex]||v||=\sqrt{90}[/tex]

[tex]||v||=3\sqrt{10}[/tex]

The vector's reference angle would be:

[tex]tan\alpha =|\frac{b}{a}|[/tex]

[tex]tan\alpha =|\frac{9}{3}|[/tex]

[tex]tan\alpha =|3|[/tex]

[tex]tan\alpha =3[/tex]

[tex]\alpha = 71.56[/tex]

If [tex]\alpha[/tex] is your reference angle, then your direction angle ∅ depends on what quadrant the vector is located in. Since <3,9> is located in Quadrant I, then ∅= [tex]\alpha[/tex], which means your direction angle is also 71.56°

Answer:

9.5; 72°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:Min:2

Q1:5

Med:7

Q3:13

Max:15

The perimeter of the parallelogram with the given vertices is 33.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Given that:

A = (3, 6)

B = (-5, 6)

C= (6 , -1)

D = (-2, -1)

The length of side is given by the formula:

[tex]L = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Substitute the values in the formula to find the sides of the parallelogram.

[tex]AB= \sqrt{(-5 -3)^2 + (6-6)^2} = 8\\ \\BC = \sqrt{(6+5)^2 + (-1 - 6)^2} = 13\\\\CD= \sqrt{(-2+6)^2 + (-1 +1)^2} = 4\\\\\DA= \sqrt{(3+2)^2 + (6+1)^2} = 8[/tex]

The perimeter is obtained by adding all the sides of the given two-dimensional shape.

P = 8+13+4+8

P = 33

Hence the perimeter of the parallelogram is 33.

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Answer:

9 is yes.

5 is no

12 is no

8 is no

7 1/8

You divide 4 3/4 by 2/3

The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.

Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.

When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.

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The square of the given numbers 3, 4, and 5 are 9, 16, and 25 respectively.

The square of a number is the product of the number with itself. Therefore, if there is a number x then its square will be the product of x and x. It is denoted by 2 in superscript form over the number whose square is needed to be calculated.

The squares of the given numbers are,

3² = 3 × 3 = 9

4² = 4 × 4 = 16

5² = 5 × 5 = 25

Hence, the square of the given numbers 3, 4, and 5 are 9, 16, and 25 respectively.

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Answer:

137 cm. are the volume each con... because of 2 serinemital factors...

Step-by-step explanation:

HOPE IT HELPS!!

The equation of line is given by y = 13.45x - 7.95 where the slope of the line is m = 13.45 and y is the weight in kilograms , x is the number of months

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The weight in kilograms = y

The number of months = x

Let the first point be represented as P = P ( 11 , 140 )

Let the second point be represented as Q = Q ( 1 , 5.5 )

Now , the slope of the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 140 - 5.5 ) / ( 11 - 1 )

Slope m = 134.5 / 10

Slope m = 13.45

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 140 = 13.45 ( x - 11 )

On simplifying the equation , we get

y - 140 = 13.45x - 147.95

Adding 140 on both sides of the equation , we get

y = 13.45x - 7.95

when x = 11 months

y = 13.45 ( 11 ) - 7.95

y = 147.95 - 7.95

y = 140 kilograms

Therefore , the value of A is y = 13.45x - 7.95

Hence , the equation is y = 13.45x - 7.95

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The numbers are sort from least to greatest as 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

A fraction can be defined as the part of a whole number, variable or element.

There are several types of fractions, some of which includes;

From the information given, we have the fractions;

0, 1, 1/2, 8/9, 49/100, 11/10, 1/13

To arrange the values from least to greatest, we have to divide the fractions and find their decimal forms, we have;

1/2 = 0.5

8/9 = 0.89

49/100 = 0.49

11/10 = 1.1

1/13 = 0. 08

However, the arrangement is 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

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The regular price of a ticket to the game was $204.00.

We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.

We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.

We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:

x + $5.75 = (x + $5.75) * 16 = 16x + $92

So the regular price of a ticket is x = $296.00 - $92 = $204.00

Therefore, the regular price of a ticket to the game was $204.00.

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value of x = 8 as per logarithm laws.

In mathematics, logarithm is an exponent or power for which a particular number is raised to achieve a required number. In other words, logarithm is a mathematical expression that states about how many times a number can be multiplied by the same number to get some required numbers.

The method of expressing any exponential relationship in the inverse form is called log notation.

In this question, we are given a log base 2 or binary logarithm.

given, ㏒₂ x = 3

     as per the logarithm laws ㏒a y = m

                                          y = a∧m

                               we write. ㏒₂ x = 3

                                                  x = 2³

                            hence, x = 8

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