2/5 = k x 1/6

its k times 1/6 not kx

Answer:

8200+1894.40 = $10,094.40

Step-by-step explanation:

The formula we'll use for this is the simple interest formula, or:

I = P x r x t

Where:

P is the principal amount, $8200.00.

r is the interest rate, 4.4% per year, or in decimal form, 4.4/100=0.044.

t is the time involved, 5.5....year(s) time periods.

So, t is 5.5....year time periods.

To find the simple interest, we multiply 8200 × 0.044 × 5.5 to get that:

The interest is: $1984.40  + add to Investment ($8000) and you'll get the answer.

Answer:A

Step-by-step explanation:

A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 2 to 15, and the box ranges from 3 to 8. A line divides the box at 6. Option A is correct.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value. Horizontal lines on both sides of the rectangle show the lower and upper quartiles.

Here,

The lower quartile (Q1) of the data set is 3, so the bottom of the box must start at 3.
The interquartile range (IQR) is 5, so the upper quartile (Q3) must be
Q1 + IQR = 3 + 5 = 8

The median (also called the first quartile) is halfway between Q1 and Q3, so it must be at (Q1 + Q3) / 2 = (3 + 8) / 2 = 6.

The whiskers extend to the minimum and maximum values within 1.5 * IQR of the box, so they must range from 2 to 15.

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Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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The only choice that is equivalent to this expression is (E) 3.(3-4), which simplifies to -1. All the other choices are not equivalent to the given expression.

When two expressions can be reduced to a single third expression or when one of the expressions could be written in the same way as the other, they are said to be equivalent.

The phrase (3-4)3 can be made simpler as follows:

(3-4)

³ = (-1)³

= -1

Hence, (E) 3.(3-4) is the only option that is identical to this formula and simplifies to -1. None of the alternative options are identical to the stated expression.

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Answer:

Step-by-step explanation:

Corresponding sides have same ratio in similar figures:

Correct option is A

we know ,

the probability=no of repeated value/total number

factorial of 3 and 2

and factorial of total number

=3ḷ×2ḷ/7ḷ

=3×2×1×2×1/7×6×5×4×3×2×1

=1/7×5×4×3

=1/420

=0.23809

or

=0.238

what is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

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The type of bias/error being made in this sampling procedure is selection bias or sampling bias.

The sampling procedure described in the scenario is prone to selection bias or sampling bias. This bias occurs because the sample is being collected only from individuals entering a particular church on a Sunday. This sampling method may not accurately represent the broader population's frequency of attending religious services, as it disproportionately includes individuals who actively participate in religious activities or attend services regularly.

This selection bias can lead to an overestimate of the frequency of attendance as it does not account for individuals who may attend services less frequently or not at all. To mitigate this bias, a more diverse and representative sampling method should be employed, such as random sampling from different locations or days of the week to capture a broader range of individuals' attendance habits.

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Answer:

see below

Step-by-step explanation:

We want to solve each equation for y, so y must be alone on one side of the equation.

a) 10x + 5y = 20

Subtract 10x from both sides.

5y = 20 - 10x

Place the x term in front to follow  y = mx + b form.

5y = -10x + 20

We want to isolate y completely, so divide both sides by 5. On the right side, be sure to divide each component by 5.

5y/5 = -10/5x + 20/5

y = -2x + 4

This equation is in slope-intercept form.

b) 3x - 2y = 10 + 4x

We can see that y is negative in this original equation. Let's add 2y to both sides to make y positive.

3x = 10 + 4x + 2y

Now we want to isolate y, so subtract 4x from both sides.

3x - 4x = 10 + 2y

Simplify.

-x = 10 + 2y

Isolate y further by subtracting 10 from both sides.

-x - 10 = 2y

Again, we want to isolate y completely, so divide both sides by 2. On the left side, be sure to divide each component by 2.

-x/2 - 10/2 = 2y/2

-1/2x - 5 = y

This looks backwards (although it is in slope-intercept form), so let's rearrange it just to make it more clear.

y = -1/2x - 5

This equation is in slope-intercept form.

Hope this helps!

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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By using probability, it can be calculated that-

the optimal number of cookies to make is 2400 dozens

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here

Each dozen of cookies is sold for $1.99 and cost $0.99

Shortage = $(1.99 - 0.99) = $1

Cookies that are not sold at the end of the day are reduced to $0.49

Overage = $(0.99 - 0.49) = $0.5

Service = \(\frac{1}{1 + 0.5}\\\)

              \(=\frac{1}{1.5}\\\\=\frac{2}{3}\\\\=0.67\)

Now the table is

Demand               Probability of demand             Cumulative probability  

(Dozen)

1800                          0.05                                             0.05

2000                         0.15                                              0.2

2200                         0.2                                               0.4

2400                         0.3                                                0.7

2600                         0.2                                               0.9

2800                         0.1                                                 1

Here the closest to service is 0.7

So the optimal number of cookies to make is 2400 dozens

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Complete Question

Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are specialty of his shop. Each dozen sells for $1.99 and costs $0.99, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.49 and sold the following day as day-old merchandise. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand he estimates demand for cookies as

Demand                Probability of demand            Cumulative probability    

(Dozen)

1800                          0.05                                          

2000                         0.15                                            

2200                         0.2                                              

2400                         0.3                                              

2600                         0.2                                            

2800                         0.1                                                

Using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen

2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen

Answer:

Amount needed by her \(=\$(5x+5)\)

Step-by-step explanation:

Given: Susie wants to buy 5 slices of pizza and a litre of soda that cost $5 for her and her friends

To find: amount needed by her

Solution:

Let cost of 1 slice of pizza be \(\$x\). Also, a litre of soda costs $5.

Cost of 5 slices of pizza \(=\$5x\)

Cost of a litre of soda \(=\$5\)

Total amount needed by her \(=\$(5x+5)\)

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

Given: Mount Everest is the tallest mountain in the set of data

Required:

Question 1: Use the scatter plot to estimate the height of Mount Everest

From the plot,

Question 2: Year of the first recorded ascent of mount Everest

From the plot,

Yes, the given curves are orthogonal.

In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.

Given equation is,

x²+y²=ax

Differentiating,

2x+2yy'=a

y' = (a-2x)/2y = m1

Again,

x²+y²=by

Differentiating,

2x+2yy'=by'

y' = -2x/(2y-b) = m2

For both curves are orthogonal, we have

m1*m2 = -1

(a-2x)/2y*-2x/(2y-b)  = -1

-2ax+4x² = -4y²+2yb

4(x²+y²) = 2ax+2yb

Since, ax = (x²+y²)

by = (x²+y²)

Then,

4(x²+y²) = 2(x²+y²) +2(x²+y²)

4(x²+y²) = 4(x²+y²)      (true)

Hence, the above response is appropriate.

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The possible value of positive constant b for an absolute maximum value of function g(x), \(g(x) = xe^{-x} + be^{-x} \) at x = \( \frac{2}{3} \) is equals to the \( \frac{1}{3} \).

An absolute maximum point is a point where the function acquires its largest possible value. To drive the max or min absolute value, we have to substitute the derivative value of function equals to zero. We have a function, \(g(x) = xe^{-x} + be^{-x} \), where b is positive constant. We have to determine the possible value of b for absolute maximum of g at x= 2/3.

Differentiating the function g(x) with respect to x

=> \(g'(x) = - x e^{-x} + e^{-x} - be^{-x} \)

\(= (1 - x - b )e^{-x}\)

\(= \frac{1 - x - b }{e^{x}}\)

For obtaining absolute maximum value put, g'(x) = 0

=> \(\frac{1 - x - b }{e^{x}} = 0\)

Substitute x = 2/3, in above expression,

\( \frac{1 - \frac{2}{3} - b }{e^{\frac{2}{3}}} = 0\)

=> \(1 - \frac{2}{3} - b = 0\)

=> \( b = \frac{1}{3}\)

Hence, the required value of b is \( \frac{1}{3} \).

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Complete question:

Let g(x)=xe^(-x)+be^(-1), where b is a positive constant. For what positive value of b does g have an absolute maximum at x=2/3 .Justify your answer.

Answer:

f(n) = -7+3n

Step-by-step explanation:

I plugged the values into the equation and they work.

f(n) = -7 + 3(10) = 27

f(n) = -7 + 3(12) = 26

f(n) = -7 + 3(16)= 32

None of the statements are true for the given angle θ = 2π/3.

For the given angle θ = 2π/3, let's evaluate the statements:

1. cos(theta) = √3/2

To determine if this statement is true, we can calculate the cosine of θ:

cos(2π/3) = -1/2

The statement cos(theta) = √3/2 is not true for θ = 2π/3.

2. The measure of the reference angle is 30°.

The reference angle is the positive acute angle between the terminal side of the angle and the x-axis. Since the given angle θ = 2π/3 is in the second quadrant, the reference angle cannot be 30°.

3. The measure of the reference angle is 45°.

Similar to the previous statement, since θ = 2π/3 is in the second quadrant, the reference angle cannot be 45°.

4. The measure of the reference angle is 60°.

Again, considering the quadrant of θ = 2π/3, the reference angle cannot be 60°.

5. tan(theta) = -√3

To verify this statement, we can calculate the tangent of θ:

tan(2π/3) = √3

The statement tan(theta) = -√3 is not true for θ = 2π/3.

In summary, none of the statements are true for the given angle θ = 2π/3.

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The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).

This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.

For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.

Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.

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The steps to evaluate an exponential expression include:

First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.

Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.

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The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.

According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.

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The measure of angle HBG to 3 significant figures is 48.2°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The trigonometric functions are;

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

In the cuboid, Triangle BHG is a right triangle

since BG = 24 cm = adj

BH = 36cm = opp

represent angle HBG by x

cos x = 24/36

cos x = 0.667

x = 48.2

Therefore the measure of angle HBG is 48.2°

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Answer:

At year 3 and beyond, The investment will have a value less than $2,000.

t=3.

Step-by-step explanation:

The total number of dots in the first n rows of the triangular arrangement is equal to the sum of the first n positive integers. This can be represented by the formula: n(n+1)/2.

Based on the triangular arrangement mentioned in your question, the total number of dots in the first n rows can be described using the formula for the sum of the first n terms of an arithmetic series. This formula is:

Total number of dots = n(n + 1) / 2

Here, 'n' represents the number of rows. Using this formula, you can easily calculate the total number of dots for any given number of rows in the triangular arrangement.

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The graph belοw shοws the graphs οf the linear functiοn y = 7x and the expοnential functiοn, y = 7ˣ.

Any subset οf a Cartesian prοduct is a relatiοn.

These οrdered pairings make up a binary relatiοn frοm A tο B. (a,b),

A relatiοnship οn A, mοre precisely, an A tο B relatiοnship.

These οrdered pairs (a, b) make up a binary relatiοn frοm A tο B, where the first cοmpοnent is frοm A and the secοnd cοmpοnent is frοm B.

A cοnnectiοn knοwn as a functiοn links each item in a set X tο a single item in a different set Y. (pοssibly the same set).

A graph, which is a cοllectiοn οf all οrdered pairs (x, f (x)), is the sοle way

A subset οf, fοr instance, is referred tο as a "binary relatiοnship frοmtο describe a functiοn.

Accοrding tο οur questiοn-

Bοth οf the functiοn have same value οf rate =7

But in linear functiοn y=7x , 7 is the cοnstant οf prοpοrtiοnality.

In expοnential functiοn ,y=7ˣ ,7 is the multiplicative rate οf change.

Fοr y=7x ,

x    y

1     7

2    14

3    21

y = 7ˣ

x    y

1    7

2   49

3    343

We can οbserve that the expοnential functiοn grοws faster than the linear functiοn dοes fοr. 1≤x≤3

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Answer:

27.6

Step-by-step explanation:

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77