Given the following exponential function, identify whether the
change represents growth or decay, and determine the
percentage rate of increase or decrease.
y = 3300(0.949)^x

The mean age of the combined distribution of both men and women in the course is 20.47 years

What is average/mean ?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Mean age of men , M = 20.7 years

Mean age of Women , W = 20.2 years

Percentage of Men = 54%

Percentage of Women = 46%

Recall, :

Mean, μ = np

The mean age of men in the distribution = (20.7 × 54%) = 11.178 years

The mean age of women in the distribution = (20.2 × 46%) = 9.292 years

The mean age of the combined distribution is :

11.178 + 9.292 = 20.47 years

Therefore, the mean age of the combined distribution is 20.47 years

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Answer:

55.8,117

Step-by-step explanation:

62 times 0.9 is 55.8

130 times 0.9 is 117

I hope this helps!

The polynomial 25x² + 36y²  is the sum of the squares.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, 25x² + 36y² which can be written as,

= 5²x² + 6²y².

= (5x)² + (6y)² it is the sum of the squares, The difference of squares would be (5x)² - (6y)².

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Answer: 76.2

Step-by-step explanation:

54/17=3.176

3.176=the scale factor

3.176(24)=76.224

Rounded=76.2

Answer:

---------------------------------------------------

If two figures are similar then their corresponding sides have same ratio.

Find ratios:

Substitute and find the value of PM:

(x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.

A quadratic function has the vertex form f(x) = a(x - h)2 + k, where a, h, and k are constants.

Obtain the equation y = ax2 + bx + c.

Determine -b / 2A.

The vertex's x-coordinate is given here.

Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate.

The vertex's y-coordinate is given here.

So, we have the equation:

Y = X² - 2x + 5

Now, calculate as follows:

⇒ y = (x2 - 2x + 1) + 5 -1

⇒ y - 4 = (x -1)2

⇒ (x -1)2 = y - 4

Therefore, (x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.

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Yes, a test of statistical significance be conducted before or after computing d and interpreting its value.

The p-value is an important phrase for hypothesis testing in the context of statistical significance of data.

The p-value is defined as a function of observed sample outcomes that is used to evaluate statistical hypotheses. Before running the test, a threshold value must be chosen.

The significance is a figure that represents the probability that the outcome of a study occurred entirely by chance. The statistical significance can be low or high. It does not always imply practical significance. When a researcher does not use language carefully in their experiment report, the significance may be misconstrued.

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Question:

To find :

solution:

[tex] ln\dfrac{1}{\sqrt{e^{3}}}=x\\\\ e^{^{({ln\dfrac{1}{\sqrt{e^{3}}}})}}=e^{x}\\\\ \dfrac{1}{\sqrt{e^{3}}}=e^{x} \\\\ (\dfrac{1}{\sqrt{e^{3}}})^{2}=e^{2x}\\\\ \dfrac{1}{e^{3}}=e^{2x}\\\\ e^{-3}=e^{2x}\\\\ -3=2x \\\\\sf{x=\dfrac{-3}{2}} [/tex]

final answer:

Answer:

$7800

Step-by-step explanation:

1 year = 10%

3 years = 30%

30% = 0.3

6000 times 0.3 = $1800

6000 + 1800 = $7800

So, they will pay $7800

the confidence interval for 90% plus four is 0.4±0.067

It refers to an average value of our estimated value plus and minus the variation of the estimated value.

In the statistics confidence level indicates the level of reliability of a particular estimation.

Let, p is the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.

as per above question p=80

number of random samples = n

 n=200

now q is the ratio of p/ number of random samples

 q= 80/200 = .04

now confidence interval for 90% plus 4 that means 94% confidence interval is calculated by the formula = q±Zc√{q(1-q)/n}

                                                       = 0.4±1.94√{0.4(1-0.4)/200}

                             where, zc is the z-score for 94% confidence interval and  zc=1.94,

        hence, confidence interval for 94% = 0.4±0.067

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The number of balls that must be chosen to be certain we have One red and one green is; 5 balls.

We are given;

Number of green balls in box = 95 balls

Number of red balls in box = 90 balls

Thus;

Total number of balls in the box = 95 + 90

Total number of balls in the box = 185 balls

Now, the probability of getting one red from selection = 90/185

Probability of getting one green ball = 95/185

P(Red and Green) = P(R) * P(G)

P(R and G) =  = (90/185) * (95/185) = 0.2418

However, in this case we will make use of the unitary method which is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Thus, minimum number of balls to get the given selection = 95 - 90 = 5 balls

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Here is sufficient evidence that revenue and the number of downloads are linearly related.

A computer software developer would like to use the number of downloads for the trial version of his new shareware to predict the amount of revenue.

The Null hypothesis is the common statistical theory that asserts that no statistical relationship or significance exist between two sets of observed data and measure phenomena based on a single observed variable.

Therefore the null hypothesis become,

H₀ : ρ₁ = 0

and the adjacent hypothesis will become,

H₁ : ρ ≠ 0

Now we will calculate test statistic,

t = r × [tex]\sqrt{\frac{n-2}{1-r^{2} } }[/tex]

 = (0.8691) × [tex]\sqrt{\frac{30 - 2}{0.1309^{2} } }[/tex]

t = 9.2974

we know that degree of freedom = n - 2 = 28

p-value at t = 9.2974 is 0.00

α = 0.05

since p-value < α

so null hypothesis will be rejected.

Hence we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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Answer:

120

Step-by-step explanation:

Don't know if this is a joke, but have a great day regardless!

Answer:

I  added a picture, hope this helps!

Step-by-step explanation:

Let me know if you need to show work

The following numbers will be illustrated in the table:

Those that said yes = 10

Those that said no = 20

Those that said don't know = 10

It should simony be noted that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Number of pupil = 40

25% said ‘Yes’. This will be:

= 25% × 40.

= 10

50% said ‘No’. This will be:

= 50% × 40

= 20

The rest said ‘Don’t know’. This will be:

= 25% × 40

= 10

In conclusion, those who said yes are 10 while those who said no are 20.

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Answer: $12.60

Step-by-step explanation:

Take 9 divided by 5 = $1.80 per light bulb

Then take 1.80 times 7 = $12.60

Answer:

The answer is 12

Step-by-step explanation:

8/x = 28/42

8/x = 2/3

(8) × 3 = (2) × (x)

2x = 24

2x/2 = 24/2

y = 12

y = 12Thus, The value of y is 12

Answer:

12

Step-by-step explanation:

use the theory of cross multiply

so 8•42=28x

        336=28x

             x=12

Answer:

Correct answer is ([7],[5])

Step-by-step explanation:

For the vertex form of the parabola, y = a(x – h)2 + k, the coordinates (h, k) of the vertex are:

(h, k) = (-b/2a, -D/4a)

where,

a is the coefficient of x2,

b is the coefficient of x,

D = b2 – 4ac is the discriminant of the standard form y = ax2 + bx + c.

The required amount of her commission is given as $3937.5.

Given that,
A real estate agent sold a house for $315,000 last week. The commission is 1.25% of the selling price of the home,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Commission = 1.25% of $315000
Commission = 1.25× 315000/100
Commission = $3,937.5

Thus, the required amount of her commission is given as $3937.5.

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Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.

What do you mean by rates?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

1. Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.

2. From 1988 to 1989 the cost of a ticket decreased. Also from 1991 to 1992 the cost decreased a little. The graph slants a little downward.\

3. From 1990 to 1994 the cost stayed pretty much the same. Those years on the graph look almost level... not sloping upward or downward.

4.  1980-1988 price increased from about $2.75 to about $4.25 $1.50 over 8 years = $0.19 per year 1989-1993 price increased from about $4.00 to about $4.20 = $0.20 over 4 years = $0.05 per year 1994-2011 price increased from about $4.20 to about $8.00 $3.80 over 7 years = $0.54 per year

5. Maybe 2012 will be $8.20, 2013 will be $8.30, 2014 will be $8.50, 2015 will be $8.60 ish
Maybe I should make the price go up about $0.17 cents per year ... on average.

6.  1979 maybe $2.52
     1978 maybe $2.36
     1977 maybe $2.19
     1976 maybe $2.02
      975 maybe $1.85
I figured that the price was going down, on average, at about $0.17 per year.

7. one possibility might be y=$5.30/31 x + $2.70 or y = 0.17x+2.7.

8.Using the equation that we fit to this data y = 0.17x + 2.7 we get 0.17(40) + 2.7= $9.50 for the year 2020 and for the year 2030 we get 0.17(50)+2.7 $11.20

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Answer:

Step-by-step explanation:

its b like this the aetter  number g

Answer: c:ray

Step-by-step explanation:

A ray is like a line, but the line takes off in one direction to infinity while the other side is like a line segment. The end of the line is called the endpoint. That's why it is a defined term.

The total length of a boundary defines the perimeter of an equilateral triangle.

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Answer:

The equation for scenario is 2(l + b) = 3a

The rectangle’s perimeter is 2(l + b)

The equilateral triangle’s perimeter is 3a

What is perimeter ?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

According to question

The perimeters of a rectangle and an equilateral triangle are equal.

So

let,

The length and breadth of the rectangle are l & b

And

Side of an equilateral triangle is a

Now

The rectangle’s perimeter = 2(length + breadth)

⇒ 2(l + b)

And

The equilateral triangle’s perimeter = Sum of All sides

⇒ a + a + a

⇒ 3a

Therefore

    perimeters of a rectangle = perimeters an equilateral triangle

              2(l + b) = 3a

hence, 2(l + b) = 3a is the equation which show that perimeter of rectangle and equilateral triangle is equal.

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The correct statement regarding whether Maple Street and Elm Street are parallel lines is given as follows:

Yes, because angles 1 and 2 are supplementary.

Parallel lines are two lines that do not intersect, or technically, intersect only at infinity.

In this problem, we have that angles 1 and 2 are supplementary angles, hence:

m<1 + m<2 = 180º

As the sum of the measures of supplementary angles is of 180º.

Then these two angles are classified as consecutive interior angles, meaning that Maple Street and Elm Street are parallel lines cut by the transversal River Drive.

Thus the second option is the correct option.

The situation is represented by the image shown at the end of the answer.

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The required equation of the line having a slope of 33 and passing through (-3, - 3) is y = 33x + 96.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Let the required line be y = mx + b.

∴ - 3 = (33)(-3) + b.

- 3 = - 99 + b.

b = 96.

∴ y = 33x + 96 is the required line.

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The series in question converges.

If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on rising or dropping as the terms of the series go to infinity, it is said to be divergent.

The geometric sequence is as follows:

10 - 4 + 1.6 - 0.64 +...

If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.

The common ratio in this case is

r = -4/10

r = -0.4, or -1 -0.4 1.

The presented series is hence convergent.

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The value of m in the triangle XYZ is 16. option D

It is important to note that the sum of angles in a triangle is 180 degrees.

From the information given, we have that;

Then we have that;

Angle MZ + Angle Z = 180

Now, substitute the values into the formula, we have;

(5m - 15) + (7m + 3) = 180°

expand the bracket

5m - 15 + 7m + 3 = 180°

collect like terms

12m - 12 = 180°

12m = 180 + 12

Add the like terms

12m = 192

Make 'm' the subject of formula by dividing both sides by 12, we get;

12m/12 = 192/12

m = 16

The value is 16.

Thus, the value is 16

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Answer:

θ = 56°

Step-by-step explanation:

As OA and OB are both radii, triangle AOB is an isosceles triangle:

⇒ m∠ABO = m∠OAB = 48°

Interior angles of a triangle sum to 180°:

⇒ m∠ABO + m∠OAB + m∠AOB = 180°

⇒ 48° + 48° + m∠AOB = 180°

⇒ m∠AOB = 180° - 48° - 48°

⇒ m∠AOB = 84°

Angles on a straight line sum to 180°:

⇒ m∠AOB + m∠DOB = 180°

⇒ 84° + m∠DOB = 180°

⇒ m∠DOB = 180° - 84°

⇒ m∠DOB = 96°

The tangent of a circle is always perpendicular to the radius.

Therefore, tangent BC is perpendicular to radius OB, and tangent DE is perpendicular to radius OD, so:

OBCD is a quadrilateral.

The interior angles of a quadrilateral sum to 360°:

⇒ m∠OBC + m∠BCD + m∠CDO + m∠DOB = 360°

⇒ 90° + θ + 28° + 90° + 96° = 360°

⇒ θ + 304° = 360°

⇒ θ = 360° - 304°

⇒ θ = 56°

Answer: $96.25

Step-by-step explanation:

Take 89.75 divided by 100% = 0.8975

Then times 7.25% = $6.5

Total is 89.75 + 6.5 = $96.25

The angle, to the degree, that the string makes with the ground is

34.33.

A right-angled triangle can be formed by the string, the height of the kite, and the horizontal distance along the ground to a point directly beneath the kite.

The string represents the hypotenuse (200 feet), and the height (120 feet) represents the opposite side.

The trigonometric ratio sin can be used to calculate the angle between the string and the ground.

sinθ= Perpendicular/hypotenuse

sinθ=120/200

=0.6

Now sin(0.6) = 0.5646

sinθ=0.5646

therefore ,θ

=sin⁻¹(0.5646)

=34.33°

Heights and Distances is a study of Trigonometry applications. It has many real-world applications, such as measuring the height of an object, the depth of an object, the distance between two celestial objects, and so on.

Trigonometric formulas and ratios are useful in the study of heights and distances.

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Answer:

Slope:  - 4/3

Point (4,1)

Step-by-step explanation:

hope this helps