Rodger has 22 coins, all quarters and nickels. The total value of the coins is $2.70. How many of each type of coin does he have?

Answer:

A

Step-by-step explanation:

A

Answer:

9600 words in an hour.

Step-by-step explanation:

There are sixty minutes in an hour.

60/6=10

multiply 960 by 10

960*10=9600

The secretary can type 9600 words in 1 hour.

After the 10th iteration, the estimated value of the root obtained by the bisection method is approximately 0.517. Option B

To solve the equation cos(x) - x * e = 0 in the interval [0, 1] using the bisection method, we start by checking the function values at the endpoints of the interval.

For x = 0:

cos(0) - 0 * e = 1 - 0 = 1

For x = 1:

cos(1) - 1 * e ≈ 0.54 - 2.72 ≈ -2.18

Since the function values at the endpoints have opposite signs, we can apply the bisection method to find the root within the interval.

The bisection method involves repeatedly dividing the interval in half and checking the function value at the midpoint until a sufficiently accurate approximation is obtained. In this case, we will perform 10 iterations.

After the 10th iteration, the estimated value of the root obtained by the bisection method is approximately 0.517.

Therefore, the correct answer is OB) 0.517.

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Since we don't have the initial population size N(0), we'll represent it as a variable. The logistic equation for this population will be: N(t) = 2506 / (1 + (2506 - N0) / (N0 * e^(-0.018 * t))). This equation describes the population growth over time based on the given r value and carrying capacity.

The logistic model is used to describe population growth that is limited by a carrying capacity. In this case, the carrying capacity is given as 2506. The value of r, which represents the maximum growth rate of the population, is given as 0.018.
The logistic equation is given by:
dN/dt = rN(1-N/K)
where N is the population size, t is time, r is the intrinsic growth rate, and K is the carrying capacity.
Given that the carrying capacity is 2506 and the initial population size is n(0), we can rewrite the equation as:
dN/dt = 0.018N(1-N/2506)
This equation describes how the population size changes over time based on the initial population size and the carrying capacity. The equation predicts that as the population approaches the carrying capacity, the growth rate slows down until it eventually levels off.
In summary, the logistic equation satisfied by the population with an initial size of n(0) is dN/dt = 0.018N(1-N/2506), and it can be used to predict how the population size changes over time. This equation shows that population growth is not always unlimited and can be influenced by environmental factors such as carrying capacity.
Based on the information provided, we can construct a logistic equation for the given population growth model. The logistic model is represented by the equation:
N(t) = K / (1 + (K - N0) / (N0 * e^(-r * t)))
Where:
- N(t) is the population size at time t
- K is the environmental carrying capacity (in this case, 2506)
- N0 is the initial population size (N(0))
- r is the intrinsic growth rate (0.018)
- e is the base of the natural logarithm (approximately 2.718)
- t is the time
Since we don't have the initial population size N(0), we'll represent it as a variable. The logistic equation for this population will be:
N(t) = 2506 / (1 + (2506 - N0) / (N0 * e^(-0.018 * t)))
This equation describes the population growth over time based on the given r value and carrying capacity.

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Answer:

x = 1/4

Step-by-step explanation:

The local maximum and minimum values of the function are as follows: maximum at (smaller x value), minimum at (larger x value), and there are no saddle points.

To find the local maximum and minimum values of the function, we need to analyze its critical points, which occur where the partial derivatives are equal to zero or do not exist.

Let's denote the function as f(x, y) = -8 - 2x + 4y - x^2 - 4y^2. Taking the partial derivatives with respect to x and y, we have:

∂f/∂x = -2 - 2x

∂f/∂y = 4 - 8y

To find critical points, we set both partial derivatives to zero and solve the resulting system of equations. From ∂f/∂x = -2 - 2x = 0, we obtain x = -1. From ∂f/∂y = 4 - 8y = 0, we find y = 1/2.

Substituting these values back into the function, we get f(-1, 1/2) = -9/2. Thus, we have a local minimum at (x, y) = (-1, 1/2).

There are no other critical points, which means there are no local maximums or saddle points. Therefore, the function has a local minimum at (x, y) = (-1, 1/2) but does not have any local maximums or saddle points.

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Answer:

Step-by-step explanation:

4\(x^{2}\) - 6 = 394

4\(x^{2}\)  = 400

\(x^{2}\) = 100

x = 10

As per the given graph, the price per gallon at Miguel's Gasoline station is $4.4

Graph:

Graph means a pictorial representation or a diagram that represents data or values in an organized manner.

Given,

Question 6

Six customers are buying gasoline at Miguel's Gasoline Station. The number of gallons bought and the total cost of their purchases are plotted on the graph.

Here we need to find the price per gallon at Miguel's Gasoline Station.

In order to find the price, we have to take the points from the given graph.

Then we the points as, (4,10) and (9, 22)

By looking in the graph, the plotted points will form the straight line on the graph.

So, we have to use the formula for straight line to find the cost on one liter,

For, that we have to find the following,

m = (22 - 10) / (9 - 4)

m = 12/5

And the value of y intercept is,

10 = 12/5 (4) + c

50 = 48 + c

c = 2

The equation for the graph is y = 12/5x + 2

Therefore, the cost of 1 liter of the material is,

y = 12/5 (1) + 2

y = 12/5 + 2

y = 12+10/5

y = 22/5

Therefore, the cost is 4.4.

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Answer:

-8>x

Step-by-step explanation:

-64>8x

divide each side by 8 to get x alone

-8>x

Divide the numerator by the denominator.

When a letter like a, b, x or y pops up in a mathematical expression, it's called a variable, but really it's a placeholder that represents a number of unknown value. You can perform all the same mathematical operations on a variable that you'd perform on a known number. That fact comes in handy if the variable pops up in a fraction, where you'll need tools like multiplication, division and canceling of common factors to simplify the fraction.

Combine like terms in both the numerator and the denominator of the fraction. When you first start handling fractions with variable, this may be done for you. But later on, you might encounter "messier" fractions like the following:

(a + a) / (2_a_ - a)

When you combine like terms, you end up with a much more civilized fraction:

2_a_/a

Factor the variable out of both numerator and denominator of the fraction if you can. If the variable is a factor in both places, you can then cancel it. Consider the simplified fraction just given:

2_a_/a

As a quick aside, any time you see a variable by itself, it's understood to have a coefficient of 1. So this could also be written as:

2_a_/1_a_

Which makes it more obvious that when you cancel the common factor a from both the numerator and denominator of the fraction, you're left with the following:

2/1

Which, in turn, simplifies to the whole number 2.

What if you have a fraction like 3_a_/2? You can't factor a out of both the numerator and the denominator of the fraction, but because it's in the numerator, you can treat it as a whole number. To make sense of this, first write the fraction out thusly:

3_a_/2(1)

You can insert the 1 in the denominator thanks to the multiplicative identity property, which states that when you multiply any number by 1, the result will be the original number you started with. So you haven't changed the value of the fraction at all; you've just written it a little differently.

Next, separate the factors thusly:

a/1 × 3/2

And simplify a/1 to a. This gives you:

a × 3/2

Which can be simply written as the mixed number:

a (3/2)

What if you end up with a messy fraction like the following?

(b2 - 9) / (b + 3)

At first glance there's no easy way to factor b out of both numerator and denominator. Yes, b is present in both places, but you'd have to factor it out of the entire term in both places, which would give you the even messier b(b - 9/b) in the numerator and b(1 + 3/b) in the denominator. That's a dead end.

But if you've been paying attention in your other lessons, you might notice that the numerator can actually be rewritten as (b2 - 32), also known as "the difference of squares," because you're subtracting one squared number from another squared number. And there's a special formula that you can memorize to factor the difference of squares. Using that formula, you can rewrite the numerator as follows:

(b - 3)(b + 3)

Now, take a look at that in the context of the entire fraction:

(b - 3)(b + 3) / (b + 3)

Thanks to that standard formula you either memorized or looked up, you now have the identical factor (b + 3) in both the numerator and the denominator of your fraction. Once you cancel that factor, you're left with the following fraction:

(b - 3) / 1

Which simplifies to just:

(b - 3)

The answer to your question is c

The conclusion VY / WX = UZ / VY satisfies the diagram

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the parallel lines be l , m and n

Now , the transversal line goes through the points W , V and U

The second transversal line goes through the points X , Y and Z

From the parallel lines , we can deduct that

VY / WX = UZ / VY

Hence , the conclusion is VY / WX = UZ / VY

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Answer:

315 Children

Step-by-step explanation:

a+c=330

21a=c

Substitute the c's

a+(21a)=330

22a=330

Divide by 22 on each side

a=15

15 Adults

Now put "a" back into one of the equations.

21(15)=c

315=c

So 315 children and 15 adults.

Answer: 60 square units

Area of a triangle formula: 1/2 * base * height

So, the height is 10 units and base is 12 units

1/2 * 10 * 12

= 60 square units

Answer:

volume of cylinder : πr²×h = π × 5² × 15 = 375π ≈ 1177.5 cm³

Answer:

190.5cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{a}{A}=\frac{\theta }{360^o}\\ \\ a=\frac{\pi r^2 \theta}{360^o}\\ \\ a=\frac{\pi (8.7)^2(126^o)}{360^o}\\ \\ a=\frac{9536.94\pi}{360}in^2\\ \\ a\approx 83.23 in^2\)

Answer:

As the number of retail stands increase by one, the daily revenue increases by $2,298.36 on average, provided that the number of female visitors and food stands remains constant.

Step-by-step explanation:

This is gross relationship of regression model, multiple regression model describes net relationship. The net effect on number of retail stands on daily revenue. The average increase in daily revenue as the number of retail stands increases by one while other variables remains constant.

Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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Answer:

25 to 3 power ÷ 3 = 69

Answer:

3.25 x 10^-5

Step-by-step explanation:

( 5 x 10^-2 ) x ( 6.5 x 10^-4 )

1/20 x 13/20000

13/400000

3.25 x 10^-5

Answer:

Step-by-step explanation:

is it possible to form a triangle with side lengths 3,3, and 4?

3 + 3 = 6 (greater then 4)

4 + 3 = 7 (greater then 3)

so, the answer is yes

in the picture your isosceles acute triangle

Answer: it has no solutions so the answer would be none.

Step-by-step explanation:

Shaded area = (9 + x)(16 + x) = 198

Expand.

x^2 + 25x + 144 = 198

x^2 + 25x - 54 = 0

(x - 2)(x + 27) = 0

x = 2, -27

but x > 0, so

x = 2 cm

Answer:

44

Step-by-step explanation:

thats a right angle, 90 degrees total.

90- 46 = 44.

Try 44 !!

After using the formula for the circumference of a circle, radius of the Ferris wheel is 2.5 ft

To find the radius of the Ferris wheel, we can use the formula for the circumference of a circle:

C = 2πr

Given that there are 16 evenly spaced cars on the Ferris wheel, we can consider the distance between adjacent cars as the circumference of the circle, which is 15.5 ft.

Therefore, we have:

C = 15.5 ft

Substituting this into the formula, we get:

15.5 ft = 2πr

To find the radius (r), we can rearrange the equation:

r = 15.5 ft / (2π)

Using a calculator, we can evaluate this expression:

r ≈ 15.5 ft / (2 * 3.14159) ≈ 2.466 ft

Therefore, the radius of the Ferris wheel is approximately 2.5 ft (rounded to the nearest 0.1 ft).

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Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

Independent samples,Random sampling,  Large sample size and Normal distribution these assumptions are met, you can confidently use the two-sample z-test for a difference in proportions.

In order to use the two-sample z-test for a difference in proportions, the following assumptions must be met:
1. Independent samples: The two samples must be independent of each other. This means that the observations in one sample should not affect the observations in the other sample.
2. Random sampling: The data in each sample should be collected through random sampling. This ensures that each individual in the population has an equal chance of being included in the sample.
3. Large sample size: The sample size of both samples should be large enough to meet the criteria of the Central Limit Theorem. A general guideline is that each sample should have at least 30 observations (n1 ≥ 30 and n2 ≥ 30).
4. Normal distribution: The sampling distribution of the difference in proportions should be approximately normally distributed. This is achieved when the sample sizes are large and the proportions are not too close to 0 or 1. You can check this using the following conditions:

n_1×p_1 > 5, n_1×(1-p_1) > 5, n_2×p_2 > 5, and n_2×(1-p_2) > 5.
If these assumptions are met, you can confidently use the two-sample z-test for a difference in proportions.

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Answer:

D

Step-by-step explanation:

area of triangle  = 1/2*B*H

Assuming its one leg we write

24 = 1/2*6*h

h= 8

With this info we can use Pythagoras Theorum

\(a^{2} = b^{2} + c^{2}\)

\(x^{2} = 8^{2} + 6^{2}\)

\(x^{2} = 100\)

\(\sqrt{100}\)

\(x = 10\)