now assume that a1 = 5, a2 = 6, b1 = 7 and b2 = 4. furthermore, you may now assume that t r1 = t r2 = 40. find the range of distances from the center each sector will be located.

The function represents exponential decay with a rate of 4.98% per time unit.

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant (called the base) and x is a variable that can take on any real value. The exponent x determines how quickly the function grows or decays.

If a is greater than 1, the function represents exponential growth, since each increment of x leads to a proportionally greater increase in the function value. If a is between 0 and 1, the function represents exponential decay, since each increment of x leads to a proportionally smaller decrease in the function value.

For example, the function f(x) = 2^x represents exponential growth, since each time x increases by 1, the value of the function doubles. On the other hand, the function g(x) = (1/2)^x represents exponential decay, since each time x increases by 1, the value of the function is halved.

The given function is y = 990(0.95)ˣ.

We can determine whether the change represents growth or decay by looking at the base of the exponential term, which is 0.95. Since this value is between 0 and 1, we know that the function represents decay.

To determine the percentage rate of decrease, we can compare the value of the function at x=0 (the initial value) with the value of the function at x=1 (one time unit later).

When x=0, we have:

y = 990(0.95)⁰ = 990

When x=1, we have:

y = 990(0.95)¹ = 940.5

Therefore, the percentage rate of decrease is:

[(990-940.5)/990] x 100% = 4.98%

So the function represents exponential decay with a rate of 4.98% per time unit.

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Answer:

Find the perimeter first then the are

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This makes the most sense.

Check the picture below.

Step-by-step explanation:

\( {c}^{2} = {a}^{2} + {b}^{2} \\ {c}^{2} = {15}^{2} + {15}^{2} \\ {c}^{2} = 450 \\ c = \sqrt{450} = \sqrt{ {15}^{2} \times 2 } = 15 \sqrt{2} \)

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:

A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)

A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²

A = 276 cm²

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

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To find c, cdf and P(. 1 ≤ X <. 5), the calculation is given.

Suppose that X has the density function f (x) = cx² for 0 ≤ x ≤ 1 and f (x) = 0 otherwise.
a. Find c.
To find c, we need to use the fact that the integral of the density function over the entire range of x should equal 1. That is,
∫0¹ f(x) dx = 1
Substituting the given density function, we get
∫0¹cx² dx = 1
Integrating and simplifying, we get
c(1/3) = 1
Solving for c, we get
c = 3
So, the value of c is 3.
b. Find the cdf.
The cdf is the integral of the density function from the lower limit of x to a given value of x. That is,
F(x) = ∫₀ˣ f(t) dt
Substituting the given density function and simplifying, we get
F(x) = ∫₀ˣ 3t²dt
Integrating and simplifying, we get
F(x) = x³
So the cdf is F(x) = x³
c. What is P(.1 ≤ X < .5)?
To find this probability, we need to find the difference between the cdf at the upper limit and the cdf at the lower limit. That is,
P(.1 ≤ X < .5) = F(.5) - F(.1)
Substituting the cdf that we found earlier, we get
P(.1 ≤ X < .5) = (0.5)³ - (0.1)³
Simplifying, we get
P(.1 ≤ X < .5) = .125 - .001
P(.1 ≤ X < .5) = 0.124
So the probability that X is between .1 and .5 is .124.

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A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.

Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.

Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.

Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.

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Answer:

68°

Step-by-step explanation:

since the ball is placed or comes from a straight line (which is the wall) it means that when you add all those angles the final answer has to be 180 because angles in a straight line add up to 180°

68°+44°+1=180

112°+1=180

1=180-112

=68°

I hope this helps

The measure of ∠1 is 68 degrees.

We have Lisa who kicked a ball against the wall at the indicated angle.

We have to determine the measure of the angle 1 in degrees.

A straight line has an angle of 180 degrees.

According to question, we have -

∠3 = 68 degrees

∠2 = 44 degrees

Therefore -

∠3 + ∠2 + ∠1 = 180

68 + 44 + ∠1 = 180

112 + ∠1 = 180

∠1 = 180 - 112

∠1 = 68 degrees

Hence, the measure of ∠1 is 68 degrees.

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The computation shows that the number of years ruled is 41 years.

From the information, Octavian became the emperor of Rome in 27 B.C and he ruled until his death in A.D. 14.

Therefore, the number of years that he rules will be:

= 14 - (-27)

= 14 + 27

= 41

Therefore, the number of years will be 41.

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Answer:

x=10

Step-by-step explanation:

-3+x=7

Add 3 to both sides.

7+3=10

x=10

Answer:

x=10

Step-by-step explanation:

-3+x=7

You have to add 3 to both sides to cancel out the -3

x=10

That leaves you with x=10

The probability that both marbles are blue is 1/4.

Since the marble is put back into the bag before the second draw, the probability of drawing a blue marble on the first draw is 3/6 or 1/2, and the probability of drawing a blue marble on the second draw is also 3/6 or 1/2.

The probability of both events happening together (drawing a blue marble on the first and second draws) is equal to the product of the probabilities of each event occurring separately, since the two events are independent of each other:

P(Blue on first draw AND Blue on second draw) = P(Blue on first draw) x P(Blue on second draw)

= 1/2 x 1/2

= 1/4

Therefore, the probability of drawing two blue marbles in a row with replacement is 1/4 or 25%.

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Answer:

Solve.

Step-by-step explanation:

make the 2 3 and 1 then turn them into 20 30 and 10 then you need to add them together to get the answer divide that by thirty and if its more than half yes, less than half no.

Answer:exact form: decimal form=

70082

Explanation=Write in radical form: exact form: decimal form: ...

Answer: exact form: decimal form: ...

Answer:              

(Theres not much of a way for me to type the answer, so i added it into a png. hope it helps!)

The equation that models the amount of gas left in the car as Phan drives is \((g = 18 - 2h)\) and the total amount of gasoline does it take to fill her tank is 18 gallons.

Given :

The following steps can be used in order to determine the equation that models the amount of gas left in the car as Phan drives and the total amount of gasoline:

Step 1 - The two-point form of the line can be used in order to determine the equation that models the amount of gas left in the car as Phan drives.

\(\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}\)

Step 2 - Now, substitute the value of \((x_1,y_1)\) and \((x_2,y_2)\) in the above expression.

\(\dfrac{g-12}{h-3}=\dfrac{8-12}{5-3}\)

Step 3 - Simplify the above equation.

\(\begin{aligned}\\(g - 12)&=-2(h-3)\\g - 12&=-2h+6\\g &= 18-2h\\\end{aligned}\)

Step 4 - Now, substitute the value of (h = 0) in the above equation.

\(g = 18-2(0)\\g = 18 \; {\rm gallons}\)

Therefore, the correct option is A).

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Answer:

g = 18 – 2h; 18 gallons

Step-by-step explanation:

The answer above is correct.

The coordinates of the point N dividing the line LM, with L(-3, 1) and N(4, 9) in the ratio 2:3, found using the internal section formula is \(\left(-\frac{1}{5} ,\, \frac{21}{5} \right)\)

A ratio indicates the number of times one quantity a is contained in another quantity b.

The coordinates of the point L = (-3, 1), the coordinates of the point M = (4, 9)

The ratio in which the point N divides LM = 2:3

The specified ratio of the sides are;

\(\dfrac{LN}{MN} = \dfrac{2}{3}\)

The coordinates of the points N is found using the internal section  formula as follows;

\(C(x, y) = \left(\frac{m\times x_2 + n\times x_1}{m+n} , \,\frac{m\times y_2 + n\times y_1}{m+n} \right)\)

Where;

(x₁, y₂), and (x₂, y₂) are the endpoints of the line

m:n is the ratio the point C divides the line

Which indicates;

\(N(x, y) = \left(\frac{2\times 4 + 3\times (-3)}{2+3} , \,\frac{2\times 9 + 3\times 1}{2+3} \right) = \left(-\frac{1}{5} ,\, \frac{21}{5} \right)\)

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Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation:

x and y-intercept :

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

Absolute min:

An absolute maximum point is a point where the function obtains its greatest possible value.

Absolute max :

An absolute minimum point is a point where the function obtains its least possible value.

Local Extrema (Local Maxima/Minima): The local maxima and minima on a graph refer to the maximum and minimum points of the graph over a specific interval of the graph as opposed to the entire graph, so there can be multiple local maxima and minima of a given graph.

When considering which points are the absolute maximum and the absolute minimum of a graph, we not only need to consider local extrema (a maximum/minimum of a graph on some interval that contains the point), but we also need to consider the endpoints (the furthest left/right points on our graph). By looking at the y-values for each of these points, we can identify the absolute maximum of the graph as the point with the highest y-value, and we can identify the absolute minimum as the point with the lowest y-value.

Step 1: Identify local maxima/minima, as well as the endpoints.

From this graph, we can see that our graph is on the interval

This means we have our endpoints at [-1,-1] , [4,1] ,

to consider. We also observe that we have one local minima and one local maxima in between these points on our interval. The estimated points are all shown in the image.

absolute minimum point : [-1,-1]

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Answer: The area of the circle that passes through the three vertices of the isosceles triangle is (3sqrt(2))/2 pi square units.

Step-by-step explanation:

Since the circle passes through the three vertices of the isosceles triangle, the center of the circle must be the midpoint of the base of the triangle. Let's call this point O.

Let's draw a perpendicular from O to the midpoint of the third side of the triangle. This will bisect the base and form two right triangles. Let's call the height of each of these triangles h.

Since the isosceles triangle has two sides of length 3, we can use the Pythagorean theorem to find h:

h^2 + (3/2)^2 = 3^2

h^2 + 9/4 = 9

h^2 = 9 - 9/4

h^2 = 27/4

h = sqrt(27)/2 = (3sqrt(3))/2

Now, we know that the radius of the circle is equal to the distance from O to any of the vertices of the triangle. Let's call this distance r.

From the right triangle, we know that r^2 + h^2 = (2/2)^2 = 1

r^2 = 1 - h^2

r^2 = 1 - (27/4)

r^2 = -23/4

Since r is the distance from the center of the circle to a point on the circle, it must be positive. However, we see that r^2 is negative, which is impossible. Therefore, the circle cannot exist.

Since it is impossible for the circle to exist, we cannot find its area.

In this particular data set, 10 is the only value that occurs more than once, so it is the only mode

The mode is the value that occurs most frequently in a data set. In the given data set {10, 30, 10, 36, 26, 22}, we can see that the value 10 occurs twice, and all other values occur only once. Therefore, the mode of the data set is 10, since it occurs more frequently than any other value in the set.

Note that a data set can have multiple modes if two or more values occur with the same highest frequency. However, in this particular data set, 10 is the only value that occurs more than once, so it is the only mode.

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\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

Answer: relation 3 function relation 4 not a function

Step-by-step explanation:

The amount in the account two years from now will be $17,548.09. The correct option is D.

Calculate the amount in the account two years from now, we need to consider the compounding of interest over the two-year period.

Calculate the amount after one year. The initial deposit of $5,000 will accumulate interest compounded every 6 months at a nominal rate of 12%.

Since the compounding period is every 6 months, there will be a total of 4 compounding periods over the course of one year.

Using the formula for compound interest, the amount after one year will be:

A1 = P(1 + r/n)^(nt)\(P(1 + r/n)^{(nt)\)

P = Principal amount (initial deposit) = $5,000

r = Nominal interest rate = 12% = 0.12

n = Number of compounding periods per year = 2 (compounded every 6 months)

t = Time in years = 1

A1 = 5000\((1 + 0.12/2)^{(2*1)\) = $5,000\((1 + 0.06)^2\) = $5,000\((1.06)^2\) ≈ $5,638.00

After one year, the amount in the account will be approximately $5,638.00.

Next, we add $10,000 to the account, resulting in a total balance of $5,638.00 + $10,000 = $15,638.00.

Finally, we calculate the amount after the second year by compounding the interest on the new balance. Again, there will be 4 compounding periods over the two-year period.

A2 = \(P(1 + r/n)^{(nt)\)

P = Principal amount (new balance after one year) = $15,638.00

r = Nominal interest rate = 12% = 0.12

n = Number of compounding periods per year = 2 (compounded every 6 months)

t = Time in years = 1

A2 = 15638\((1 + 0.12/2)^{(2*1)} = 15638(1 + 0.06)^2 = 15638(1.06)^2\) ≈ $17,548.09

Therefore, the amount in the account two years from now will be $17,548.09.

The closest answer choice to this amount is D. 17,548.

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The maximum and minimum measurements are 5 and -3 respectively.

f ( x ) = -x^3 +3x^2+ 45 x + 10

f' l x ) = 0

0 = - 3x^2 +6x +45

x = 5,- 3.

f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174

f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58

f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1

+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185

Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}

                        = 185 at x=5

Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}

                      = - 71 at x= -3

In light of this, the maximum and minimum values are 5 and -3, respectively.

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The height of the triangle whose base is 4 cm and area is 20 cm² is 10 cm .

It is given that base is 4 cm and area is 20 cm² .

Putting above values in area formula , we get

         Area = 1 / 2 × base × height

            20  = 1 / 2 × 4 × height

             20 = 2 × height

              10 cm = height

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The complete question is given below :

Find the height of the triangle whose base is 4cm and area is 20 cm².

diameter (d)= 2r=2*4=8ft

Step-by-step explanation:

circumference =2πr

=2 *4*22/7

=25.14 ft

also

Area=πr^2

=4^2 *22/7

50 .28 sq ft

Answer:

Diameter: 8ft

circumference: 25.12

area: 50.24 square feet

Step-by-step explanation:

radius is 4ft

Diameter is 8ft

circumference 2×pi×radius

2×3.14×4

25.12

area (pi)radius^2

3.14×(4)^2

3.14×(16)

50.24

50 square feet

Answer:

18x + 96

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

x=-11/3

Step-by-step explanation:

expand the brackets: 4x+12= 1

this is now a normal equation

solve the equation

-12 from both sides

4x=-11

divide by 4 both sides

x= -11/4

this is because 11 cannot be divided by 4 exactly so we put it in fraction form .

Answer: y= -7

Step-by-step explanation:

First you need to rearrange one of the equations(6x+2y=4)so that x is equal to some equation in order to substitute it( you can do x or y depends which u want to solve)

Then u get x= 2/3 - 1/3y, now that you have an equation to replace x in the second one. Now you have 3(2/3-1/3y) -5y=44

Now all u do is solve for y

And u get the answer

Answer: y=-7

Step-by-step explanation:

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces