Please help me answer these two questions!!!

For function f(t) = 1.25^t, it is an exponential growth.

The percent rate of change per unit t is found by taking the derivative of the function:

f'(t) = ln(1.25) * 1.25^t ≈ 9.2%

Since f'(t) is positive, the function represents exponential growth.

For function g(t)=5^-t:

The percent rate of change per unit t is found by taking the derivative of the function:

g'(t) = -ln(5) * 5^-t ≈ -13.9%

Since g'(t) is negative, the function represents exponential decay.

For function h(t) = 1.20(t/11):

The percent rate of change per unit t is found by taking the derivative of the function:

h'(t) = 1.20/11 ≈ 10.9%

Since h'(t) is positive, the function represents exponential growth.

For function k(t) = 0.63t:

The percent rate of change per unit t is found by taking the derivative of the function:

k'(t) = 0.63 ≈ 63.0%

Since k'(t) is positive, the function represents exponential growth.

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Therefore, her net income is $77408.

A coefficient is a numerical factor that is multiplied by a variable or a term in an algebraic expression. In mathematics, coefficients are commonly used in polynomial functions, where they determine the degree of the polynomial and the specific values of the function.

For example, in the polynomial function[tex]f(x) = 3x^2 + 2x - 1[/tex], the coefficients are 3, 2, and -1. The coefficient 3 is multiplied by the variable. [tex]x^2[/tex], the coefficient 2 is multiplied by the variable x, and the coefficient -1 is the constant term.

Coefficients are also commonly used in statistics, where they are used to describe the relationship between variables in a statistical model. In regression analysis, for example, coefficients are used to represent the slope and intercept of a line that best fits the data.

by the question.

To calculate her net income, we need to subtract the total tax paid from her gross income:

[tex]Net Income = Gross Income - Income Tax - Medicare Levy[/tex]

Substituting the given values, we get:

[tex]Net Income = $105500 - $26982 - $2110[/tex]

[tex]Net Income = $77408[/tex]

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Answer: 4

Step-by-step explanation:  8x11=88.

352=88x

x=352/88

x=4

Check:

11x8x4=352

The values of Mean = 6.3 and Median = 6

A dot plot is a type of data visualization that displays data points as dots on a number line. Each dot represents a single data point and is placed at the corresponding value on the number line.

Here, each dot corresponds to a particular value in the data set, below diagram.

Mean: The mean is calculated by dividing the total value of all the data sets by the total number of data sets.

You can figure out the total as follows:

0 (1) = 0            4 (3) = 12             5(8) = 40          6(3) = 18

7(1) = 7              8(5) = 40             9(2) = 18           10 (3) = 30

Sum = 0+12+40+18+7+40+18+30 = 165

Number of data set = 26

⇒Mean = 165/26

             = 6.346 ≈ 6.3               (nearest tenth place)

⇒Median: The center value in the data collection is known as the median. Since there are 26 data points total, the middle value is located between data points 13 and 14. The median value will be determined by averaging the 13th and 14th data points.

So, the 13th and 14th values both are 6.

Therefore, median = {6+6} ÷ 2 = 12/2 = 6

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Complete Question-

Answer:

$35.75

Step-by-step explanation:

$6.50 + $3.90(7.5) = $6.50 + $29.25 = $35.75

The answer is 8.6+(-6.1). This is because addition and subtraction are inverse operations.

Subtraction that involves taking one number away from another. It is the inverse of addition and is represented by the minus sign (-).

This means that when you add two numbers and then subtract the same amount, the result is the same as just adding the two numbers.

Similarly, when you subtract two numbers and then add the same amount, the result is the same as just subtracting the two numbers.

Therefore, 6.1+8.6 is equivalent to 8.6+(-6.1).

Using mathematical notation, we can represent this expression as 6.1+8.6 = 8.6+(-6.1).

To add and subtract the numbers, we can use the traditional column method.

First, we write out 6.1+8.6 as 6.1 - (-8.6). Then, we add the numbers in each column, starting with the ones column:

Ones column: 1+6=7

Tens column: 8-8=0

And our answer is 7,0. We can also write this as 8.6+(-6.1) to show that the two expressions are equivalent.

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(i) The domain of f(x) is all real numbers, since there are no restrictions on the input variable x.

(ii) We have:

f(x) = x^4 - 2x^3

f'(x) = 4x^3 - 6x^2

f''(x) = 12x^2 - 12x

(iii) To find the critical points, we need to solve the equation f'(x) = 0:

4x^3 - 6x^2 = 0

2x^2(2x - 3) = 0

x = 0 or x = 3/2

So the critical points are (0,0) and (3/2, -27/16).

(iv) To determine where f(x) is increasing or decreasing, we need to examine the sign of f'(x) on different intervals. We can make a sign chart for f'(x):

| x | -∞ | 0 | 3/2 | +∞ |

|---------|--------|-------|-------|--------|

| f'(x) | - | 0 | + | + |

From the sign chart, we see that f(x) is decreasing on the interval (-∞, 0) and increasing on the interval (0, 3/2) and (3/2, +∞).

(v) To find the relative extrema, we need to examine the sign of f'(x) around the critical points. We can make a table:

| x | 0- | 0+ | 3/2- | 3/2+ |

|---------|-------|-------|-------|-------|

| f'(x) | - | + | - | + |

| f(x) | 0 | 0 | -27/16| -27/16|

From this table, we see that f(x) has a relative minimum of -27/16 at x = 3/2, and no relative maximum or minimum at x = 0.

(vi) To find the intervals where f(x) is concave up or concave down, we need to examine the sign of f''(x) on different intervals.

We can make a sign chart for f''(x):

| x | -∞ | 0 | 1 | +∞ |

|---------|--------|-------|------|--------|

| f''(x) | + | - | + | + |

From the sign chart, we see that f(x) is concave down on the interval (-∞, 0) and concave up on the intervals (0, 3/2) and (3/2, +∞).

(vii) To find the points of inflection, we need to solve the equation f''(x) = 0:

12x^2 - 12x = 0

12x(x - 1) = 0

x = 0 or x = 1

So the points of inflection are (0,0) and (1, -1).

(viii) To sketch the graph of f(x), we can use the information we have gathered so far.

At x = 0, f(x) has a relative minimum of 0 and is concave down. At x = 3/2, f(x) has a relative minimum of -27/16 and is concave up. The point (1, -1) is a point of inflection.

Based on this information, we can sketch a graph of f(x) that looks like this:

```

|

|

|

|

|

|

|

--------o------------o-------

0 3/2 x-axis

```

The graph is a "U" shape that opens upward, with a relative minimum at (3/2, -27/16) and a point of inflection at (1, -1).

For any rectangle ABCD the statement;

1. ∠A ≅ ∠D is always true

2. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is sometimes true

A rectangle is a quadrilateral that has two pairs of parallel and congruent opposite sides and four right angles (90 degree angles). A rectangle is a special case of a parallelogram.

1. ∠A ≅ ∠D

The above statement is always true for rectangles. In Euclidean geometry, by the definition of a rectangle, the four interior angles are right angles, which means m∠A = m∠B = m∠C = m∠D = 90°, therefore; ∠A ≅ ∠B ≅ ∠C ≅ ∠D.

The statement; ∠A ≅ ∠D, according to the above expression and the transitive property of congruence, is always true.

Please find attached the drawing of the rectangle, created with MS Word that can be used to illustrate the congruence of the angles with the angle marks indicating perpendicular sides, forming 90° angles, which indicates that the angles are congruent.

   A_____[tex]{}[/tex]_____B

    |            [tex]{}[/tex]          |

    |           [tex]{}[/tex]           |

    |          [tex]{}[/tex]            |

    |          [tex]{}[/tex]            |

    |           [tex]{}[/tex]           |

    |____[tex]{}[/tex]______|

    D                     [tex]{}[/tex] C

2. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]

The above statement is sometimes true for rectangles. The definition of a rectangle indicates that the two pairs of opposite sides are congruent. In particular, [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are congruent, aa well as sides [tex]\overline{BC}[/tex] and [tex]\overline{AD}[/tex] are also congruent. The sides [tex]\overline{BC}[/tex] and [tex]\overline{CD}[/tex] are congruent if or when the rectangle is a square, therefore, the statement [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is sometimes true.

Please find attached the drawings created with MS Word which illustrates when [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] and when [tex]\overline{BC}[/tex] [tex]\ncong[/tex] [tex]\overline{CD}[/tex]

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The formula for Py(Y) = ∑P y,z (y, z) for z ∈ Z is consistent with the third Axiom of the probability measure.

The third Axiom of the probability measure states that the sum of probabilities of all possible outcomes of an event is equal to 1. In the context of two discrete random variables Y and Z, this axiom means that the sum of probabilities of all possible pairs (y, z) is equal to 1.

The formula PY(Y) = ∑P y,z (y, z) for z ∈ Z is related to this axiom because it represents the probability of the random variable Y taking on a specific value y, regardless of the value of Z. The summation is taken over all possible values of z in Z, and P y,z (y, z) represents the joint probability of Y and Z taking on the specific values (y, z).

Since the sum of probabilities of all possible pairs (y, z) is equal to 1, the sum of probabilities of all possible values of Y, represented by PY(Y), must also be equal to 1.

Therefore, the formula for PY(Y) is consistent with the third Axiom of the probability measure.

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Answer:

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a simple fraction. Therefore 0.6263646 is irrational.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{257}}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ (\sqrt{257})^2= (x)^2 + (15)^2\implies 257=x^2 + 225 \\\\\\ 32=x^2\implies \sqrt{32}=x\implies 4\sqrt{2}=x\implies 5.66\approx x[/tex]

Answer:

9 x 17 is greater than 9 x 15

Step-by-step explanation:

You can tell without finding the product because 17 is greater than 15, and the higher the number you multiply by, the larger the solution will be. I hope this helped :)

Answer:

165.5

Step-by-step explanation:

Because you have to add them together and then divide

Answer:

The answer is A: 2500 pi

Step-by-step explanation:

To find the volume of a cylinder use the formula:

π[tex]r^{2}h[/tex]

So we know that the diameter is 10, so radius must be 10/2 or 5.

Now we square 5 to get 25.

Multiply 25 times height which is 100.

So 25 x 100 is equal to 2500

Now multiply the pi or just let it stay like that

The answer is 2500π.

Hope this helps!

The inequality that has the solutions represented by the graph?

2x - 5 > 3

The solution of the inequality represented by the graph is x > 4

The solution of the given inequalities are:

5 - x > 4;

solution: x < 1

2x + 1 ≥ 9;

solution: x ≥ 4

2x - 5 > 3

solution: x > 4

6x - 7 > 5

solution: x > 3

2. Considering the inequality statement given:

n ≤ 3: This is a solution.

If we substitute n with 3, we get 5 + 2(3) ≤ 11, which simplifies to 11 ≤ 11, which is true. And if we substitute n with any number less than 3, the inequality will still hold.

3 ≥ n: This is also a solution.

If we substitute n with 3, we get 5 + 2(3) ≤ 11, which simplifies to 11 ≤ 11, which is true. And if we substitute n with any number greater than 3, the inequality will still hold.

n ≤ 8: This is a solution.

If we substitute n with 8, we get 5 + 2(8) ≤ 11, which simplifies to 21 ≤ 11, which is false. But if we substitute n with any number less than or equal to 8, the inequality will still hold.

3 ≥ n: This is the same as the second representation, so it is also a solution.

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Complete question:

Which inequality has solutions represented by the graph?

5 - x > 4

2x + 1 ≥ 9

2x - 5 > 3

6x - 7 > 5

Consider the inequality Five plus two times a number n is less than or equal to eleven. Indicate whether each representation is or is not a solution.

n ≤ 3

3 ≥ n

n ≤ 8

3 ≥ n

[tex]\tan(68^o )=\cfrac{\stackrel{opposite}{AC}}{\underset{adjacent}{7}}\implies 7\tan(68^o)=AC\implies 17.3\approx AC[/tex]

Make sure your calculator is in Degree mode, as opposed to Gradians or Radians mode.

Quick Clarification:

if your put in your calculator tan(68) in Radians mode, your calculator assumes you meant 68 radians, if in Gradians mode, your calculator assumes you meant 68 Gradians, now, if you have it on Degree mode, your calculator thinks you meant tan(68°).

All trigonometric calculations depend on the mode used, since a circle can be divided in many ways and thus different modes mean, different angles, 68 Radians are extremely different than 68°.

After answering the provided question, we can conclude that Therefore, circle the length of the minor arc AB is approximately 50.9 cm.

A circle appears to be an a double component that is defined as the collection of all points in a jet that are equidistant out from hub. A circle is typically depicted with a capital "O" for the centre and a bottom end "r" for the radius, which represents the distance from where it started to any point on the circle. The formula 2r gives the girth (the distance from the center of the circle), where (pi) seems to be a proportionality steady roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which is the quantity of space inside the circle. To calculate the length of the minor arc AB, we need to first find the central angle that it subtends.

C = 2πr

r = C/(2π)

r = 65/(2π) ≈ 10.34 cm

angle = (arc length / radius) x (180/π)

ADB = 360° - AOB

ADB = 360° - 72° = 288°

angle ADB = (arc length AB / 10.34) x (180/π) = 288°

arc length AB = (288° x 10.34 cm x π) / 180 ≈ 50.9 cm

Therefore, the length of the minor arc AB is approximately 50.9 cm.

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Let's assume that the width of the rectangular poster is "x".

According to the problem, the length is 8 more inches than half the width, which can be expressed as:

length = (1/2)x + 8

The area of the poster is given as 40 square inches, so we can write the equation:

Area = length × width

Substituting the values of length and width in terms of "x", we get:

40 = ((1/2)x + 8) × x

Simplifying the equation:

40 = (x^2)/2 + 8x

Multiplying both sides by 2 to eliminate the fraction:

80 = x^2 + 16x

Rearranging the equation in standard quadratic form:

x^2 + 16x - 80 = 0

Using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 16, and c = -80

x = (-16 ± sqrt(16^2 - 4(1)(-80))) / 2(1)

x = (-16 ± sqrt(736)) / 2

x = (-16 ± 8sqrt(9)) / 2

We can discard the negative solution since width cannot be negative:

x = (-16 + 24) / 2

x = 4

So, the width of the poster is 4 inches.

Using the equation for length:

length = (1/2)x + 8

length = (1/2)(4) + 8

length = 2 + 8

length = 10

Therefore, the dimensions of the poster are 10 inches by 4 inches.

Answer:

43. All real numbers

44. x = 1/4

45. No solution

Step-by-step explanation:

The technique here is two write two expressions with the same base that are equal. Then set the exponents equal and solve for the variable.

43.

[tex] 3^{3x + 6} = 27^{x + 2} [/tex]

[tex] 3^{3x + 6} = (3^3)^{x + 2} [/tex]

[tex] 3^{3x + 6} = 3^{3(x + 2)} [/tex]

[tex] 3^{3x + 6} = 3^{3x + 6} [/tex]

[tex] 3x + 6 = 3x + 6 [/tex]

Answer: all real numbers

44.

[tex] 3^{4x + 3} = 81 [/tex]

[tex] 3^{4x + 3} = 3^4 [/tex]

[tex] 4x + 3 = 4 [/tex]

[tex] 4x = 1 [/tex]

[tex]x = \dfrac{1}{4}[/tex]

45.

[tex] 4^{x + 3} = 2^{2(x + 1)} [/tex]

[tex] (2^2)^{x + 3} = 2^{2(x + 1)} [/tex]

[tex] 2^{2(x + 3)} = 2^{2(x + 1)} [/tex]

[tex] 2(x + 3) = 2(x + 1) [/tex]

[tex] x + 3 = x + 1 [/tex]

[tex] 3 = 1 [/tex]

No solution.

The triangles on the front of the Louvre Pyramid are all isosceles triangles.

The building acts as a visible reminder of the importance of the museum's Egyptian Antiquities collections.

The primary entry point to the Louvre is the I.M. Pei Pyramid, which is situated in the courtyard. The building acts as a visible reminder of the importance of the museum's Egyptian Antiquities collections.

A graph on the right AB = 35 meters {Given}

AE = 32 meters {Given}

Because AE = BE = 32 meters

So <EAB = <ABE By measure,

<EAB=663°

So <ABE=663°.

So <AEB = 180° - LEAB-LABE.

= 180°-66.3° - 66.3° =47.4°

So, ΔABE is an isosceles triangle.

And the four triangles are all isosceles triangles.

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Step-by-step explanation:

N = 50 000   and  N = 1000 * 2^t

so

50 000 = 1000 2^t      divide both sides of the equation by 1000

50 = 2^t      LOG both sides

log 50 = t log 2

log 50 / log 2 = t = 5.64 hours

I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

There are 2,000 pounds in one ton. Therefore, to convert 25 tons to pounds, we can multiply 25 by 2,000:

25 tons x 2,000 pounds/ton = 50,000 pounds

So there are 50,000 pounds in 25 tons.

Answer:

There are 32 apples in the bag.

Step-by-step explanation:

To find the number of apples in the bag, we can use the formula:

number of apples = total mass of apples / average mass of each apple

Given that the bag of apples has a mass of 4 kg, and the average mass of each apple is 1/8 kg, we can substitute these values into the formula to get:

number of apples = 4 kg / (1/8) kg/apple

Simplifying the right-hand side by dividing 4 kg by (1/8) kg/apple, we get:

number of apples = 4 kg * 8/apple = 32 apples

Therefore, there are 32 apples in the bag.

Answer:

Step-by-step explanation:

It is simple by averaging formula as follows
Total mass/average mass = Total apples
4/(1/8)= 32 Apples

The 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is (62.49,69.51). So, the Lower and Upper end point are 62.49, 69.51 respectively.

We have a survey of 53 randomly selected homeowners. So,

Sample size, n = 53

Mean spend of home maintenance, μ

= $66 per month

Standard deviations, σ = $ 11 per month

We have to determine the Lower and Upper end point or bound of confidence interval. First we calculate the Z score for 98% of confidence interval. The level of significance, α = 0.02 and α/2 = 0.01, so using distribution table [tex]z_{ \frac{\alpha}{2}} = 2.326[/tex]

Now, Margin of error , [tex]MOE = z_{\frac{\alpha}{2}} ( \frac{\sigma }{\sqrt{}n}) [/tex]

[tex] = 2.326 ( \frac{11}{ \sqrt{}53 })[/tex]

=> E = 3.51

At 98% confidence interval estimate of the population mean is, [tex]\bar x - E < \mu < \bar x + E[/tex]

[tex]66 - 3.51 < \mu < 66 + 3.51[/tex]

=> 62.49 < μ < 69.51

Therefore, Lower end point or bound

= 62.49 and Upper end point or bound

= 69.51.

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Answer:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Step-by-step explanation:

All of these work. I hope this helps! Pls give brainliest!

Answer:

Your answer would be  

x/3<12

Let us assume that the variables:

d = distance

t = time (in seconds)

~

The question assumes that the horse will move 15 meters every second. Therefore:

d = 15t

IF:

t (time) = 1 seconds, then:

d = 15(1)

d = 15

IF:

t (time) = 2 seconds, then:

d = 15(2)

d = 30

IF:

t (time) = 5 seconds, then:

d = 15(5)

d = 75

~

As you can see, the graphed numbers are much more larger than the numbers that you have already written, and so it is best to change the numbers. Generally the y-axis is used for time (in this case, seconds), whlie the x-axis is used for distance (in this case, meters).

~

Answer:

a.) P(x)= 3x - 1120

b.) make $1,180 profit in 1 week by selling 800 calculators

Step-by-step explanation:

a.) P(x)=R(x)-C(x)

R(x)=11x; C(x)=8x + 1220   assuming they are asking for profit in a week

P(x)= 3x - 1220

b.) P(800) = 3(800) -1220 = 1180

The area of the shaded region is,

(3) 100.28 sq. unit

(4) 72 sq.m

(5) 49.09  sq.m

What is the area?

The area of an object is the amount of room it occupies in two dimensions. It is the calculation of how many unit squares entirely encircle the area of a closed figure.

The accepted measure of area is the square unit, which is frequently expressed as square inches, square feet, etc. Most shapes and objects have edges and angles.

(3)

To calculate the area of the semi-circle having a radius of 3 cm,

[tex]A_1=\frac{1}{2} \pi r^2\\A_1=\frac{1}{2} \pi(3)^2\\A_1=14.14 \ \ sq. \ cm[/tex]

To calculate the area of the rectangle having a width of 12 cm and a height of 6 cm,

[tex]A_2=l*w\\A_2=12*6\\A_2=72 \ sq.cm[/tex]

To calculate the area of the semi-circle having a radius of 3 cm,

[tex]A_3=\frac{1}{2} \pi (3)^2\\A_3=14.14[/tex]

The shaded region's size was calculated using

[tex]A=A_1+A_2+A_3\\A=14.14+72+14.14\\A=100.28 \ \ sq.cm[/tex]

(4)

To calculate the area of the rectangle having a width of 13 m and a height of 8 m,

[tex]A_1=l*w\\A_1=13*8\\A_1=104 \ sq.m[/tex]

To calculate the area of an unshaded triangle,

[tex]A_2=\frac{1}{2} *b*h\\A_2=\frac{1}{2} *8*8\\\\A_2=32 \ sq.m[/tex]

The shaded region's size is thus,

[tex]A=A_1-A_2\\A=104-32\\A=72 \ sq.m[/tex]

(5)

The shaded region's size was calculated using

[tex]A=Area \ of \ circle-Area \ of \ square\\A=\pi (6)^2-(8)^2\\A=36\pi -64\\A=49.09 \ sq.m[/tex]

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