need someone to help me understand how to do an Exponential Equation

Answer:

x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x + 5

2x - 3 < x + 2 and x + 2 ≤ 5

x < 5 and x ≤ 3

Answer: x < 5

Option (b) "3/4 to the power of 2 - 6/16" is the expression that is  equivalent to 3/16.

A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:

The expression is (number/variable, arithmetic operator, number/variable).

Solution according to the given information:

Given, x = 3/4

Option(a): 2x+1/16 = (2×3/4) +1/16

                              = 3/2 + 1/16

                              =25/16

Which is not equal to 3/16

Option(b): (3/4)² - 6/16 = 9/16 - 6/16 = 3/16

Which is equivalent to 3/16

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[tex]Area = \dfrac{6(7)}{2} = \dfrac{42}{2} = 21 \ cm^{2}[/tex]

It takes approximately0.082 seconds for the eraser to hit the student in the head.

The equation that models the flight of the eraser is h(t)=-16t^(2)+35t+6. We need to find the time it takes for the eraser to hit the student's head, which is 3 feet off the ground. This means that we need to solve the equation h(t)=3 for t.

First, we will set h(t) equal to 3 and rearrange the equation:

-16t^(2)+35t+6=3

Next, we will subtract 3 from both sides of the equation and simplify:
-16t^(2)+35t+3=0

Now, we will use the quadratic formula to solve for t:
t= (-35±√(35^(2)-4(-16)(3)))/(2(-16))

Simplifying further, we get:
t= (-35±√(1417))/(-32)

Using a calculator, we can find the approximate values of t:
t≈0.082 or t≈2.27

Since we are looking for the time it takes for the eraser to hit the student's head, we will choose the larger value of t, which is 0.082.

Therefore, it takes approximately0.082 seconds for the eraser to hit the student in the head.

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Answer:

2/3 (-9+3) simplifies to 2/3 (-6) which is equal to -4.

Step-by-step explanation:

To simplify 2/3(-9+3), we need to start by simplifying the expression inside the parentheses, which is -9+3=-6. Therefore, we can rewrite the expression as 2/3(-6).

Now we can apply the distributive property of multiplication over addition/subtraction to simplify further. This property states that a(b+c) = ab + ac. So, 2/3(-6) can be written as:

2/3 x -6 = 2/3 x (-1 x 6) = 2/3 x (-1) x 6 = -2/3 x 6

Now we just need to multiply -2/3 by 6, which gives us -12/3 or -4. Therefore, 2/3(-9+3) simplifies to -4.

Hence, the shape is rectangular prism with the dimensions 10mm, 8mm, and 8mm has a surface area of 448mm2.

We must first calculate the surface area of each face of a rectangular prism with 10mm, 8mm, and 8mm measurements before adding them all up.

The top and bottom faces, which are both rectangles with measurements of 10 mm by 8 mm, are first measured for area:

Area of the top and bottom faces is equal to 2 (10 x 8 mm) or 160 mm2.

The area of the front and back faces, which are both rectangles measuring 10 mm by 8 mm, is then determined: Area of the front and back faces is equal to 128mm2 (8mm x 8mm).

The area of the two side faces, which are both rectangles with dimensions of 10 mm by 8 mm, is then determined: Area of the side sides is equal to 2 (10mm x 8mm) = 160mm2.

We add up the areas of all the faces to determine the overall surface area:

Whole surface area equals the sum of the areas of the top and bottom faces, the front and back faces, and the side faces.

Surface area total = 160 mm2 + 128 mm2 + 160 mm2

448 mm2 is the total surface area.

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Answer: The plane traveled 15838.5 feet from point A to point B.

In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.

How is area determined?

The length of the other leg of the right triangle can be determined using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where the hypotenuse is c and the triangle's legs are a and b.

We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:

[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]

[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]

Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:

[tex](1/2) * Base * Height = Area[/tex]

We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:

Area: (1/2) * 4 feet * 4 square feet (3)

= 8sqrt(3) square feet

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Answer:

4.2 represents the initial height of the ball.

Step-by-step explanation:

h(x) = -16x² + 24x + 4.2

At x = 0, h(0) = 4.2

4.2 represents the initial height of the ball.

The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

What are algebraic expressions?

An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and arithmetic operations (such as addition, subtraction, multiplication, and division). It can also include exponents, roots, and other mathematical symbols.

Algebraic expressions are used to represent mathematical relationships and to solve problems in various areas of mathematics, science, and engineering. Examples of algebraic expressions include 3x + 5, 2y - 7, and 4x² - 3xy + 2.

A. The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

B. The expression that is equivalent to m + m + m + m that is the sum of two terms is 2m + 2m, where 2m is one term and the other term is also 2m.

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The inequalities shown by the graph are y < 3, x > -1, x < 3, and y >-2.

The given graph has four lines showing different inequalities.

One undotted line is parallel to the x-axis and is at y = 3. The shaded region is below y = 3

Hence, the inequality will be y < 3

Another dotted line is parallel to the x-axis and is at y = -3. The shaded region is above y = -2

Hence, the inequality will be y > -2

Another dotted line is parallel to the y-axis and is at x = -1. The shaded region is to the right of x = -1

Hence, the inequality will be x > -1

Another dotted line is parallel to the y-axis and is at x = 3 The shaded region is to the left of x = 3

Hence, the inequality will be x < 3

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If Rοy is οn the 10th rung, then Bοb is οn the 30 - 2t = 30 - 20 = 10th rung as weII, since they wiII be at the same height at this pοint. Therefοre, the answer is that Bοb and Rοy were οn the 10th rung when they were at the same height.

Let's start by figuring οut hοw fast each persοn is mοving in terms οf rungs per secοnd. We knοw that Bοb is gοing dοwn twο rungs every secοnd, sο his speed is -2 rungs/secοnd (the negative sign indicates that he is gοing dοwn). SimiIarIy, we knοw that Rοy is gοing up οne rung every secοnd, sο his speed is +1 rung/secοnd.

We want tο knοw at which rung Bοb and Rοy wiII be at the same height, sο Iet's caII that rung "R". We can set up an equatiοn tο describe this situatiοn:

30 - 2t = R (Bοb's pοsitiοn at time t)

R = rt (Rοy's pοsitiοn at time t)

Here, t is the time that has eIapsed since Bοb and Rοy started cIimbing. We knοw that they started at the bοttοm οf their respective Iadders, sο we can assume that t is the same fοr bοth οf them.

Nοw we can sοIve fοr R by setting the twο expressiοns equaI tο each οther:

30 - 2t = rt

We can sοIve fοr t by rearranging the equatiοn:

t = 30/(r+2)

Substituting this vaIue οf t back intο either οf the οriginaI equatiοns wiII give us the vaIue οf R:

R = rt = r * 30 / (r+2)

Tο find the vaIue οf r that makes R an integer (since we're Iοοking fοr the rung they're οn), we can try different vaIues οf r untiI we find οne that wοrks. Starting with r=1:

R = 1 * 30 / (1+2) = 10

This means that if Rοy is οn the 10th rung, then Bοb is οn the 30 - 2t = 30 - 20 = 10th rung as weII, since they wiII be at the same height at this pοint. Therefοre, the answer is that Bοb and Rοy were οn the 10th rung when they were at the same height.

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1. 1920 Beetle Population

Beetle Type #Beetles #Beetle % Frequency

BB 22 22/86 ≈ 0.26

bb 14 14/86 ≈ 0.16

Bb 50 50/86 ≈ 0.58

2. 2020 Beetle Population

Beetle Type #Beetle % Frequency

BB 0 0/14 = 0

bb 14 14/14 = 1

Bb 0 0/14 = 0

3. Gene pool for the beetle population: The gene pool for the beetle population consists of the two alleles for the coloration gene, which are represented by "B" (dominant allele) and "b" (recessive allele).

4. Allele frequency for the 1920 Homozygote dominant Beetle population:

5. The allele frequency for the heterozygote population in 2020 is B = 0 and b = 1.

6. Yes, the beetle population experienced evolution because the allele frequencies changed from 1920 to 2020.

For question 1 and 2 above, The % frequency for each beetle type was calculated by dividing the number of beetles of that type by the total number of beetles in the population, and then multiplying the result by 100 to get a percentage.

For example, in the 1920 beetle population, the frequency of BB beetles was calculated as follows:

% Frequency of BB = (# of BB beetles / Total # of beetles) x 100

% Frequency of BB = (22 / 86) x 100

% Frequency of BB ≈ 25.58 or 26% (rounded to the nearest whole number)

Similarly, the % frequency for bb and Bb beetles in the 1920 population were calculated as:

% Frequency of bb = (14 / 86) x 100 ≈ 16%

% Frequency of Bb = (50 / 86) x 100 ≈ 58%

The same process was used to calculate the % frequency for the 2020 beetle population.

4. The frequency of the dominant allele (B) in the 1920 population is the sum of the number of copies of B (from BB and Bb beetles) divided by the total number of alleles (2x the total number of beetles).

Frequency of B = (22 + 50/2) / (86x2) ≈ 0.55

5. Allele frequency for the 2020 heterozygote beetle population:

Since only the frequency of the heterozygote (Bb) is given, the frequency of both alleles (B and b) can be calculated as follows:

Frequency of b = 1 - Frequency of B = 1 - 0 = 1

Frequency of B = frequency of Bb / 2 = 0 / 2 = 0

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1. The median of the sample is obtained through the expression 3+5 / 2. The correct answer is option b.

2. The mean of the ungrouped data distribution is 1.98. The correct answer is option C.

1. The median of a set of data is the middle value when the data is arranged in ascending or descending order. In this case, the data set is (1.9, 3, 5, 7). The middle values are 3 and 5, so the median is the average of these two values, which is (3+5) / 2 = 4.

2. The mean of a set of data is the sum of all the data values divided by the number of data values. In this case, the mean is [(3.2)(2) + (1.3)(5) + (2.4)(3)] / (2+5+3) = 19.8 / 10 = 1.98.

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Answer:

1 3/4

Step-by-step explanation:

To turn 7/4 into a mixed number, you have to look at the numerator and the denominator. 4 can go into 7 once (with 3 left over), so it would be 1 and 3/4

The total cost of the dress including sales tax is 95.21.

The amount of discount that Isabella received on the dress is:

35% of 135.00 = 0.35 x 135.00 = 47.25

So, the price she paid for the dress after the discount is:

135.00 - 47.25 = 87.75

To find the total cost including sales tax, we need to add the sales tax to the price of the dress:

Sales tax = 8.5% of 87.75 = 0.085 x 87.75 = 7.46

Total cost = Price of dress after discount + Sales tax

= 87.75 + 7.46

= 95.21

Therefore, the total cost of the dress including sales tax is 95.21.

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If a poisson process rate was 1.5 (15 events in 10 min) with a mean of 0.387, then

a) p(no events for 3 min) - 0.0498

b) p(1 event in 1 min) - 0.3347

c) p(>= 1 event in 1 min) - 0.7769

d) uncertainty for a, b, c - For a), σ = 1.732 and for b) and c), σ = 1.225

A Poisson process is a stochastic process that counts the number of events in a given time interval. It is characterized by two parameters: the rate, λ, which is the average number of events in a given time interval, and the mean, μ, which is the average number of events in the entire process.

a) The probability of no events in 3 minutes is given by the Poisson probability mass function:

P(X = 0) = (λt)^0 * e^(-λt) / 0! = e^(-λt)

Where t is the time interval (3 minutes), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 0) = e^(-1.5 * 3) = 0.0498

b) The probability of 1 event in 1 minute is given by the Poisson probability mass function:

P(X = 1) = (λt)^1 * e^(-λt) / 1! = λt * e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 1) = 1.5 * e^(-1.5) = 0.3347

c) The probability of at least 1 event in 1 minute is given by the complement of the probability of no events:

P(X >= 1) = 1 - P(X = 0) = 1 - e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X >= 1) = 1 - e^(-1.5) = 0.7769

d) The uncertainty for each of the probabilities is given by the standard deviation of the Poisson distribution:

σ = sqrt(λt)

For a), the standard deviation is:

σ = sqrt(1.5 * 3) = 1.732

For b) and c), the standard deviation is:

σ = sqrt(1.5 * 1) = 1.225

Therefore, the uncertainty for each of the probabilities is given by the standard deviation.

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ds/dt = sec(t)

To find the length of the curve, we need to find the arc length. The arc length of the curve r(t) is given by:

LENGTH = $\int_{0}^{1} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)} dt$

To find ds/dt, we can take the derivative of the above equation with respect to t:

$\frac{ds}{dt} = \frac{d}{dt} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}$

$\frac{ds}{dt} = \frac{6^2\cos(t)\sin(t) + 10\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$

$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$

$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{1+tan^2(t)}}$

Thus, ds/dt = sec(t).

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If Allister’s father measures 180 cm, then the height of Allister would be 150 cm

Let us assume that 'h' represents the height of Allister and 'm' represents the height of Allister’s father.

Here, Allister’s father is 120% of Allister’s height.

This means that m is 120 percent of 'h'

Using the formula of percentage,

m = 120% of h

m = 120/100 × h

m = 6h/5

But Allister’s father actually measures 180 cm

This means m = 180

so , 180 = 6h/5

We solve this equation to find the value of h.

⇒ h = 180 × 5/6

⇒ h = 150 cm

Therefore, Allister's height = 150 cm.

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The complete question is:

Allister’s father is 120% of Allister’s height. If his father measures 180 cm, how tall is Allister?

Tthe total cost for each club after 7 months will be $123.

To find out when the total cost of each health club will be the same, we can use the equation:

Club A total cost = Club B total cost

18 + 15x = 11 + 16x

Where x is the number of months. We can rearrange the equation to solve for x:

15x - 16x = 11 - 18
-x = -7
x = 7

So the total cost of each health club will be the same after 7 months. To find the total cost for each club, we can plug x = 7 back into the equation:

Club A total cost = 18 + 15(7) = $123

Club B total cost = 11 + 16(7) = $123

So, the total cost for each club after 7 months will be $123.

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Answer:

u>36

Step-by-step explanation:

u>36

9×4=36

so u>36

Answer:

Let's first define our variables:

Let x be the number of students in each van and bus.

Using substitution:

From the problem, we know that:

High School A rented 8 vans and 8 buses, with a total of 240 students. So we can write the equation:

8x + 8x = 240

High School B rented 4 vans and 1 bus, with a total of 54 students. So we can write the equation:

4x + 1x = 54

Now, we can solve for x in one of the equations and then substitute that value into the other equation to solve for the other variable. For example, let's solve for x in the second equation:

5x = 54

x = 10.8

Now, we can substitute this value of x into the first equation to solve for the number of students in each van and bus for High School A:

8x + 8x = 240

8(10.8) + 8(10.8) = 172.8

So each van and bus for High School A has 10.8 students in it.

Using elimination:

We can rewrite the equations we used above in standard form:

8x + 8y = 240

4x + y = 54

We can eliminate y by multiplying the second equation by -8 and adding it to the first equation:

8x + 8y = 240

-32x - 8y = -432

-24x = -192

x = 8

Now, we can substitute this value of x into either equation to solve for y:

4(8) + y = 54

y = 22

So each van and bus for High School A has 8 students in it and each van and bus for High School B has 22 students in it.

Using graphing:

We can graph the two equations on the same coordinate plane and find the point where they intersect, which represents the solution:

8x + 8y = 240

4x + y = 54

To graph these equations, we can first solve for y in each equation:

y = -x + 30

y = -4x + 54

Then, we can plot these two lines on the same coordinate plane and find their intersection:

(6, 24)

So each van and bus for High School A has 6 students in it and each van and bus for High School B has 24 students in it.

Three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°). These points are equivalent because they all have the same magnitude of 7, but their angles differ by multiples of 360°.

In polar form, these points are written as:
- (7,400°) = 7cis(400°)
- (7,-320°) = 7cis(-320°)
- (7,760°) = 7cis(760°)

These points are equivalent because the angle in polar coordinates is measured modulo 360°. This means that any angle that differs by a multiple of 360° will be equivalent. For example, 40° is equivalent to 400° because 400° - 40° = 360°. Similarly, -320° is equivalent to 40° because -320° + 360° = 40°, and 760° is equivalent to 40° because 760° - 720° = 40°.

In conclusion, the three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°), and they are written in polar form as 7cis(400°), 7cis(-320°), and 7cis(760°).

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Answer:

8183

Step-by-step explanation:

Plug in calculator

500(1+0.15)^20

Answer:

I found this

Step-by-step explanation:

To simplify 3x² * 4x⁵, we can multiply the coefficients (numbers in front of the variables) and add the exponents of x:

3x² * 4x⁵ = (3 * 4) x^(2+5) = 12x^7

Therefore, the simplified expression is 12x^7.

The unknown measures are given as follows:

BC = 2.52, AB = 1.28, m < C = 27º.

The three trigonometric ratios are defined as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle C is given as follows:

63 + 90 + m < C = 180

m < C = 27.

Side BC is opposite to the angle of 63º, while the hypotenuse is the square root of 8, hence it is obtained as follows:

sin(63º) = BC/sqrt(8)

BC = square root of 8 x sine of 63 degrees

BC = 2.52.

Side AB is opposite to the angle of 27º, hence it's length is given as follows:

sin(27º) = AB/sqrt(8)

AB = square root of 8 x sine of 27 degrees

AB = 1.28.

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Answer:

No solution

Step-by-step explanation:

Use the given functions to set up and simplify f(9)

As a result, the park's estimated area, calculated using a trapezoidal sum with three equally spaced subintervals, is 50 square miles.

A quadrilateral with at least one set of parallel edges is known as a trapezoid. The bases and legs of a trapezoid are referred to by their parallel and non-parallel edges, respectively. The space between the bases of a trapezoid measured perpendicularly is its height. A = (1/2)h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the two bases, is the formula for a trapezoid's area.

given

By calculating the function's average at the left and right ends of the subinterval, it is possible to determine the height of each trapezoid.

A1 = (1/2) * (base1 + base2) * height

= (1/2) * (2 + 2) * 9 = 18 is the area of the first trapezoid.

A2 = (1/2) * (base1 + base2) * height

= (1/2) * (2 + 2) * 11 = 22 is the formula for the area of the second trapezoid.

The third trapezoid's area is given by

A3 = (1/2) * (base1 + base2) * (1/2) * (2 + 2). * 10

= 10

The three trapezoids' combined areas make up the entire area under the curve, which roughly corresponds to the size of the park:

A total = A1 + A2 + A3 

= 50

As a result, the park's estimated area, calculated using a trapezoidal sum with three equally spaced subintervals, is 50 square miles.

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Answer:

Step-by-step explanation:

d^2

When dividing subtract indices OR

dxdxdxdxd /dxdxd

d's cancel out leaving dxd=d^s