(Q5) Decide if the function is an exponential function. If it is, state the initial value and the base. y=3.1^x

Answer:

2nd graph

Step-by-step explanation:

Exponential increase will be a graph that increase all throughout and the rate of increase "increases" with age.

The 2nd graph is correct because it shown "increase" as well as "exponential" increase (the rate of increase increases).

Answer: 2nd graph

Your answer is going to be the second graph

Answer:

The value of x = -0.17

Step-by-step explanation:

∵ [tex]2e^{8x}=1-e^{4x}[/tex]

Let [tex]e^{4x}=y[/tex]

∴ [tex]e^{8x}=y^{2}[/tex]

∴ 2y² = 1 - y

∴ 2y² + y - 1 =0 ⇒ factorize

∴ (2y - 1)(y + 1) = 0

∴ 2y - 1 = 0 ⇒ 2y = 1 ⇒ y = 1/2

∴ y + 1 = 0 ⇒ y = -1

∵ [tex]y=e^{4x}[/tex]  

Note: [tex]e^{4x}=-1[/tex] ⇒ refused

         ([tex]e^{ax}[/tex] never gives -ve values)

∴ [tex]e^{4x}= 1/2[/tex] ⇒ insert ln in both sides

∵ [tex]ln(e)^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1

∴ 4xln(e) = ln(1/2) ⇒ 4x = ln(1/2)

∴ x = [ln(1/2)]/4 = -0.17

To find the sale price of a $384 skateboard with a 24% discount, convert the paid percentage to a decimal (76% to 0.76) and multiply with the original price, resulting in a sale price of $291.84.

To calculate the sale price of a skateboard originally priced at $384 with a 24% discount, we first need to determine what percentage of the original price will actually be paid. Since the discount is 24%, that means 76% of the original price will be paid (100% - 24% = 76%). To convert this percentage to a decimal, we divide by 100, getting 0.76.

Next, we find the sale price by multiplying the original price by the decimal form of the percentage paid:
$384 × 0.76 = $291.84 as the sale price of the skateboard.

Answer: the answer should be A= Parallel

Step-by-step explanation:

Answer:

C. Neither

Step-by-step explanation:

The first equation is [tex]y=2x+13[/tex]

This equation is already in the slope-intercept form; [tex]y=mx+c[/tex]

The slope of this equation is 2.

The second equation is [tex]y=-2x+2[/tex].

This equation is also already in the slope-intercept form.

The slope of this equation is [tex]-2[/tex].

Since the two slopes are not the same, the two lines are not parallel.

If these two lines are perpendicular, then the product of their slopes is -1.

But [tex]2\times -2=-4[/tex] which is not equal to -1.

Therefore the two lines are also not perpendicular.

The correct choice is C.

Answer: [tex]b=10^3[/tex]

Step-by-step explanation:

You know that there are 10 blueberries in each muffin. There are 10 muffins in each box and the total number of boxes is 10.

Then, to calculate the total number of blueberries, you need to multiply the total number of boxes by the number of muffins in each box and multiply this by the number of blueberries in each muffin.

Let be "b" the total number of blueberries. Then:

[tex]b=10*10*10[/tex]

By the Product of powers property:

[tex]a^m*a^n=a^{(m+n)}[/tex]

Then you can write the expression:

[tex]b=10^3[/tex]

Answer:

B

Step-by-step explanation:

The exponential function is the function of the form

[tex]y=a\cdot b^x,[/tex]

where [tex]b[/tex] is the base and [tex]a[/tex] is the initial value.

The function [tex]y=x^2[/tex] is the quadratic function, which cannot be represented as [tex]y=a\cdot b^x.[/tex] Thus, this function is not exponential.

Answer:

The answer is B.

Step-by-step explanation:

To find P(2.5≤X≤4), calculate the length of the interval between 2.5 and 4, and divide by the total length of the distribution's support.

For a uniform distribution U(0.5, 4), this would result in a probability of ¾ or 0.75.

To calculate the probability P(2.5≤X≤4) for a random variable X, given the graph of the probability distribution, you would typically integrate the probability density function (pdf) from 2.5 to 4 (in the case of a continuous distribution) or sum the probabilities for each whole number value of X between 2.5 and 4 (in the case of a discrete distribution).

For a uniform distribution U(0.5, 4), the probability is uniform (constant) across the interval.

Since the total area under the distribution is equal to 1, the probability of any interval can be found by calculating the length of the interval divided by the total length of the distribution's support (4 - 0.5).

For P(2.5≤X≤4), this would be ¾ or 0.75 since the interval length from 2.5 to 4 is 1.5 and the total length of distribution's support is 3.5 (4-0.5).

Answer:

  3/8

Step-by-step explanation:

You want the probability P(2.5 ≤ x ≤ 4), given X has a uniform distribution between 0 and 4.

The probability can be found by integrating the PDF over the interval [2.5, 4]:

  [tex]\displaystyle\int_{2.5}^4{\dfrac{1}{4}}\,dx=\dfrac{1}{4}(4-2.5)=\dfrac{1}{4}\cdot\dfrac{3}{2}=\dfrac{3}{8}[/tex]

The probability is 3/8.

Trigonometric ratios are vital in real-world applications such as construction for measuring building heights, in navigation or aviation for determining distances, and in physics for predictions and descriptions of natural phenomena.

Trigonometry and special right triangles are fundamental in various real-world scenarios, especially in fields such as engineering, astronomy, and construction. One example where trigonometric ratios are crucial is in construction when determining the height of a building using a measured baseline and the angles of elevation. If a surveyor knows the distance from his point of observation to the base of the building (the adjacent side in a right triangle) and the angle of elevation to the top of the building, they can use the tangent ratio (opposite over adjacent) to calculate the building's height.

Another scenario involves navigation or aviation, where knowing the distance between two locations is necessary. By measuring the angle from two different points to a third point, one can apply the basic problem of trigonometry to find the distance to the third point using a known baseline and the measured angles, a process often referred to as triangulation.

Lastly, in physics, the principles of special right triangles like the Pythagorean theorem are used to predict certain outcomes. Whether a calculation is made using trigonometry or some other physics principle, the predictions must agree and accurately describe natural phenomena. The Pythagorean theorem is always reliable as long as the algebra and arithmetic are correctly done, illustrating the logic and interconnectedness of mathematical postulates.

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Answer:

Step-by-step explanation:

[tex]x^2-2x+17=0\qquad\text{subtract 17 from both sides}\\\\x^2-2x=-17\\\\x^2-2(x)(1)=-17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2(x)(1)+1^2=-17+1^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-1)^2=-17+1\\\\(x-1)^2=-16<0\Rightarrow\boxed{\text{NO REAL SOLUTION}}\ because\ x^2\geq0\\\\\text{In the set of complex numbers}\\\\i=\sqrt{-1}\\\\(x-1)^2=-16\iff x-1=\pm\sqrt{-16}\\\\x-1=-\sqrt{(16)(-1)}\ \vee\ x-1=\sqrt{(16)(-1)}\\\\x-1=-\sqrt{16}\cdot\sqrt{-1}\ \vee\ x-1=\sqrt{16}\cdot\sqrt{-1)[/tex]

[tex]x-1=-4i\ \vee\ x-1=4i\qquad\text{add 1 to both sides}\\\\x=1-4i\ \vee\ x=1+4i[/tex]

Answer:

72 voters

Step-by-step explanation:

Total surveyed members: 40

Total members with a yes vote: 12

Percentage of the voters (voting yes): [tex]\frac{12}{40} * 100 = 30%[/tex]

From analysis, it is observed that 30% of the voters are expected to vote yes in a sample.

Therefore, the number of voters expected to vote yes out of 240 are: 30% of 240

=> [tex]\frac{30}{100} * 240 = 72[/tex]

Answer:

72 voters

Step-by-step explanation:

To find the equation of the perpendicular bisector, find the midpoint of the line segment and determine the slope of the perpendicular line.

To find the equation of the perpendicular bisector of a given line segment, we need to find the midpoint of the segment and then determine the slope of the perpendicular line. Let's denote the coordinates of the endpoints of the line segment as (x1, y1) and (x2, y2). The midpoint of the segment can be found using the formula:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

The slope of the perpendicular line can be found using the negative reciprocal of the slope of the given line segment:

Perpendicular slope = -1 / slope of given line segment

Once we have the midpoint and the slope of the perpendicular line, we can use the point-slope form of a linear equation to write the equation of the perpendicular bisector:

y - y1 = perpendicular slope * (x - x1)

Answer:

Step-by-step explanation:

If y = 2x + 1, then dy/dt = 2(dx/dt).

If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x.  y = 81.

(a) if dx/dt = 3, find dy/dt when x = 4:

       Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.

(b) if dy/dt = 2, find dx/dt when x = 40:

        Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.

First, you differentiate the given function. Next, apply the chain rule which states dy/dt = dy/dx * dx/dt. Substitute the known values to find dy/dt. For the second part, rearrange the chain rule to find dx/dt = dy/dt / dy/dx and substitute the known values.

This question deals with the basic application of the chain rule in differentiation. The given function is y = 2x + 1, where both y and x are functions of t. You are supposed to determine dy/dt and dx/dt.

(a) First, differentiate y = 2x + 1 with respect to x to obtain dy/dx = 2. According to the chain rule in calculus, dy/dt = dy/dx * dx/dt. Substituting the known values from the question, we have dy/dt = 2 * 3 = 6 when x = 4.

(b) For dy/dt = 2, you need to rearrange dy/dt = dy/dx * dx/dt to find dx/dt = dy/dt / dy/dx. As dy/dx = 2, you can evaluate dx/dt = 2 / 2 = 1 when x = 40.

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Answer:

The measure of the angle is [tex]30\°[/tex]

Step-by-step explanation:

Let

x-----> the measure of the angle in degrees

we know that

The measure of a complete circle is [tex]360\°[/tex]

so

by proportion

[tex]\frac{360}{1}\frac{degrees}{circle}=\frac{x}{(1/12)}\frac{degrees}{circle}[/tex]

[tex]x=\frac{1}{12}(360\°)[/tex]

[tex]x=\frac{360\°}{12}[/tex]

[tex]x=30\°[/tex]

An angle that represents 1/12 of a circle measures 30 degrees. We found this by understanding that a full circle is 360 degrees and then multiplied 1/12 by 360.

The question is asking for the measure in degrees of an angle that represents 1/12 of a circle. As we know, a circle consists of 360 degrees next we measure the angle just like when we are measuring the angle in the sky. To find the angle, we can use a simple proportion. Since the whole circle is 360 degrees, we know that 1/12 of the circle will be equal to 1/12 of 360 degrees.

So, the calculation will be like: 1/12 x 360 = 30 degrees. Therefore, an angle that represents 1/12 of a circle measures 30 degrees.

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The probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz is approximately 60%.

To find the probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz, we need to sum the frequencies for the 41-55 age group and the frequency for Dr. Fizz, and then divide by the total number of people.

From the table:

- Frequency of 41-55 age group = 30

- Frequency of Dr. Fizz preference = 30

Total number of people = 100

Therefore, the probability is:

[tex]\[ \text{Probability} = \frac{\text{Frequency of 41-55 age group} + \text{Frequency of Dr. Fizz}}{\text{Total number of people}} \][/tex]

[tex]\[ = \frac{30 + 30}{100} \][/tex]

[tex]\[ = \frac{60}{100} \][/tex]

[tex]\[ = 0.60 \][/tex]

Converting to a percentage, rounded to the nearest whole percent:

[tex]\[ \text{Probability} \approx 60\% \][/tex]

So, the correct answer is: 60%.

Multiply total sales by 11%

4265 x 0.11 = 469.15

His commission was $469.15

Final answer:

Wilson Green's commission is calculated by multiplying his total sales of $4265.00 by his commission rate of 11 percent, which equals $469.15.

Explanation:

Wilson Green earns an 11 percent commission on every home security system he sells. For the month, his total sales amounted to $4265.00. To calculate Wilson's commission, we need to find 11 percent of $4265.00.

The formula for calculating the commission is:

Commission = Total Sales × Commission Rate

By plugging in the numbers:

Commission = $4265.00 × 0.11

Now, let's do the math:

Commission = $469.15

Therefore, Wilson's commission for the month is $469.15

Answer:

The correct answer option is 0.67.

Step-by-step explanation:

We are given that the probability that a child eats popcorn and cotton candy is 0.58, probability that a child eats popcorn is 0.69 and the probability that a child eats cotton candy is 0.87.

We are to find the probability that a child eats popcorn given that the child has already eaten cotton candy.

P (eats popcorn and has already eaten cotton candy) = [tex]\frac{0.58}{0.87}[/tex] = 0.67

In a parallelogram, adjacent angles sum to 180. Since the labeled angle is adjacent to the 124° angle, we have

[tex] 2z+16 +124 = 180 \iff 2z = 180-124-16 \iff 2z= 40 \iff z = 20[/tex]

The mode is the number that appears most often.

Looking at the chart, there are two 1's on the right side, so the mode would be 31

Answer:

A

Step-by-step explanation:

Add up the votes for each person and order them greatest to least and pick the top 4.

Answer:

28.26

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and/or area.

Substitute C = 18.84 and solve for r. Then substitute r into the area formula.

C = 2πr

18.84 = 2πr

3 = r

A = πr² = π(3)² = 28.26

Answer:

28.26

Step-by-step explanation:

Answer:

12 and 15     or

12 and 18    or

15 or 18

Step-by-step explanation:

The two numbers have to both be divisible by 3, since their greatest common factor is 3.  This only leaves..

12, 15, or 18     (no other numbers between 10 and 20 are divisible by 3)

The factors of 12 are: 2, 3, 4, 6, and 12

The factors of 15 are: 3, 5, and 15

The factors of 18 are: 2, 3, 6, 9, and 18

All three numbers have 3 as a greatest common factor, so we have 3 pairs of numbers they could be...

12 and 15     or

12 and 18    or

15 or 18

Answer:

15 and 18

Step-by-step explanation:

Because The number 3 is the greatest common factor of 15 and 18, and both numbers are between 10 and 20.

Answer:

40 yes it is i got 100 on this

Step-by-step explanation:

There are 2.4 hours of infomercials in a 24-hour day if they account for 10% of the daily broadcast.

The question asks us to calculate the amount of time designated for infomercials in a 24-hour day if they make up 10% of the day's broadcast. To find the answer, we can use the basic percentage calculation.

To calculate 10% of a day, we need to know that a day has 24 hours. So 10% of 24 hours is calculated as follows:

(10/100) × 24 = 2.4

Therefore, there are 2.4 hours of infomercials in a 24-hour day.

Answer:

48 miles

Step-by-step explanation:

The volume of a sphere with a radius of 4 centimeters is calculated using the formula V = (4/3)πr³. Substituting 4 cm for the radius and 3.14 for π, the volume is approximately 268 cubic centimeters.

To calculate the volume of a sphere with a given radius, you can use the formula V = (4/3)πr³, where V represents the volume and r is the radius. In our case, the radius is 4 centimeters. Substituting the values into the formula gives us V = (4/3) * 3.14 * (4 cm)³.

Performing the calculation: V = (4/3) * 3.14 * 64 cm³ = 267.94666666666666 cm³. Therefore, the volume of the sphere is approximately 268 cm³ when rounded to a whole number.

Answer:

Option b

Step-by-step explanation:

The equation [tex]4x ^ 2 + 5y ^ 2 = 20[/tex] has center in (0,0).

But the transformation [tex]T(5, -6)[/tex] shifts the center of the equation to the point (5, -6).

Therefore, when applying [tex]T(5, -6)[/tex] we will have the following equation translated.

[tex]4(x-5) ^ 2 + 5(y - (-6)) ^ 2 = 20[/tex].

Simplifying we have:

[tex]4(x-5) ^ 2 + 5(y + 6) ^ 2 = 20[/tex]

Now we expand [tex](x-5) ^ 2[/tex] and [tex](y + 6) ^ 2[/tex]

[tex]4(x ^ 2 -10x +25) + 5(y ^ 2 + 12y +36) = 20\\\\4x ^ 2 -40x + 100 + 5y ^ 2 + 60y + 180 = 20\\\\4x ^ 2 + 5y ^ 2 -40x + 60y +260 = 0[/tex]

The equation of a circle has the form

[tex]h(x-a) ^ 2 + q(y-b) ^ 2 = r[/tex]

For h = 1 and q = 1.

If [tex]h \neq 1[/tex] and [tex]q\neq 1[/tex] then the graph becomes an ellipse.

In this problem h = 4 and q = 5 therefore the figure is an ellipse

Answer:

Step-by-step explanation:

[tex]\text{The quadratic equation:}\ ax^2+bx+c=0.\\\\\text{We have}\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\text{Substitute to}\ b^2-4ac:\\\\b^2-4ac=(-4)^2-4(1)(2)=16-8=8[/tex]

Answer:

I am assuming it is the same table as mine. So it would be 0.56

Step-by-step explanation:

The correct equation representing the time Bailey spends in the weight room each week is 2w=3. By solving this equation, we find Bailey spends 1.5 hours in the weight room each week.

The question tells us that Baily spends 3 hours each week playing soccer and this is two times the amount of time she spends working out in the weight room. We can represent the time she spends in the weight room as w. So, the question gives us the equation 2w=3. Since 2 times what number gives us 3, we can solve for w by dividing both sides of the equation by 2. When we do this, we have w=3/2, which means Baily spends 1.5 hours in the weight room each week.

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