To solve the exercise, we can use the following property of logarithms:

[tex]\ln (e^x)=x[/tex]Then, we can solve the equation like this:

[tex]\begin{gathered} 1.5e^{-0.4t}=1.506 \\ \text{ Divide by 1.5 from both sides of the equation} \\ \frac{1.5e^{-0.4t}}{1.5}=\frac{1.506}{1.5} \\ e^{-0.4t}=1.004 \\ \text{ Apply }\ln \text{ from both sides of the equation} \\ \ln (e^{-0.4t})=\ln (1.004) \\ \text{ Apply the mentioned property of logarithms} \\ -0.4t=\ln (1.004) \\ \text{ Divide by -0.4 from both sides of the equation} \\ \frac{-0.4t}{-0.4}=\frac{\ln(1.004)}{-0.4} \\ t\approx-0.01\Rightarrow\approx\text{ it reads "approximately"} \end{gathered}[/tex]Therefore, **the solution of the equation rounded to two decimal places is -0.01.**

This figure shows a circle with a radius of 3.

A circle with its radius labeled as 3.

What is the circumference of the circle?

The **circumference **of the **circle **has a value of 18.86 units

From the question, we have the following parameters:

Radius, r = 3 units

The **circumference **of the circle can be calculated using the following **circumference **formula

C = 2πr

Where

π = 22/7 (a constant)

r = 3

Substitute the known values in the above equation

So, we have the following equation

C = 2 * 22/7 * 3

Evaluate the products

So, we have the following equation

C = 18.86

Hence, the **circumference **is 18.86 units

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A sequence is defined recursively using the formula f(n+1) =-0.5f(n) . If the first term of the sequence is 120, what is f(5)?

−15

−7.5

7.5

15

Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:

[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]

Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:

[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]

Then substitute f(3) down to f(1):

[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]

Therefore, **f(5) = 7.5**

A student incorrectly simplifies an expression. The expression and work is shown below.

-(-6)(-3) - 2/3 (22 - 7)

3/5

Step 1: -(-6) (-3) - 2/3 (15)

3/5

Step 2: 18 - 2/3 (15)

3/5

Step 3: 18 - 10

3/5

Step 4: 8_3_5

Answer they got: 4 4/5

Idetnfiy which step is incorrect.

.

PLSSS HELP MEEEEEE

**Answer:**

so in the second step you see how the 18 is a positive

its supposed to be a negative

in the step 1, the part is -(-6)(-3), right?

so the negative symbol outside the negative 6 cancels out the negative, making it a positive number

it becomes 6(-3), which them multiplies into -18

so, i think the explanation is "the person forgot to change the 18 to a negative in the second step"

yea lol i think thats it

Points B and C are on parallel lines with s and T, respectively. The size of the angle BAC is 96 degrees. Find the acute angle between straight AC and straight t if it is known that it is three times the size of the acute angle between straight AB and straight S.

**Answer:**

**Step-by-step explanation:**

Let the **acute angles** be **B** and **C**.

If we add a **parallel line through the point A**, we'll see that:

And **we know **that:

**Plug in** the known parameters to get:

We are looking for the **value of C**:

in the figure shown Line O is parallel to line P and line M is Parallel to linea N

we have that

In this problem angle x and angle of 62 degrees are supplementary angles

that means

x+62=180

solve for x

x=180-62

x=118 degreesThe graph below plots the values of y for different values of x: plot the ordered pairs 1, 3 and 2, 4 and 3, 9 and 4, 7 and 5, 2 and 6, 18 What does a correlation coefficient of 0.25 say about this graph? (1 point) x and y have a strong, positive correlation x and y have a weak, positive correlation x and y have a strong, negative correlation x and y have a weak, negative correlation

The presented data for** x and y **show a significant, **positive correlation **with 0.78 serving as the coefficient of correlation.

The intensity and direction of a relationship between two variables are indicated by a **correlation coefficient**, which is a number between -1 and 1. In other words, it shows how comparable two or more** variables' **measurements are across a dataset. The other variables shift in the same direction when one changes.

The intensity and direction of a** relationship **between two** variables **are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a **dataset.**

Given** x and y **values in this case

x 1 2 3 4 5 6

y 3 4 9 7 2 18

xy 3 8 27 28 10 108

x² 1 4 9 16 25 36

y² 9 16 81 49 4 324

**∑x = 21, **

**∑y = 43, **

**∑xy = 194, **

**∑x² = 91, **

**∑y² = 483, **

**n = 6**

the relationship between x and y now:

r = (n∑xy - ∑x.∑y)/ √[{n∑x²- (∑x)²}{n∑y² - (∑y)²}]

r = ( 6 X 194 - 21 X 43 ) / √[ {6 X 91 - (21)²}{ 6 X 483 - (43)²}]

r = ( 1164 - 903) / √( 546 - 441)(2898 - 1849)

r = 261 / √ 105 X 1049

r = 261 / √110145

r = 261 / 331.88

**r = 0.78**

As a result, the x and y data's** correlation** coefficient is 0.78.

The strong, **positive** association between x and y

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Find a degree 3 polynomial having zeros -8, 2 and 8 and the coefficient of x3 equal 1.

The degree 3 **polynomial** is "**x³-2x²-64x+128**".

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Find the rates of change in population for both parks between 2009 and 2014, and determine which park showed faster population growthduring those years.

The table and graph given show the information about two national parks.

It is required to find the rate of change of the population of the two parks between 2009 and 2014, and then determine the park that shows faster population growth during those years.

Notice that the variable x represents the number of years after 2005.

Hence, the years 2009 and 2014 represent, x=4 and x=9, respectively.

The formula for the **rate of change of a function **f(x) between x=a and x=b is given by the formula:

Calculate the rate of change for park A:

Substitute **a=4** and** b=9** into the formula:

Substitute **f(9)=2870** and **f(4)=2370** from the table for park A into the expression for the rate of change:

Calculate the rate of change for park B:

[tex]\frac{f(9)-f(4)}{9-4}[/tex]Substitute **f(9)=2800** and **f(4)=2200 **from the graph of park B:

Notice that the rate of change in population for park B is higher than that of park A.

Hence, park B showed faster population growth during those years.

**Answers****:**

**Rate of change for park A= 100 swallows per year.**

**Rate of change for park B= 120 swallows per year.**

**Park B showed faster population growth during those years.**

Please explain and help me get the correct answer. Thank you. Practice work that is not graded.

First, from the formula given we solve the equation for D:

[tex]\begin{gathered} 4PD=D^2LN\pi, \\ \frac{4PD}{LN\pi}=D^2, \\ \sqrt{\frac{4PD}{LN\pi}}=D^{}. \end{gathered}[/tex]Now, substituting the given data:

(a) PD=405 cu in, L=4.7 in, and N=7,

in the above equation we get:

[tex]D=\sqrt[]{\frac{4\times405}{4.7\times7\times\pi}}in=\sqrt[]{15.6736175}in\approx3.96\text{ in}[/tex](b) PD=399.4 cu in, L=2 in, and N=6,

in the above equation we get:

[tex]D=\sqrt[]{\frac{4\times399.4}{2\times6\times\pi}}in=\sqrt[]{42.37765618}in\approx6.51\text{ in}[/tex]**Answer:**

(a) 3.96 in.

(b) 6.51 in.

Three cubes of side 10 cm are joined end to end to form a cuboid as given in the figure. Find is total surface area.

**Solution:**

The cuboid is a solid-shaped figure formed by six faces. A cuboid is a simple figure. It has three dimensions - width, length, and height. Thus, the cuboid is a parallelepiped. Now, the surface area of the parallelepiped is the sum of the areas of all sides, that is:

[tex]S\text{ =2(}lw+lh+wh\text{)}[/tex]where

l is the lenght

w is the width

and

h is the height

According to the figure given in the problem, we have that:

l = 30

w = 10

h = 10

thus, the surface area of the given cuboid would be:

[tex]\begin{gathered} S\text{ =2(}lw+lh+wh\text{)} \\ \text{ = 2((}30\cdot10\text{)+(30}\cdot10\text{)+(10}\cdot10\text{))=}1400 \end{gathered}[/tex]So that, we can conclude that **the correct answer is:**

[tex]1400[/tex]

find volume of hemisphere who’s great circle has an area of 12.5 ft squared

The surface area of a hemisphere is given as 12.5 square feet. It is required to find the volume of the hemisphere.

To do this, equate the given surface area to the formula, find the radius, and then substitute the radius into the volume formula to find the volume.

The **surface area **of a hemisphere radius, **r** is given as:

Substitute **S=12.5** into the formula and solve for **r** in the resulting equation:

The **volume of a hemisphere **is given as:

Substitute the calculated value of **r** into the volume formula:

**The required volume is about 3.2 square feet.**

I need help with this practice Please read below ‼️‼️Use pencil and paper to graph the function, if you can’t, please use a drawing/writing tool that is *NOT* a graphing tool. If you cannot do this let me know

**Answer:**

**Step-by-step explanation:**

The trigonometric functions are represented by the following function form:

[tex]\begin{gathered} f(x)=\text{Atrig(Bx-C)}+D \\ \text{where,} \\ A=\text{ amplitud} \\ B,C=\text{ phase shift} \\ D=\text{ vertical shift} \end{gathered}[/tex]Then, for the following function:

[tex]f(x)=-\cot (x+\frac{\pi}{6})[/tex]Since it is an arctan function reflected the y-axis:

micrometers, T is measured in seconds, and D accounts for the weakening of the earthquake due to the distance from the epicenter.

If an earthquake occurred for 4 seconds and D = 2, which graph would model the correct amount on the Richter scale?

The **graph that** can be used to **model** the correct amount on the **Richter** scale is r = log(a/4) + 2.

It should be noted that the magnitude of an **earthquake** is gotten by using the **equation**:

r = log(a / t) + d.

where

r = magnitude of an **earthquake**

a = amplitude

t = time

d = distance.

In this case, the **earthquake** occurred for 4 seconds and D = 2. We'll substitute the value into the equation and this will be r = log(a/4) + 2.

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What is the image of ( − 8 , 0 ) after a dilation by a scale factor of 1/4 centered at the origin?

**Step-by-step explanation:**

it is then simply scanned (multiplied).

the new point is

(-8 × 1/4, 0 × 1/4) = (-2, 0)

What is the magnitude (size) of -7.5?_______________________________O A. -7.5, because |-7.5| = 7.5O B. 7.5, because |-7.5 = 7.5O C. 7/5, because |-7.5| = 7/5O D. 7.5, because | -7.5| = - 7.5

it is given that the expression is -7.5

the magnitude of -7.5 is,

I-7.5I = 7.5

t**hus, the answer is option A**

The figure shows a circle inscribed into a regular pentagon.Cis the center of the circle and the regular pentagon.G and H are on the edge of both the circle and the regular pentagon.The radius of the circle is 3 inches.GHCPart A. Find the area of the dark shaded region. Show your work.Part B. Find the area of the light shaded region. Show your work.

Solution

**Part A**: The area of the dark shaded region = **S1**,

where

The radius of the circle is 3 inches.

[tex]\begin{gathered} S_1=\frac{4}{5}\pi r^2 \\ =\frac{4}{5}\pi.3^2 \\ S_1=\frac{36}{5}\pi in^2 \end{gathered}[/tex]**Part B**: The area of the light shaded region = **S,**

In 5 minutes, a conveyor belt moves 100 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans thesame distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area.The conveyor belts can move the 100 pounds of recyclable aluminum from the delivery truck to a storage area in minutes.(Simplify your answer. Type an integer, fraction, or a mixed number.)

we know that

a greater conveyor belt moves 100 pounds ------------> 5 minutes

so

Applying proportion

1-minute ---------> move 100/5=20 pounds

a smaller conveyor belt moves 100 pounds ------> 9 minutes

so

Applying proportion

1-minute --------> move 100/9 pounds

therefore

If both belts are used

then

1-minute --------> move 20+(100/9)=(180+100)/9=280/9 pounds

Applying proportion

Find out how long it takes to move 100 pounds

[tex]\begin{gathered} \frac{1}{\frac{280}{9}}=\frac{x}{100} \\ \\ solve\text{ for x} \\ x=\frac{100}{\frac{280}{9}}=\frac{900}{280} \end{gathered}[/tex]Simplify the fraction

45/14

Convert to a mixed number

45/14=42/14+3/14=3 3/14 minutes

The answer is 3 3/14 minutesIS THIS A FUNCTION YES OR NO?? (ALGEBRA 1)

**Answer: Yes**

**Step-by-step explanation:**

Yes, the numbers in the table are a function. The equation for the equation would be

y = 2x

Yes the numbers in the table are a function the equation for this would be y = 2x

Analyzing Graphs of Functions

Which graph shows a function where f(2)= 4?

21

12

12y

12ty

8

8

8

8

4

4

4

х

4 8 12

-12-8 -4

4 8 12

-12-8-4

4 8 12

12-48-4

4 8 12

4

-12-84

8-44

-8

-12

8

-8

-12

-12 V

Intro

Done

From the graphs we can conclude:

[tex]undefined[/tex]Which four groups make up nearly one half of the male population?

We are given the percentages for males on the left side and the percentages for females on the right side.

We are trying to find four groups that make up nearly 1/2 of the male population, so we want the percentages for these groups to add up to nearly 50%.

Let's take a look at the lowest age groups of the male population, which in turn make up the highest proportion of the male population.

We have the age group 0-4, which makes up roughly 12%.

We have the age group 5-9, which makes up roughly 11%.

We have the age group 10-14, which makes up roughly 11%.

We have the age group 15-19, which makes up roughly 12.5%.

If we add all of these percentages together, we get:

12% + 11% + 11% + 12.5% = 46.5%

Since we cannot go any smaller than 46.5% because this is the closest percentage to 50%, the four groups that make up nearly one half of the male population must be:

**Ages 0-4, 5-9, 10-14, and 15-19**

Drop down options for 1 2 and 4 are Forest A or Forest B

Given :

[tex]A(t)=107(1.015)^t[/tex][tex]B(t)=88(1.025)^t[/tex]1)

Set t=1 we get

[tex]A(t)=107(1.015)^t[/tex]Oscar drew a scale drawing of a house. The garage, which is 8 meters long in real life, is 4centimeters long in the drawing. What is the drawing's scale factor?Simplify your answer and write it as a fraction.

**Answer:**

1/200

**Explanation:**

Length of the garage in the drawing = 4 centimeters

Length of the garage in real life = 8 meters

The ratio of the lengths = 4 cm : 8m

Divide both sides by 4

[tex]\begin{gathered} \frac{4\operatorname{cm}}{4}\colon\frac{8m}{4} \\ 1\operatorname{cm}\colon2m \end{gathered}[/tex]1 m =100cm

2m= 2 x 100 =200cm

Converting both to the same unit, we have:

[tex]\begin{gathered} 1\operatorname{cm}\colon200\operatorname{cm} \\ =\frac{1}{200} \end{gathered}[/tex]**The drawing's scale factor in fraction form is 1/200.**

Questions 24-25

The scores of a standardized IQ test are normally distributed with a mean score of 100 and a standard deviation of 15.

Question 24 2

Find the probability that a randomly selected person has an IQ score higher than 105.

Question options:

0.9522

0.3694

-1.15

0.6306

Question 25

A random sample of 55 people is selected from this population. What is the probability that the mean IQ score of the sample is greater than 105?

Question options:

0.0067

0.3694

0.6306

0.9933

Using the** normal distribution **and the **central limit theorem**, it is found that the **probabilities **are given as follows:

**24. **Single person has an IQ score above 105: 0.3694.

**25. **Sample mean (55 people) above 105: 0.0067.

The** z-score **of a **measure X** of a variable that has **mean **[tex]\mu[/tex] and **standard deviation** [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-scoreThe **mean **and the **standard deviation** of IQ scores are given as follows:

[tex]\mu = 100, \sigma = 15[/tex]

The probability that a** single person** has an IQ score **higher **than 105 is one subtracted by the p-value of Z when X = 105, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (105 - 100)/15

Z = 0.33

Z = 0.33 has a p-value of 0.6306

1 - 0.6303 = 0.3694.

For the **sample **of 55, the **standard error** is:

[tex]s = \frac{15}{\sqrt{55}} = 2.02[/tex]

Hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (105 - 100)/2.02

Z = 2.48

Z = 2.48 has a p-value of 0.9933.

1 - 0.9933 = 0.0067.

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A journal on how to determine a quadratic equation given the roots

**Answer:**

this is your answer hope this helps you

What **the roots of the equations?**

The **roots **of an equation is "**solutions**" of the equation. Solutions are the numerical values equal to the variable after solving it.

To determine the sum and product of the **roots **of a **quadratic equation**, the equation has to be written in the form ax²+bx+c = 0

From that form, the sum of the **roots **is given by -b/c and the product is c/a

For example, we want to find the sum and product of the **roots **of the quadratic equation 3x²-x = 2

Notice that the equation is not written in the form described above. So, it has to be written as 3x²-x - 2 = 0

From this form, we see that and a = 3, b = -1 and c = -2

Therefore, the sum is -b/a = 1/3 while the product is c/a = -2/3 = -2/3

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Megan is in a musical production. She was at practice for 2 hours yesterday and 3 hours today. Altogether she spent of her practice hours dancing. How many total hours did Megan spend dancing yesterday and today?

**Answer:**

2.0833

**Step-by-step explanation:**

2 3/4 + 3 1/2 =6.25

6.25(1/3)=2.0833

Graph the image of ∆KLM after a dilation with a scale factor of 4, centered at the origin.

The red triangle is the original figure

The green triangle is the image

Scale factor is 4

Triangle BCD is similar to triangle EFG. Find the measure of side EF. Round youranswer to the nearest tenth.

Triangle BCD is similar to triangle EFG.

8. Tabitha made 12 out of 23 free throw attempts in the first half of practice and 20 out

of 27 attempts in the second half of practice. What is her free throw average for the

whole practice, written as a decimal?

**Answer: 0.64 ...........**

A rectangular garden has one side with a length of x + 7 and another with a length 2x + 3. Find the perimeter of the garden.

A rectangular garden has one side with a length of **x + 7 **another with a length** 2x + 3**

We are asked to find the **perimeter** of the garden

Let me draw this rectangular garden to better understand the problem

Recall that the **perimeter** of a **rectangular** shape is given by

Where W is the width and L is the length of the rectangular garden

Let us substitute the given values into the above formula

[tex]P=2(x+7+2x+3)[/tex]Now simplify the equation

[tex]\begin{gathered} P=2(x+2x+7+3) \\ P=2(3x+10) \\ P=6x+20 \end{gathered}[/tex]**Therefore, the perimeter of the rectangular garden is equal to 6x + 20.**

Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).

The **x–intercept** of g(h(x)) is the option;

[tex] \displaystyle {-\frac{2}{3}}[/tex]

What is a The x–intercept of a function?The x–intercept of a **function** is given by the point where the function **intersects** the **x–axis**.

From the given table, the slope of the graph of g(x), [tex] m_1 [/tex] is given by the equation;

[tex] \displaystyle{ m_1 = \frac{ - 4 - ( - 8)}{ - 4 - ( - 6))} = \frac{4}{2} = 2}[/tex]

The equation of g(x) in point slope form is therefore;

g(x) - (-4) = 2×(x - (-4)) = 2•x + 8

g(x) = 2•x + 8 - 4 = 2•x + 4

g(x) = 2•x + 4

The **slope** of the **function** h(x), [tex] m_2 [/tex] is found using the **equation**;

[tex] \displaystyle{ m_2 = \frac{ 8 - 14}{ - 4 - ( - 6))} = \frac{ - 6}{2} = - 3}[/tex]

h(x) presented in point and slope form is therefore;

h(x) - 8 = (-3)×(x - (-4)) = -3•x - 12

h(x) = -3•x - 12 + 8 = -3•x - 4

h(x) = -3•x - 4

g(h(x)) = 2•h(x) + 4

Plugging in the value of h(x) gives,;

g(h(x)) = 2×(-3•x - 4) + 4 = -6•x - 8 + 4

g(h(x)) = -6•x - 4

The x–intercept of g(h(x)) is given by the point where g(h(x)) = 0, which gives;

At the x–intercept, g(h(x)) = 0 = -6•x - 4

[tex] \displaystyle{ x = \frac{4}{-6} = -\frac{ 2}{3} }[/tex]

The x–intercept is [tex] \displaystyle{ -\frac{ 2}{3} }[/tex]

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poornima gupta is retiring soon, so she is concerned about her investments providing her steady income every year. she is aware that if interest rates rise, the potential earnings power of the cash flow from her investments will increase. in particular, she is concerned that a decline in interest rates might lead to decrease in annual income from her investments. what kind of risk is poornima most concerned about protecting against?
What is the main precursor derived mostly from carbohydrates to start fat biosynthesis?.
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