can someone help me solve this logarithm function

We are given:

f(x) = 3x + 8

g(x) = -x³

__________________________________________________________

The Concept:

We have to find the values of f(g(3)), which means that we have to apply the function g() on 3 and apply the function f() on the value we get.

Finding f(g(3)):

Finding g(3):

g(x) = -x³

g(3) = -(3)³

g(3) = -27

Finding f(g(3)):

f(x) = 3x + 8

f(g(3)) = 3(g(3)) + 8

f(g(3)) = 3(-27) + 8

f(g(3)) = -81 + 8

f(g(3)) = -73

Hence, f(g(3)) = -73

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Step-by-step explanation:

\(15 = - 5x + 10 \\ - 5x = 15 - 10 \\ - 5x = 5 \\ x = \frac{5}{ - 5} \\ x = - 1 \\ thank \: you\)

Answer:

28p + 14q + 21r

Step-by-step explanation:

7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside

= 28p + 14q + 21r

With respect to the linear function, the monthly cost for 68 minutes of calls is $19.28 if 51 minutes and 95 minutes cost $17.24 and $22.52 respectively.

The slope of the cost function which is the same as the variable charge per minute of call is determined by:

(the total costs of the highest activity - the total cost at the lowest activity) /the difference between the number of call minutes slope (cost per minute)

= ($22.52-$17.24)/(95-51)

Slope (cost per minute) =$0.12y

=a+bxy

=total cost

=$22.52

Note that:

a = fixed charge = unknown

b = slope = $0.12x = number of minutes = 9522.52

= a+(0.12*95)22.52

= a+11.40a =22.52-11.40a

=11.12y

= 11.12+0.12x

when x = 68y

= 11.12+(0.12*68)y

= total cost for 68n minutes

=$19.28

Find out more about cost on:

https://brainly.com/question/24516871

#SPJ1

The monthly cost for 68 minutes of calls is $19.28

What is the equation of straight-line?

The equation of straight-line considers the fixed charge of using phone plan per month plus the total variable cost of minutes of call, I mean the cost per minute of the plan can be determined by computing the slope of the straight-line equation

slope=(total cost for 95 minutes-total cost of 51 minutes)/(95-51)

total cost for 95 minutes=$22.52

total cost of 51 minutes=$17.24

slope=($22.52-$17.24)/(95-51)

slope= variable cost per minute=$0.12

We can determine the fixed charge per month using the straight-line equation and cost for 95 minutes

y=a+bx

y=total cost=$22.52

a=fixed charge per month=unknown

b=cost per minute=$0.12

x=number of minutes=95

$22.52=a+($0,12*95)

$22.52=a+$11.40

a=$22.52-$11.40

a=$11.12

total cost(68 minutes)=a+bx

a=$11.12

b=$0.12

x=68

total cost=$11.12+($0.12*68)

total cost=$19.28

Find out more about linear function on:https://brainly.com/question/14115882

#SPJ1

We want to answer different things regarding linear equations.

The answers are:

1) We want to see which function matches the given graph.

So, we can see that this is a linear function, that passes through the origin, so the y-intercept is y = 0.

We also can see that it passes through the point (2, 1).

Then we have that:

1  = a*2 + 0

1/2 = 0.5 = a

So the linear equation is:

y = 0.5*x

Here the correct option is d.

2) We know the relation:

distance = speed*time

So any permutation of these values can be used to find the time.

Then the option that can not be used to find the travel time is:

b) 70/200 = t

Because in this case, we are taking:

speed/distance = time

And that is incorrect.

3)  We have the formula:

500 = 100*x

Again, using:

Distance = speed*time

The options that are correct are the ones where 500 represents a distance and the 100 represents time or speed, then the correct options are:

a and c.

If you want to learn more, you can read:

https://brainly.com/question/2263981

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

For more questions on BODMAS

https://brainly.com/question/24383445

#SPJ8

The correct answer is: The median is the best measure of center, and it equals 19.

A box plot, also known as a box-and-whisker plot, is a graph that displays the distribution of a dataset.

The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3). The line inside the box represents the median.

The "whiskers" extend from the box to the dataset's minimum and maximum values or, in the case of outliers, a specific distance from the box (often 1.5 times the interquartile range).

The box plot in this instance reveals that the median number of tickets sold was 19, with the middle 50% of the data falling between 17 and 21 tickets sold.

A minimum of 10 and a maximum of 27 tickets may be sold before the whiskers are removed.

The median is the most suitable measure of the center for this dataset since it is the measure of the center that represents the middle of the dataset.

In light of this, the answer is "The median is the best measure of center, and it equals 19."

Learn more about Mean here:

https://brainly.com/question/521501

#SPJ1

Answer:

none are

Step-by-step explanation:

Answer :

None of them actually

The given expression is:

When r=6 and s=2, we need to replace those values into the expression and solve:

The answer is a. 25

Pythagorean Theorem: a^2 + b^2 = c^2

a = 5

b = ?

c = \(\sqrt{61}\)

5^2 + b^2 = (\(\sqrt{61}\))^2

25 + b^2 = 61

b^2 = 36

b = 6

Hope this helps!

Answer:

a)  See attachment 1.

b)  t² and D

c)  See attachment 2.

d)  g = 9.8 m/s² (1 d.p.)

Step-by-step explanation:

See attachment 1.  The line of best fit is shown in red.

The quantities the student should graph in order to produce a linear relationship between the two quantities are t² and D.

Make a table of values of t² and D:

\(\begin{array}{|l|l|l|l|l|l|}\cline{1-6} \rm t^2& 0.0196& 0.1024& 0.2116 & 0.3481& 0.3969\\\cline{1-6} \rm D & 0.10 & 0.50& 1.00 & 1.70 & 2.00\\\cline{1-6}\end{array}\)

Plot a graph of D against t² and draw a line of best fit (see attachment 2).

From inspection of the graph, the line of best fit passes through the origin (0, 0) and (0.1024, 5.0).  Therefore, use these two points to find the slope of the line:

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0.5-0}{0.1024-0}=4.8828125...\:\rm m/s^2\)

Therefore:

\(\rm \implies \dfrac{1}{2}g=4.8828125...\:\rm m/s^2\)

\(\rm \implies g=2 \cdot 4.8828125...\:\rm m/s^2\)

\(\rm \implies g=9.8\:\rm m/s^2\:(1\:d.p.)\)

Answer:

Step-by-step explanation:

We can start by simplifying the denominator, which is cot(a) + tan(a):

cot(a) + tan(a) = cos(a)/sin(a) + sin(a)/cos(a)

To combine these terms, we can find a common denominator of sin(a)cos(a):

cos^2(a)/(sin(a)cos(a)) + sin^2(a)/(sin(a)cos(a))

= (cos^2(a) + sin^2(a))/(sin(a)cos(a))

= 1/(sin(a)cos(a))

Now we can substitute this expression into the original equation:

sec(a)/(cot(a) + tan(a))

= sec(a) / (1/(sin(a)cos(a)))

= sec(a) * (sin(a)cos(a))

= (1/cos(a)) * (sin(a)/cos(a))

= sin(a)/cos^2(a)

= csc(a)sec(a)

Therefore, the simplified form of sec(a)/(cot(a) + tan(a)) is csc(a)sec(a).

The estimate for when the population will exceed 6371 is t > 20.33. This means that at a time greater than 20.33 units

To estimate when the population will exceed 6371, we can set up the inequality:

p(t) > 6371

where p(t) is the population at time t, as given by the equation \(p(t) = 1950e^{0.16t}\)

Substituting the expression for p(t) into the inequality, we get:

\(1950e^{0.16t} > 6371\)

Next, we can divide both sides of the inequality by 1950 to isolate the exponential term:

\(e^{0.16t} > 6371 / 1950\)

To solve for t, we can take the natural logarithm (ln) of both sides, which will eliminate the exponential term:

\(ln(e^{0.16t} > ln(6371 / 1950)\)

Using the property of logarithms that ln(e^x) = x, we get:

\(0.16t > ln(6371 / 1950)\)

Now, we can divide both sides of the inequality by 0.16 to solve for t:

\(0.16t / 0.16 > ln(6371 / 1950) / 0.16\)

Simplifying, we get:

\(t > ln(6371 / 1950) / 0.16\)

Using a calculator, we can find the approximate value of \(ln(6371 / 1950) / 0.16\), which is approximately 20.33 (rounded to two decimal places).

So, the estimate for when the population will exceed 6371 is t > 20.33. This means that at a time greater than 20.33 units

To know more about Exponential function visit:

brainly.com/question/14355665

#SPJ1

Answer:

29 - 6 = x

x = 23

The backpack without the sleeping bag weighs 23 pounds

Step-by-step explanation:

Sleeping bag = 6 lbs

Backpack and sleeping bag = 29

The per capita GDP can be calculated by dividing the total GDP by the population.

$1.65 trillion (GDP) / 36,732,000 (population) = $45,073.58 (per capita GDP)

This means that, on average, each person in Canada has a GDP of $45,073.58. However, it's important to note that this number doesn't necessarily reflect the distribution of wealth within the country. It's just a way of measuring the overall economic output of a country on a per person basis.

Additionally, it's worth noting that this number only takes into account the GDP and population at the time of the calculation. The inflation rate of 2.5% would increase the GDP but not the population so it's not considered in this calculation

Learn more about economic output here:

brainly.com/question/13718196

#SPJ4

Digoxin has a half-life of 35 hours, so it takes 70 hours for the toxic plasma concentration to decline to a therapeutic plasma concentration of 2ng/ML.

Digoxin has a half-life of 35 hours, which means it takes 35 hours for the quantity of digoxin in the body to be decreased by half. The dangerous plasma concentration of 8ng/ML must be decreased to a therapeutic plasma concentration of 2ng/ML in this circumstance.

To calculate how long this will take, we need to use the formula:

Time = (Toxic Concentration - Therapeutic Concentration) / (0.5 x Half-Life)

Time = (8ng/ML - 2ng/ML) / (0.5 x 35hrs)

Time = 6ng/ML / (17.5hrs)

Time = 0.342hrs

Time = 70hrs

As a result, the dangerous plasma concentration of 8ng/ML will take 70 hours to decrease to a therapeutic plasma concentration of 2ng/ML.

To know more about digoxin, visit

brainly.com/question/15180878

#SPJ1

Answer:

this means that the figures given to you , sketch and label the ones described and use dashes for hidden one

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

Height= 8341.6 feet

Step-by-step explanation:

A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'.

40°30'= 40.5°

37°46'= 37.767°

b = 180-40.5

b= 139.5°

a= 180-139.5-37.767

a= 2.733°

Using sine method

1000/Sina= y/sinB

1000/sin 2.733= y/sin 139.5

(1000*sin 139.5)/sin 2.733= y

(1000*0.6494)/0.04768= y

13619.96= y

Y= 13620 feet

Height/sin 37.767= 13620

Height=13620*sin37.767

Height= 8341.59

Height= 8341.6 feet

The mean is 0.477514 (rounded to 6 decimal places).

The standard deviation is 0.288919 (rounded to 6 decimal places).

To calculate the mean and standard deviation, we will use the following formulas:

Mean = (sum of all values) / (number of values)

Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]

Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:

Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514

Therefore, the mean is 0.477514 (rounded to 6 decimal places).

Now we will calculate the standard deviation:

Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919

Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).

Learn more about mean here: https://brainly.com/question/20118982

#SPJ1

Answer:

358.125

Step-by-step explanation:

8595/24=258.125

Answer:

Step-by-step explanation:

Given the values in the table, you want to know if they represent a linear or exponential relation, along with the common difference or ratio, as applicable.

The first attachment shows the differences and ratios between successive table values. Neither the differences nor the ratios are constant. The wide variation in ratios and the relatively smaller variation in differences suggests the table is best modeled by a linear function.

Changes when the function is linear are additive. That is, the function values have a common difference.

The average difference between table values is (949.92 -229.44)/3 = 240.16. A linear regression analysis gives a slope of 240.12 as the "best fit" to the table values.

You can see from the first attachment that the differences are not constant, so there isn't really a common difference. The difference is approximately 240.12.

__

Additional comment

The second attachment shows linear and an exponential regression applied to this data. The residuals are much smaller for the linear approximation.

The slope of the line (common difference) is estimated at 240.12 using the regression formula. This makes the mean square residuals a minimum. As we show above, this slope is different (slightly lower) than the slope of the line through the first and last data points.

Answer:

8 miles

Step-by-step explanation:

40 miles in five hours -> x miles in 1 hour

40/5=8

Quin covers a distance of 8 miles in an hour.

Step-by-step explanation:

we would have needed only one corresponding side length. because for similar triangles all corresponding lines (like sides but also heights and so on) would be related in size by using the same scaling factor.

going from the large to the small triangle : what do I need to multiply the large side length with to get the small one ?

27 × x = 9

x = 9/27 = 1/3

that is the scale factor.

The expression which best represents the given trigonometric expression as given is; Sin 4y.

It follows from the task content that the sine or cosine expression which represents the given expression be determined.

Recall from trigonometric identities;

Sin (a - b) = Sin (a) Cos(b) - Cos (a) Sin (b)

Therefore, it follows that;

sin (7y) cos (3y) - cos (7y) sin (3y) = Sin ( 7y - 3y )

= Sin 4y.

On this note, the written form of the given trigonometric expression as the sine or cosine of an angle is; Sin 4y.

Read more on trigonometric identities;

https://brainly.com/question/27777252

#SPJ1

The slope y is 3x - 10.When the line to be examined's slope is known, and the provided point also serves as the y intercept.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.

According to question:-

In the equation of a line's slope-intercept form, y = mx + b, we get y = 3x + 2, m1 = m2 gives us y = 3x +2, and m = 3 gives us the point (2 -4) where x = 2 and y = -4.

4 6 + b deducts 6 from both sides.

-10 = b, b = -10

After all, y = 3x - 10.

The complete question is,

y=3x+2 via (2,-4) parallel to

To know more about slope visit:

brainly.com/question/3493733

#SPJ1

Answer:

-26

Step-by-step explanation:

first, simplify the equation

2(a - 4) -4(a + 3)

distribute

2a -8 -4a -12

combine like terms

-2a - 20

now plug in a =3

-2 (3) -20

simplify by distributing then solving

-6 -20

= -26

The company sales in year 14, given the rate of increase and the amount made in sales would be C $3,656,872.

In the first year, the sales of the company were $ 475, 000 and this sales is scheduled or predicted to grow at 17 %.

This means that the company sales in year 14 would be :

= Initial sales x ( 1 + rate ) ^ number of years

Initial sales = $ 475, 000

Rate = 17 %

Number of years = 14 years

The company sales in year 14 is:

= 475, 000 x ( 1 + 17 %) ¹⁴

= $3, 656, 872

Find out more on company sales at https://brainly.com/question/29342346

#SPJ1