Find a logarithmic function to model the data.


x y

1 60


2 54


3 51


4 50


5 46


6 45


7 44




f(x) = 60.73(0.95)x Please help:(


f(x) = 0.93(60.73)x


f(x) = 60.04 – 8.25 ln x


f(x) = 8.25 – 60.04 ln x

Answer:

Correct option is:

A. 486 units²

Step-by-step explanation:

We have to find the surface area of cube with side length 9 units

We know that surface area of cube is:

6s²

where s is the side of the cube

Here, s=9 units

Surface area=6×9×9

                    = 486 units²

Hence, Correct option is:

A. 486 units²

486 units²

Given:

s = 9 units

Let us find out the surface area of a cube.

The formula of the surface area of a cube is [tex]\boxed{ \ S = 6(s^2) \ }[/tex],

where s is the length of one of the sides.

[tex]\boxed{ \ S = 6(9^2) \ }[/tex]

[tex]\boxed{ \ S = 6(81) \ }[/tex]

[tex]\boxed{ \ S = 6 \times 81 \ }[/tex]

Thus, the surface area of the cube is 486 sq. units.

Notes:

From the formula for surface area, we make it s as a subject.

[tex]\boxed{ \ 6(s^2) = S \ }[/tex]

[tex]\boxed{ \ s^2 = \frac{S}{6} \ }[/tex]

[tex]\boxed{\boxed{ \ s = \sqrt{\frac{S}{6}} \ }}[/tex] ... Equation-1

The formula of the volume of a cube is [tex]\boxed{ \ V = s^3 \ }.[/tex]

Substitute Equation-1 into the volume formula.

[tex]\boxed{ \ V = \bigg( \sqrt{\frac{S}{6}} \bigg)^3 \ }.[/tex]

Thus, we have connected formulas of surface area with the volume of the cube.

Keywords: what is the surface area of the cube, the length of the cube, volume, 9 units,  486 units², 508 units², 729 units², 405 units², the formula

Answer:

3/8

Step-by-step explanation:

8-5=3

The value of the angle measure of the dessert that was left ​is equal to

3/8.

We have given that,

Jake cut a round gelatin dessert into 8 equal parts. five of the pieces were eaten.

We have to determine the angle measure of the dessert that was left ​

An angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measured in degrees ( °), using a protractor.

Therefore

Jake cut a round gelatin dessert into 8 equal parts is given by,

[tex]\frac{360}{8}=45^0[/tex]

8-5=3

Therefore the  angle measure of the dessert that was left ​is,

[tex]3(45^0)=135^0[/tex]

Therefore the value of the angle measure of the dessert that was left ​is equal to 3/8.

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Final Answer:

The equation[tex]\(T = 45 - 7H\)[/tex] represents the relationship between temperature (T) and height above the surface (H) on the distant planet, where the surface temperature is 45 Celsius, decreasing by 7 Celsius for each kilometer of height. Graphing this equation reveals a linear line with a negative slope, portraying the systematic decrease in temperature as one moves higher above the planet's surface.

Explanation:

The equation [tex]\(T = 45 - 7H\)[/tex]  is derived from the given information about the distant planet's temperature. The surface temperature is 45 Celsius, and for each kilometer above the surface (represented by H), the temperature decreases by 7 Celsius.

The equation reflects this linear relationship. The term 45 is the starting temperature at the surface, and the term -7H represents the decrease for each kilometer above.

For example, let's substitute H = 1 into the equation to find the temperature at a height of 1 kilometer:

[tex]\[ T = 45 - 7(1) = 45 - 7 = 38 \][/tex]

This calculation shows that at a height of 1 kilometer, the temperature is 38 Celsius. Similarly, for H = 2:

[tex]\[ T = 45 - 7(2) = 45 - 14 = 31 \][/tex]

This process can be repeated for different values of H to create a set of coordinates (H, T) that form a linear relationship. Graphing these points produces a straight line with a negative slope, illustrating the temperature decrease with increasing height.

In essence, the detailed calculation demonstrates how the equation captures the specified temperature-height relationship on the distant planet. It provides a mathematical representation of the observed data and allows scientists to predict temperatures at various heights above the surface.

Answer:

x = 6

Step-by-step explanation:

Given that the line segment is an angle bisector then the following ratios are equal

[tex]\frac{42}{78}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex], that is

[tex]\frac{7}{13}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex] ( cross- multiply )

13(6x - 1) = 7(10x +5) ← distribute parenthesis on both sides

78x - 13 = 70x + 35 ( subtract 70x from both sides )

8x - 13 = 35 ( add 13 to both sides )

8x = 48 ( divide both sides by 8 )

x = 6

Answer:

A and B: {4, 6}

A or B: {2, 3, 4, 5, 6, 8}

Complement of B: {1, 2, 7, 8}

Step-by-step explanation:

A and B refer to the elements that are in both A and B at the same time

The even numbers from 1 to 8 are {2, 4, 6, 8}

The numbers from 3 to 6 are {3, 4, 5, 6}

Look for the common elements between both sets.

A and B: {4, 6}

A or B is the union of the two sets

Join the elements of both sets

A or B: {2, 3, 4, 5, 6, 8}

The complement of B are all the elements that are not in B.

Write all the elements of the sample space except those of event B

Complement of B: {1, 2, 7, 8}

Event A: 2, 4, 6, 8; Event B: 3, 4, 5, 6.

In probability theory, events are outcomes or sets of outcomes from a random experiment. They are subsets of the sample space, representing possible results. Simple events consist of a single outcome, while compound events involve more than one outcome. Probability measures the likelihood of events occurring.

Event A consists of the even numbers 2, 4, 6, and 8.

Event B consists of the numbers 3, 4, 5, and 6.

The outcomes for Event A are 2, 4, 6, and 8.

The outcomes for Event B are 3, 4, 5, and 6.

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Answer:

[tex]y=\sin(x-\frac{3\pi}{2})[/tex] is the graph of  [tex]y=\sin x[/tex] shifted to the right by [tex]\frac{3\pi}{2}[/tex] units.

Step-by-step explanation:

The given function is

[tex]y=\sin(x-\frac{3\pi}{2})[/tex]

The base function of this trigonometric function is [tex]y=\sin x[/tex]

In general, the transformation [tex]y=\sin(x-k)[/tex] will shift the graph of the base function, [tex]y=\sin x[/tex], k units to the right.

Therefore, [tex]y=\sin(x-\frac{3\pi}{2})[/tex] is the graph of  [tex]y=\sin x[/tex] shifted to the right by [tex]\frac{3\pi}{2}[/tex] units.

Answer:

B. 3pi/2 units to the right

Step-by-step explanation:

edge2021

Answer:

Domain:  (-∞, ∞); range:  (-∞, ∞).

Step-by-step explanation:

In the given function, f(x)= -2x + |3sinx|, the range of the |3sinx| term is [0, 3].  That of the -2x term is (-∞, ∞).  

The range of f(x)= -2x+|3sinx| is thus  (-∞, ∞); the |3sinx| term has no effect on this.

There are no restrictions on the input to f(x)= -2x+|3sinx|.  The domain is thus (-∞, ∞).

Answer:

(b)

Step-by-step explanation:

(b) is correct:  the distribution becomes narrower and taller.

Answer:

The answer should be 28.36

Step-by-step explanation:

You add them together

Hope this helps!

Answer:

28.36

Step-by-step explanation:

3.6 + 24.7 = 28.36

Answer:

[tex](x-9)^{2}+(y+4)^{2}=81[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

In this problem we have

[tex](h,k)=(9,-4)[/tex]

[tex]r=9\ units[/tex]

substitute

[tex](x-9)^{2}+(y+4)^{2}=9^{2}[/tex]

[tex](x-9)^{2}+(y+4)^{2}=81[/tex] ----> equation of the circle in standard form

I think 18 because 3+15=18

Answer:

I think it's 12

Step-by-step explanation:

15-3=12

Answer:

82%

Step-by-step explanation:

We let the random variable X denote the number of defective units in the production run. Therefore, X is normally distributed with a mean of 21 defective units and a standard deviation of 3 defective units.

We are required to find the probability, P(17 < X < 25), that the number of defective units in the production run is between 17 and 25.

This can be carried out easily in stat-crunch;

In stat crunch, click Stat then Calculators and select Normal

In the pop-up window that appears click Between

Input the value of the mean as 21 and that of the standard deviation as 3

Then input the values 17 and 25

click compute

Stat-Crunch returns a probability of approximately 82%

Find the attachment below.

Answer:

Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)

Step-by-step explanation:

Center at (-5,-1) because of the plus 5 added to the x and the plus 1 added to the y.

a(squared)=36 which means a=6 and a=distance from center to vertices so add and subtract 6 from the x coordinate since this is a horizontal hyperbola, which is (1,-1), (-11,-1). From there you dont need to find the focus since there is only one option for this;

Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)

Answer:

Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)

Step-by-step explanation:

Ok so we have 5x[tex]\frac{5x^{2} }{36}-\frac{y^{2} }{64}=1[/tex]

As you know we have the equation of the hyperbola as (x-h)^2/a^2-(y-k)^2/b^2, so the formula of the foci is [tex](h+-c,k) and for vertices (h+-a,k)[/tex]

then we have to calculate c using pythagoras theorem we have that

a=6 because is the root of 36

b=8 beacause is the root of 64

And then we have that [tex]c^{2}=a^{2}+b^{2}[/tex]

[tex]c=\sqrt{36+64}[/tex]

So the root of 100 is equal to 10

Hence c=10

Using the formula  given before and the equation we know that

h=-5

k=-1

And replacing those values on the equation we have that the foci are

And the vertices are:

So the correct answer is D

Answer:

Option B.) 12/2

Step-by-step explanation:

we know that

The rate of a linear equation is equal to the slope m

The slope is equal to

points (2,12) and (4,24)

m=(24-12)/(4-2)

m=12/2

m=6 balls/sec

Answer:

b

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

The circle shown is centred at the origin and has a radius of 5, thus

x² + y² = 5² ⇒ x² + y² = 25 → b

Answer:

  A.  Multiply 4 by 3. Then multiply 2 by 4. Add the two products.

Step-by-step explanation:

As with many rate problems, ...

  quantity = rate · time

The total quantity will be the sum of quantities associated with different rates or time periods:

  total quantity = quantity1 + quantity2

  = (rate 1)(time 1) + (rate 2)(time 2)

  = (4 books/week)(3 weeks) + (2 books/week)(4 weeks)

  = 4·3 books + 2·4 books . . . . . . units of (weeks/weeks) cancel

  = (4·3 + 2·4) books . . . . . . formula matches selection A

Answer:

first 25%

Step-by-step explanation:

A quartile is a quarter, so the first 25% falls between the minimum and lower quartile

Answer:

A. 25%

Step-by-step explanation:

Because it asks you where one section to another section (on a box plot there are four areas containing 25% within each one.)

Answer:  a) 6

Step-by-step explanation:

The mean is 375 which has a z-score of 0.

The standard deviation is 24 so:

A z-score of 3 is 99.85% from the left (or 1 - 99.85% from the right = 0.15%)

Since we are looking for the "more than" a z-score of 3, it is 0.15% of the total.

    4000

× 0.0015

 6.0000

Answer:

  the origin, (0, 0)

Step-by-step explanation:

The coordinates of A' are 1/2 those of A, meaning each has been multiplied by the scale factor 1/2. When the dilated points are all the original points multiplied by the scale factor, the center of dilation is the origin.

_____

For center of dilation Q, the image of a point A after dilation by a factor of k is ...

  A' = kA + (k-1)Q

Then for points A, A', and dilation factor k, the center of dilation can be found to be ...

  (A' -kA)/(k-1) = Q

Here, that is ...

  Q = ((-2, -2) -(1/2)(-4, -4))/(1/2 -1) = (0, 0)/(-1/2)

  Q = (0, 0)

Answer:

a

Step-by-step explanation:

Let's use the elimination method on equations 1 and 3 and see what happens:

x  +  y  +  3z  =  -4

-x  -  y  -  2z  =  5

It looks like both the x terms and the y terms cancel out leaving us with the fact that z = 1.  

Let's go back to the second equation now and sub in a 1 for z:

2x  -  z  =  -3 implies  2x - 1 = -3 and x = -1.

Pick any equation now to sub in the known values to find y.  I chose the first one, just because:

x + y + 3z = -4 implies -1 + y + 3(1) = -4 and

-1 + y + 3 = -4 so

y + 2 = -4 and

y = -6

So the solution set is (-1, -6, 1)

Answer:  (26996, 42744)

Step-by-step explanation:

24% of 112,483 = 26,995.92  --> rounded to the nearest person is 26,996

38% of 112,483 = 42,743.54  --> rounded to the nearest person is 42,744

The number of people who want a new restaurant is somewhere between 26,996 and 42,744.

Answer:

26,996-42,744

Step-by-step explanation:

To calculate the spam of the people that who are likely to want this restaurant you just have to multiply the total number people in the city by the two points in the extremes of the intervals.

24% * 112,483=26996

and the other one would be:

38%* 112,483= 42744

And those are the extremes of the interval of people in the city who are likely to want this new restaurant.

Answer:

Step-by-step explanation:

One

f(5a) means that wherever you see an x, you put in 5a

x = 5a

f(x) = x/5t *  5t - 2

f(x) = x - 2

===============

Two

g(2t) = 8t - 1

x = 2t

g(x) = 8t/2t*x - 1

g(x) = 4x - 1

1)for the first one you can put a=(1/5)a in the function and it will be:

[tex]f(a) = a - 2[/tex]

so in a function , alphabet is not important and you can rewrite it to this:

[tex]f(x) = x - 2[/tex]

2)the same as the first , we can put t=(1/2)t and conclusion is :

[tex]g(t) = 4t - 1[/tex]

and then change the t to x:

[tex]g(x) = 4x - 1[/tex]

Answer: Savings account - Apex

Answer:

Option D is the correct answer.

Step-by-step explanation:

The saving bonds are a good way to earn money but they work at fixed rate of interest over a set time period.

Money market accounts give a limited access to account and not more than three checks are written in a month. Its a type of short term savings.

The certificate of deposit or CD's have higher interest rate than savings account. But one cannot withdraw the money before the term maturity otherwise penalty is to be paid.

Savings account are deposit accounts that can be accessed whenever needed. These yield less interest as compared to money market accounts or CD's.

Therefore, the best option for Lionel to choose will be Savings account

Answer:

D:   {9, 21, 33}

Step-by-step explanation:

Ken worked 2, 8 and 14 hours on 3 separate days.

For working 2 hours, his earnings were f(2) = 2(2) + 5, or 9;

For working 8 hours, his earnings were f(28) = 2(8) + 5, or 21; and

For working 14 hours, his earnings were f(14) = 2(14) + 5, or 33

Thus, the range of this function for the days given is {9, 21, 33} (Answer D)

Answer:

C

Step-by-step explanation:

Finding the z-score:

z = (x - μ) / σ

z = (66 - 57) / 9

z = 1

Using a z-score table or calculator:

P(z < 1) = 0.8413

84.13% of 4000 is:

0.8413 (4000) = 3365.2

Rounding up to the nearest whole number, approximately 3366 students will score less than 66.  Answer C.

Using the normal distribution, it is found that approximately 3366 students will score less than 66 on the test.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

In this problem, the mean and the standard deviation are given as follows:

[tex]\mu = 57, \sigma = 9[/tex]

The proportion of students that scored less than 66 is the p-value of Z when X = 66, hence:

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

[tex]Z = \frac{66 - 57}{9}[/tex]

Z = 1

Z = 1 has a p-value of 0.8413.

Out of 4000 students:

0.8413 x 4000 = 3366, which means that option C is correct.

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The distance between the center to the circumcenter is called a radius. The radius can not be a chord.

It is the distance between the two points in a circle that is known as a chord.

1  Diameter - If the chord length is longest then it is called the diameter. This can be a chord.

2  Radius - The distance between the center to the circumcenter is called a radius. This can not be a chord.

3  Secant - The line passing through the circle is known as a secant. This can be a chord.

4  Tangent - The line which touches the circle then line is called a tangent. This can be a chord.

More about the chord of a circle link is given below.

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Answer:

8 hours

Step-by-step explanation:

Joe spends 18.75% of his working day washing cars.

Joe spends 1.5 hours washing car.

Therefore 18.75% is equal to 1.5 hour.

18.75% = 1.5 hour

1% = 1.5 ÷ 18.75 = 0.08 hour

100% = 0.08 x 100 = 8 hours

The answer might be 2.66

Answer:

0.5

Step-by-step explanation:

12 is the total amount of bags

(2*1/6+ 2*1/3 + 3*1/2 + 4*2/3 + 1*5/6 ) / 12 =

[1/3 + 2/3 + 3/2 + 8/3 + 5/6]/12 = [(1+2+8)/3 + (3*3+5)/6 ]/12 =

(11/3+14/6)/5 = [(22+14)/6 ]/12 = (36/6) /5 = 6/12=0.5

i am pretty sure you add up all of them

The percent change in the numerator for the cash coverage ratio, considering the changes in EBIT and depreciation, is 12.5%. Meanwhile, the percent change in the denominator, based on the interest expense, is 33.33%.

The cash coverage ratio is a measure of a company's ability to pay off its obligations and is calculated by adding depreciation and EBIT and then dividing by the interest expense. For this question, we are looking at the percent change in the numerator, which is EBIT + depreciation, and the denominator, which is the interest expense. With EBIT going from $30m to $33m, depreciation going from $10m to $12m, and interest expense going from $6m to $8m we can calculate as follows.

The original numerator value was $40m (EBIT of $30m + depreciation of $10m) and the new numerator is $45m (EBIT of $33m + depreciation of $12m). So, the percent change in the numerator of the cash coverage ratio is ((45-40)/40)*100 = 12.5%. The original denominator was $6m and the new denominator is $8m. Thus, the percent change in the denominator of the cash coverage ratio is ((8-6)/6)*100 = 33.33%.

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Answer:

[tex]V = 2622\ in ^ 3[/tex]

Step-by-step explanation:

We have a composite figure, therefore the volume of the figure will be the sum of the volume of both figures.

The volume of the rectangular prism is the product of its length by its width by its height

[tex]V_r = 7 * 12 * 19\\\\V_r = 1596\ in^3[/tex]

The volume of the triangular prism is

[tex]V_t = A_b * l[/tex]

Where [tex]A_b[/tex] is the area of the triangular base and l is the length

[tex]A_b = 0.5 * 9 * 12 = 54\ in^2[/tex]

[tex]V_t = 0.54 * 19 = 1026\ in^3[/tex]

Finally

[tex]V = 1596 + 1026[/tex]

[tex]V = 2622\ in ^ 3[/tex]

The answer is:

The total volume is equal to:  [tex]2622in^{3}[/tex]

To calculate the total volume of the composite figure, we need to calculate the volume of both of the figures that creates the composite figure.

So, calculating we have:

First figure:

The first figure has a triangular base (side for this case) and height, to find its volume, we just need to calculate the area of its base and then, multiply it by its height.

We are given that:

[tex]base_{height}=9in\\base_{base}=12in\\length=19in[/tex]

Calculating the area of the side/base, we have:

[tex]A=\frac{b*h}{2}[/tex]

[tex]A=\frac{12in*9in}{2}=54in^{2}[/tex]

Now, calculating the volume, we have:

[tex]Volume_{1}=Area*Length\\\\Volume_{1}=54in^{2}*19in=1026in^{3}[/tex]

Second figure:

The second figure is a rectangle, we can calculate its volume using the following formula:

[tex]Volume_2=base*height*width\\\\Volume_2=12in*7in*19in=1596in^{3}[/tex]

Hence, we can calculate the total volume by adding the first volumen and the second volume:

[tex]TotalVolume=Volume_1+Volume_2\\\\TotalVolume=1026in^{3} +1596in^{3}=2622in^{3}[/tex]

The total volume is equal to  [tex]2622in^{3}[/tex]

Have a nice day!