The summer reading list for your English class has twelve books, and the list for History has eight books. You need to read three books for English and two books for History. How many different sets of books can you read?

Answer:

C(x)= 41x + 680

Step-by-step explanation:

If the fixed cost is 680, that will apply regardless of how many jackets the company makes for you. The number of jackets is unknown.  However, we know that the cost of producing a single jacket is 41, so we can represent that expression as 41x.  Putting those things together gives us a function of the cost:

C(x) = 41x + 680

The equation to determine the total cost encountered by Marty's Tee Shirt & Jacket Company in producing x jackets is C(x) = 680 + 41x.

To determine the total cost, C(x), encountered by Marty's Tee Shirt & Jacket Company in producing x jackets, we need to consider both the fixed costs and the variable costs. The fixed costs, which are $680, are incurred regardless of the number of jackets produced. The variable costs, which are $41 per jacket, increase with each additional jacket produced. So the equation to calculate the total cost is:

C(x) = fixed costs + (variable costs per jacket) * x

Substituting the given values, the equation becomes:

C(x) = 680 + 41x

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Answer:

  3x ≥ -6

Step-by-step explanation:

"No less than" means "greater than or equal to". An appropriate translation of the problem statement is ...

  3x ≥ -6

Answer:

3x ≥ -6

Step-by-step explanation:

The the inequality that could be used to solve three times a number is no less than negative six is 3x ≥ -6.

Answer: 5 units

Step-by-step explanation:

The formula to find the area of a triangle is given by :-

[tex]\text{Area}=\dfrac{1}{2}\text{ base * height}[/tex]

Given : The area of a triangle = 30 square units

The length of the base of the triangle = 12 units

Let h be the height of the triangle .

Then , we have

[tex]30=\dfrac{1}{2}12\times h\\\\\Rightarrow\ h=\dfrac{30}{6}\\\\\Rightarrow\ h=5\text{ units}[/tex]

Hence, the height of a triangle = 5 units

The graph hits [tex]\fbox{\begin\\\ \dfrac{10}{T}+2\\\end{minispace}}[/tex] times over 2 feet for [tex]a>2[/tex].

Further explanation:  

The height of the wave is given by the equation as follows:  

[tex]y=asin\left(\dfrac{2\pi t}{T}\right)[/tex]                          ......(1)

Here, [tex]a[/tex] is amplitude, [tex]T[/tex] is period of wave in second and [tex]t[/tex] time in seconds.  

The height [tex]y[/tex] of the wave is given as 2 feet and time [tex]t[/tex] is given as 5 seconds.  

Substitute 2 for [tex]y[/tex] and 5 for [tex]t[/tex] in equation (1).  

[tex]2=asin\left(\dfrac{2\pi \times5}{T}\right)\\2=asin\left(\dfrac{10\pi}{T}\right)\\\dfrac{2}{a}=sin\left(\dfrac{10\pi}{T}\right)[/tex]

The above eqution is valid only for [tex]a\geq 2[/tex] because the maximum value of the term [tex]sin(10\pi /T)[/tex] is 1.  

If [tex]T[/tex] is the time period then in [tex]T[/tex] seconds the graph will hit at least 2 times over 2 feet for [tex]a>2[/tex].

T seconds[tex]\rightarrow[/tex]2 hits

1 seconds [tex]\rightarrow[/tex] [tex]\dfrac{2}{T}[/tex] hits

5 seconds [tex]\rightarrow\dfrac{2\times5}{T}[/tex]

5 seconds [tex]\rightarrow[/tex] [tex]\dfrac{10}{T}[/tex]

If [tex]T[/tex] is time period in 5 seconds then the graph will hit [tex][10/T][/tex] times in interval 0 to [tex]2\pi[/tex].

Thus, the graph hits [tex]\fbox{\begin\\\ \dfrac{10}{T}+2\\\end{minispace}}[/tex] times over 2 feet for [tex]a>2[/tex].

Learn more:  

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)  

https://brainly.com/question/1332667  

2. Which is the graph of f(x) = (x – 1)(x + 4)?  

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Answer details:  

Grade: High school.  

Subjects: Mathematics.  

Chapter: function.  

Keywords: Function, wave equation, height, amplitude, equation, period, periodic function, y=asin(2pit/T), frequency, magnitude, feet, height, time period, seconds, inequality, maximum value, range, harmonic motion, oscillation, springs, strings, sonometer.

Answer:

  18.8 cm²

Step-by-step explanation:

Sometimes, as here, when the problem is not carefully constructed, the answer you get depends on the method you choose for solving the problem.

Following directions

Using the formula ...

  Area = (1/2)ab·sin(C)

we are given the values of "a" (BC=5.9 cm) and "b" (AC=7.2 cm), but we need to know the value of sin(C). The problem statement tells us to round this value to the nearest hundredth.

  sin(C) = sin(118°) ≈ 0.882948 ≈ 0.88

Putting these values into the formula gives ...

  Area = (1/2)(5.9 cm)(7.2 cm)(0.88) = 18.6912 cm² ≈ 18.7 cm² . . . rounded

You will observe that this answer does not match any offered choice.

__

Rounding only at the End

The preferred method of working these problems is to keep the full precision the calculator offers until the final answer is achieved. Then appropriate rounding is applied. Using this solution method, we get ...

  Area = (1/2)(5.9 cm)(7.2 cm)(0.882948) ≈ 18.7538 cm² ≈ 18.8 cm²

This answer matches the first choice.

__

Using the 3 Side Lengths

Since the figure includes all three side lengths, we can compute a more precise value for angle C, or we can use Heron's formula for the area of the triangle. Each of these methods will give the same result.

From the Law of Cosines, the angle C is ...

  C = arccos((a² +b² -c²)/(2ab)) = arccos(-38.79/84.96) ≈ 117.16585°

Note that this is almost 1 full degree less than the angle shown in the diagram. Then the area is ...

   Area = (1/2)(5.9 cm)(7.2 cm)sin(117.16585°) ≈ 18.8970 cm² ≈ 18.9 cm²

This answer may be the most accurate yet, but does not match any offered choice.

Answer: Option C

No; Jamie could not have won 11 games because [tex]2x - 5 \neq 30[/tex]

Step-by-step explanation:

Let's call x the number of games that Jamie has won

Let's call y the number of games that Imani has won

We know that Imani has won 5 more games than Jamie.

Then we can say that:

[tex]y= x - 5[/tex]

We know that the total number of games that Jamie and Imani have won together is 30.

So

[tex]x + y = 30[/tex]

We want to know if it is possible that [tex]x = 11[/tex].

Then we substitute the first equation in the second and get the following:

[tex]x + x - 5 =30\\2x - 5 = 30[/tex]

Now replace [tex]x = 11[/tex] in the equation and check if equality is met.

[tex]2 (11) - 5 = 30\\22 - 5 = 30\\17 \neq 30[/tex]

Equality is not met, then the correct answer is option C

Answer: is c (no Jamie could not have won 11 games because 2x-5=/30

Step-by-step explanation:

Answer:

D x=1

Step-by-step explanation:

6^(3-x)=6^2

Since the bases are the same, the exponents have to be the same

3-x = 2

Subtract 3 from each side

3-x-3 = 2-3

-x = -1

Multiply each side by -1

x = 1

Answer: Option D

[tex]x=1[/tex]

Step-by-step explanation:

We have the following exponential equation

[tex]6^{3-x}=6^2[/tex]

We must solve the equation for the variable x

Note that the exponential expressions [tex]6^{3-x}[/tex] and [tex]6 ^ 2[/tex] have the same base: 6

So if [tex]6^{3-x}=6^2[/tex] this means that [tex]3-x = 2[/tex]

Then we have that:

[tex]3-x = 2[/tex]

[tex]x = 3-2\\x=1[/tex]

Answer:

Proofs are in the explanation.

Step-by-step explanation:

b)  My first thought is to divide top and bottom on the left hand side by [tex]\cos(\alpha)[/tex].

I see this would give me 1 on top and where that sine is, it would give me tangent since sine/cosine=tangent.

Let's do it and see:

[tex]\frac{\cos(\alpha)}{\cos(\alpha)-\sin(\alpha)} \cdot \frac{\frac{1}{\cos(\alpha)}}{\frac{1}{\cos(\alpha)}}[/tex]

[tex]=\frac{\frac{\cos(\alpha)}{\cos(\alpha)}}{\frac{\cos(\alpha)}{\cos(\alpha)}-\frac{\sin(\alpha)}{\cos(\alpha)}}[/tex]

[tex]=\frac{1}{1-\tan(\alpha)}[/tex]

c) My first idea here is to expand the cos(x+y) using the sum identity for cosine.

So let's do that:

[tex]\frac{\cos(x)\cos(y)-\sin(x)\sin(y)}{\cos(x)\sin(y)}[/tex]

Separating the fraction:

[tex]\frac{\cos(x)\cos(y)}{\cos(x)\sin(y)}-\frac{\sin(x)\sin(y)}{\cos(x)\sin(y)}[/tex]

The cos(x) cancel's in the first fraction and the sin(y) cancels in the second fraction:

[tex]\frac{\cos(y)}{\sin(y)}-\frac{\sin(x)}{\cos(x)}[/tex]

[tex]\cot(y)-\tan(x)[/tex]

d) This one makes me think it is definitely essential that we use properties of logarithms.

The left hand side can be condense into one logarithm using the product law:

[tex]\ln|(1+\cos(\theta))(1-\cos(\theta))|[/tex]

We are multiplying conjugates inside that natural log so we only need to multiply the first and the last:

[tex]\ln|1-\cos^2(\theta)|[/tex]

I can rewrite [tex]1-\cos^2(\theta)[/tex] using the Pythagorean Identity:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]:

[tex]\ln|\sin^2(\theta)|[/tex]

Now by power rule for logarithms:

[tex]2\ln|\sin(\theta)|[/tex]

Answer:

sinB is correct

Step-by-step explanation:

Calculating each of cos/ sin for ∠B

cosB = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{3\sqrt{5} }[/tex] = [tex]\frac{2}{\sqrt{5} }[/tex] and

[tex]\frac{2}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] = [tex]\frac{2\sqrt{5} }{5}[/tex] ≠ [tex]\frac{\sqrt{5} }{5}[/tex]

--------------------------------------------------------------------------------

sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{3\sqrt{5} }[/tex] = [tex]\frac{1}{\sqrt{5} }[/tex] and

[tex]\frac{1}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] = [tex]\frac{\sqrt{5} }{5}[/tex]

Answer:sinB is correct

Step-by-step explanation

Step-by-step explanation:

Calculating each of cos/ sin for ∠B

cosB =  =  =  and

×  =  ≠

--------------------------------------------------------------------------------

sinB =  =  =  and

×  =

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Hence, the average rate of change in vertical height is:

                               -6

We know that the average amount that the roller coaster's height changes over each horizontal foot is basically the slope or the average rate of change of the height of the roller coaster to the horizontal distance.

i.e. it is the ratio of the vertical change i.e. the change in height of the roller coaster to the horizontal change.

Here the vertical change= -150 feet

and horizontal change = 25 feet

Hence,

Average rate of change is:

[tex]=\dfrac{-150}{25}\\\\=-6[/tex]

So, for every change in horizontal distance by 1 feet the vertical height drop by 6 feet.

Answer:

The average amount that the roller coaster's height changes over each horizontal foot is -6.

Further explanation:

The rate of linear function is known as the slope. And the slope can be defined as the ratio of vertical change (change in y) to the horizontal change (change in x).

Mathematically, we can write

[tex]\text{Slope}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{\Delta y}{\Delta x}[/tex]

Now, we have been given that  

Roller coaster has a steep drop at a horizontal distance of 25 feet.

Thus, [tex]\Delta x=25\text{ feet}[/tex]

The height of the roller coaster at the bottom of the drop is -150 feet.

Thus, [tex]\Delta y=-150\text{ feet}[/tex]

Using the above- mentioned formula, the average rate of change is given by

[tex]\text{Average rate of change }=\dfrac{-150}{25}[/tex]

On simplifying the fraction

[tex]\text{Average rate of change }=\dfrac{-6}{1}=-6[/tex]

It means for every 1 foot of horizontal distance, the roller coaster moves down by 6 feet.  

Please refer the attached graph to understand it better.

Therefore, we can conclude that the average amount that the roller coaster's height changes over each horizontal foot is -6.

Learn more:

Average rate of change: https://brainly.com/question/10961592

Finding Average: https://brainly.com/question/9145375

Keywords:

Average rate of change, slope, change of y over change of x, the ratio of two numbers be the same.

Answer with explanation:

Pre-image =Rectangle EFGH

Image = Rectangle E'F'G'H'

Stretch Factor = 2.5

Coordinates of Point H= (-2,0)

If Coordinate of any point is (x,y) and it is stretched by a factor of k , then coordinate of that point after stretching = (k x , k y).

So, Coordinates of Point H' will be=(-2×2.5,0×2.5)

                                      = (-5,0)

Answer: (-5,0)

Step-by-step explanation:

Given : Square EFGH stretches vertically by a factor of 2.5 to create rectangle  E?F?G?H?.

The square stretches with respect to the x-axis such that the point H is located at (-2, 0).

Since , we know that to find the coordinate of image , we multiply the scale factor to the coordinate of pre-image.

Then , the coordinate of H? is given by :-

[tex](-2\times2.5, 0\times2.5)=(-5,0)[/tex]

Answer:

  291.9518 T are required for completion

Step-by-step explanation:

The remaining 0.62 part is ...

  0.62 × 470.89 T = 291.9518 T

Answer:

291.9518 metric Ton

Step-by-step explanation:

Hello

according to the data provided by the problem.

Total Iron needed to build the railing (A)= 470.89 Ton

Total Iron purchased by the factory =0.38 of total

Total Iron purchased by the factory =0.38 *470.89

Total Iron purchased by the factory (B)=178.9382metric Ton

the difference between the total iron needed and the iron supplied by the factory will be the iron we need to get

A-B=iron we need to get(c)

C=A-B

C=470.89-178.9382

C=291.9518 metric Ton

Have a great day.

[tex]\frac{3}{4} = log_{2}(\sqrt[4]{8} )\\-4 = log_{3} \frac{1}{81} \\-6= -3log_{5} 25\\\frac{1}{3} = log_{6} (\sqrt[3]{6} )[/tex]

Here's how you solve it!

[tex]log_{2} \sqrt[4]{8}[/tex]

Write it in exponential form

[tex]log_{2} (2 \frac{3}{4} )[/tex]

Then simplify

[tex]\frac{3}{4}[/tex]

[tex]log_{3} \frac{1}{81}[/tex]

Write in exponential form

[tex]log_{3} (3^{-4} )[/tex]

Simplify

-4

[tex]-3log_{5} 25[/tex]

Write in exponential form

[tex]-3log_{5} (5^{2} )[/tex]

Simplify

-3 * 2 = -6

-6

[tex]log_{6} \sqrt[3]{6}[/tex]

Write in exponential form

[tex]log_{6} (6\frac{1}{3} )[/tex]

Simplify

[tex]\frac{1}{3}[/tex]

Hope this helps! :3

The problem involves simplifying mathematical expressions, through steps as prescribed by BIDMAS/PEDMAS rules. Start by addressing anything within parentheses, follow through with multiplication or division, and finally handle addition or subtraction.

This question involves the process of mathematical simplification of expressions. To solve this, you will first need to perform any calculations within the parentheses, then handle any multiplication or division from left to right, lastly address any addition or subtraction, also from left to right (also known as the order of operations or BIDMAS/PEDMAS). For example, if you have an expression like '2(3+4)': First, process the operation within the parentheses, in this case, it's a sum so you have '2*7', resulting in '14'. This is considered the simplified version of your expression.

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Answer:

(3g-5)(2g+7)

Step-by-step explanation:

Compare

6g^2+11g-35 to

ag^2+bg+c.

We should see that a=6, b=11,c=-35.

It these is factoable over the rationals we should be able to find two numbers that multiply to be ac and add up to be b.

ac=6(-35)

b=11

Now I really don't want to actually find the product of 6(-35). I'm just going to play with the factors until I see a pair that adds up to 11.

6(-35)

30(-7)  Moved a factor of 5 around.

10(-21) Moved a factor of 3 around.

10 and -21 is almost it.  We just need to switch where the negative is because we want a sum of 11 when we add the numbers (not -11).

So b=-10+21 and ac=-10*21.

We are going to replace b in

6g^2+11g-35

with -10+21.

We can do this because 11 is -10+21.

Let's do it.

6g^2+(-10+21)g-35

6g^2+-10g+21g-35

Now we are going to factor the first two terms together and the second two terms together.

Like so:

(6g^2-10g)+(21g-35)

We are going to factor what we can from each pair.

2g(3g-5)+7(3g-5)

There are two terms both of these terms have a common factor of (3g-5) so we can factor it out:

(3g-5)(2g+7)

Answer:

only keeps-

cows=134-67-34-10=23

sheep=142-67-34-15=26

goats=76-10-34-15=17

no pets=205-23-17-26-67-10-16-34

Step-by-step explanation:

some have one pets some have two or three

total no. of family have cows is 134 then 134 minus by those with more will be no. of family only with cows

Answer:

The vertex is the point (-6,-34)

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

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

where

(h,k) is the vertex of the parabola

In this problem we have

[tex]y=x^{2}+12x+2[/tex]

Convert in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y-2=x^{2}+12x[/tex]

Complete the square . Remember to balance the equation by adding the same constants to each side.

[tex]y-2+36=x^{2}+12x+36[/tex]

[tex]y+34=x^{2}+12x+36[/tex]

Rewrite as perfect squares

[tex]y+34=(x+6)^{2}[/tex]

[tex]y=(x+6)^{2}-34[/tex]

The vertex is the point (-6,-34)

Answer:

  6 2/3 minutes

Step-by-step explanation:

Their rates in "jobs per hour" are ...

  (60 min/h)/(15 min/job) = 4 jobs/h

and

  (60 min/h)/(12 min/job) = 5 jobs/h

So, their combined rate is ...

  (4 jobs/h) + (5 jobs/h) = 9 jobs/h

The time required (in minutes) is ...

  (60 min/h)/(9 jobs/h) = (60/9) min = 6 2/3 min

Working together, it will take them 6 2/3 minutes.

To find out how long it would take the two grandparents to clean the playroom together, we can use the concept of rates and set up an equation. Solving the equation, we find that it would take them 9 minutes to clean the playroom if they work together.

To solve this problem, we can use the concept of rates to find the combined rate at which the two grandparents clean. Let's assign the variable x to represent the time it takes for them to clean together.

The rate at which the first grandparent cleans is 1/15th of the playroom per minute, while the rate at which the second grandparent cleans is 1/12th of the playroom per minute. The combined rate when they work together is the sum of their individual rates, which is given by the equation (1/15)+(1/12)=(1/x).

To solve this equation, we can find a common denominator of 60 to simplify the equation to 4/60+5/60=1/x. Adding the fractions gives us 9/60=1/x. Multiplying both sides of the equation by 60 gives us 9=x. Therefore, it would take the two grandparents 9 minutes to clean the playroom if they work together.

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Answer:

  c. 130

Step-by-step explanation:

∠FAB is a vertical angle with the one that is marked, so is 50°. ∠FAE is the complement of that, so is 40°. ∠DAF is the sum of the right angle DAE and angle FAE, so is ...

  90° + 40° = 130° = m∠DAF

Answer:

Step-by-step explanation:

1. -2y+7 < 1

Add 2y-1:

  6 < 2y

Divide by 2:

  3 < y

__

2. 4y +3 < -5

Subtract 3:

  4y < -8

Divide by 4:

  y < -2

_____

These are graphed on the number line with open circles because y=-2 and y=3 are not part of the solution set.

Answer:

Step-by-step explanation:

[tex](1)\\\\-2y+7<1\qquad\text{subtract 7 from both sides}\\-2y+7-7<1-7\\-2y<-6\qquad\text{change the signs}\\2y>6\qquad\text{divide both sides by 2}\\\boxed{y>3}\\\\(2)\\\\4y+3<-5\qquad\text{subtract 3 from both sides}\\4y+3-3<-5-3\\4y<-8\qquad\text{divide both sides by 4}\\\boxed{y<-2}\\\\\text{From (1) and (2) we have:}\ y<-2\ or\ y>3[/tex]

[tex]<,\ >-\text{op}\text{en circle}\\\leq,\ \geq-\text{closed circle}[/tex]

Answer:

The maximum area that can be obtained by the garden is 128 meters squared.

Step-by-step explanation:

A represents area and we want to know the maximum.

[tex]A(x)=-2x^2+32x[/tex] is a parabola.  To find the maximum of a parabola, you need to find it's vertex.  The y-coordinate of the vertex will give us the maximum area.

To do this we will need to first find the x-coordinate of our vertex.

[tex]x=\frac{-b}{2a}{/tex] will give us the x-coordinate of the vertex.

Compare [tex]-2x^2+32x[/tex] to [tex]ax^2+bx+c[/tex] then [tex]a=-2,b=32,c=0[tex].

So the x-coordinate is [tex]\frac{-(32)}{2(-2)}=\frac{-32}{-4}=8[/tex].

To find the y that corresponds use the equation that relates y and x.

[tex]y=-2x^2+32x[/tex]

[tex]y=-2(8)^2+32(8)[/tex]

[tex]y=-2(64)+32(8)[/tex]

[tex]y=-128+256[/tex]

[tex]y=128[/tex]

The maximum area that can be obtained by the garden is 128 meters squared.

By using the vertex formula to find the width that maximizes the area of Beth's garden, we determine that the maximum area she can enclose with 32 meters of fencing is 128 square meters when the width is set to 8 meters.

The question is about finding the maximum area that can be enclosed by Beth with 32 m of fencing for a garden, modeled by the function A(x) = -2x2 + 32x, where x is the width of the garden in meters. To find the maximum area, we need to determine the vertex of this quadratic equation since the coefficient of x2 is negative, indicating a maximum point for the area.

To find the vertex, we can use the formula x = -b / 2a, where a and b are the coefficients from the quadratic equation A(x). Thus, x = -32 / (2*(-2)) = 8 meters. Substituting x back into the function to find the maximum area, A(8) = -2(8)2 + 32(8) = -128 + 256 = 128 square meters.

This shows that the maximum area Beth can enclose with 32 meters of fencing for her garden is 128 square meters, by setting the width to 8 meters.

Answer:

  3

Step-by-step explanation:

The diagram shows the answer: 3 pictures will fit vertically.

You can solve this algebraically as well. For n pictures, there will be n-1 spaces, so the total height of the page must satisfy ...

  1 + 3n + 1/2(n -1) + 1 ≤ 12

  3.5n + 1.5 ≤ 12 . . . . . . . . . . . simplify

  3.5n ≤ 10.5 . . . . . . . . . . . . . .subtract 1.5

  n ≤ 3 . . . . . . . . . . . . . . . . . . . divide by 3.5

Up to 3 pictures will fit in a column.

Answer:  [tex]\dfrac{20}{3}\text{ hours}[/tex]

Step-by-step explanation:

Let x be the speed of slower pump and 1.5x be the speed of faster pump to fill the swimming pool .

Then , According to the given question, we have the following equation:-

[tex]x+1.5x=\dfrac{1}{4}\\\\\rightarrow\ 2.5x=\dfrac{1}{4}\\\\\Rightarrow\ x=\dfrac{1}{10}=[/tex]

Now, the time taken by faster pump to fill the pool is given by :-

[tex]t=\dfrac{1}{1.5x}=\dfrac{10}{1.5}=\dfrac{20}{3}\text{ hours}[/tex]

Hence, the faster pump would take [tex]\dfrac{20}{3}\text{ hours}[/tex]  to fill the pool if it had worked alone at its constant rate.

Answer:

t = 21.97 years

Step-by-step explanation:

The formula for the continuous compounding if given by:

A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

It is given that p = $x, r = 5%, and A = $3x. In this part, t is unknown. Therefore: 3x = x*e^(0.05t). This implies 3 = e^(0.05t). Taking natural logarithm on both sides yields ln(3) = ln(e^(0.05t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(3) = 0.05t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(3)/0.05. This means that t = 21.97 years (rounded to the nearest 2 decimal places)!!!

Answer:

t = 22 years

Step-by-step explanation:

* Lets explain the compound continuous interest

- Compound continuous interest can be calculated using the formula:

  A = P e^rt

# A = the future value of the investment, including interest

# P = the principal investment amount (the initial amount)

# r = the interest rate  

# t = the time the money is invested for

- The formula gives you the future value of an investment,  

  which is compound continuous interest plus the

  principal.  

* Now lets solve the problem

∵ The initial investment amount is P

∵ The future amount after t years is three times the initial value

∴ A = 3P

∵ The rate of interest is 5%

∴ r = 5/100 = 0.05

- Lets use the rule above to find t

∵ A = P e^rt

∴ 3P = P e^(0.05t)

- Divide both sides by P

∴ 3 = e^(0.05t)

- Insert ㏑ for both sides

∴ ㏑(3) = ㏑(e^0.05t)

- Remember ㏑(e^n) = n ㏑(e) and ㏑(e) = 1, then ㏑(e^n) = n

∴ ㏑(3) = 0.05t

- Divide both sides by 0.05

∴ t = ㏑(3)/0.05 = 21.97 ≅ 22

* t = 22 years

[tex]\bf 7~~,~~\stackrel{7+6}{13}......601\qquad \qquad \stackrel{\textit{common difference}}{d = 6} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=7\\ d=6\\ a_n=601 \end{cases} \\\\\\ 601=7+(n-1)6\implies 601=7+6n-6\implies 601=1+6n \\\\\\ 600=6n\implies \cfrac{600}{6}=n\implies 100=n \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ \cline{1-1} a_1=7\\ a_n=601\\ n=100 \end{cases}\implies S_{100}=\cfrac{100(7+601)}{2} \\\\\\ S_{100}=\cfrac{60800}{2}\implies S_{100}=30400[/tex]

Answer: 0.1210

Step-by-step explanation:

Given : The length of country and western songs is normally distributed with [tex]\mu=170 \text{ seconds}[/tex]

[tex]\sigma=40\text{ seconds}[/tex]

Sample size : [tex]n=16[/tex]

Let x be the length of randomly selected country song.

z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z=\dfrac{158.30-170}{\dfrac{40}{\sqrt{16}}}\approx-1.17[/tex]

The probability that a random selection of 16 songs will have mean length of 158.30 seconds or less by using the standard normal distribution table will be

= [tex]P(x\leq158.30)=P(z\leq-1.17)[/tex]

[tex]=0.1210005\approx0.1210[/tex]

Hence, the probability that a random selection of 16 songs will have mean length of 158.30 seconds or less is 0.1210

The probability that a random selection of 16 country and western songs will have a mean length of 158.30 seconds or less is approximately 12.10%. This is calculated using the concept of the Sampling Distribution of the Mean and a Z score.

To find the probability that a random selection of 16 songs will have a mean length of 158.30 seconds or less, we need to use the concept of the Sampling Distribution of the Mean. This is a statistical concept that involves probabilities and the distribution of sample means. We assume that the distribution of length of songs is normal.

In our case, the population mean (μ) is 170 seconds and the population standard deviation (σ) is 40 seconds. We are looking at samples of 16 songs, so the sample size (n) is 16.

The mean of the sampling distribution of the mean (also just the population mean) is μ. The standard deviation of the sampling distribution (often called the standard error) is σ/√n. Given our numbers, this would be 40/√16 = 10.

We want the probability that the sample mean is 158.30 or less. The Z score is a measure of how many standard errors our observed sample mean is from the population mean. To find the Z score we use the formula: Z = (X - μ) / (σ/√n).

Therefore: Z = (158.30 - 170) / 10 = -1.17

A Z score of -1.17 corresponds to a probability of about 0.1210 or 12.10% that a random selection of 16 songs will have a mean length of 158.30 seconds or less.

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Answer:

True

Step-by-step explanation:

Segments drawn to a circle from the same outside point are congruent.

Segments YZ and XY are tangent to circle E draw from outside point Y. The segments are congruent, so the statement is true.

Answer:

252

Step-by-step explanation:

y varies directly with x means y=kx where k is a constant.

A constant means it never changes no matter what the point (x,y) they give.

So y=kx means y/x=k (I just divided both sides by x here).

So we have the following proportion to solve:

[tex]\frac{y_1}{x_1}=\frac{y_2}{x_2}[/tex]

[tex]\frac{70}{10}=\frac{y_2}{36}[/tex]

70/10 reduces to 7:

[tex]7=\frac{y_2}{36}[/tex]

Multiply both sides by 36:

[tex]7(36)=y_2[/tex]

Simplify left hand side:

[tex]252=y_2[/tex]

So y is 252 when x is 36.

Answer:

The measure of arc BC = 124°

Step-by-step explanation:

From the figure we can write,

measure of arc AB + measure of arc BC + measure of arc AC = 360

measure of arc AB   = 146°

measure of arc BC = 90°

Therefore measure arc BC = 360 - (146 + 90)

 = 360 - 236

 = 124°

The measure of arc BC = 124°

Answer: 124 degrees

Step-by-step explanation: There is a 90 degree angle in the top right of the circle. There is a 146 degree angle. Add these two angles.

90 + 146 = 236

These two angles combined are 236 degrees. We are trying to find BC, which is the rest of the circle. There are 360 degrees in a circle. Subtract 360 from 236.

360 - 236 = 124

BC = 124 degrees.

Answer:

D.

Step-by-step explanation:

That would be D because there is a repetition of x = -6.

-6 maps to -6, 5 and -5 which is not allowed in a function.

Functions can be one-to-one or many-to-one but not one-to-many.

Answer:

Step-by-step explanation:

The given side is opposite the given acute angle in this right triangle, so the applicable relation is ...

  Sin(25°) = CB/AB

Solving for AB, we get ...

  AB = CB/sin(25°) ≈ 37.859

__

The relation involving the other leg of the triangle is ...

  Tan(25°) = CB/AC

Solving for AC, we get ...

  AC = CB/tan(25°) ≈ 34.312

__

Of course, the missing angle is the complement of angle A, so is 90-25 = 65 degrees.