Determine the sum of the first 40 terms in the geometric series: 1, 1.5, 2.25, 3.375, …

The height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches. This can be obtained by using the ratio of scale drawing to the real drawing.

Here in the question it is given that,

Thus we can say that, scale of the painting is 2 cm : 7 in

Ratio of scale drawing and real painting is 2 : 7

⇒ Similarly here height of the painting in the scale drawing to the height of the painting in the real drawing will be in the ratio 2 : 7.

We can say that,

2 cm/7 in = x cm/35 in

where x is the height of the painting in the scale drawing

2 cm × 35 in /7 in = x cm

x = 2 × 5 cm

x = 10 cm

Hence the height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches.

Learn more about ratios here:

brainly.com/question/1504221

#SPJ1

simplifying 1,615×10 to the 2 power would give 161500

Index notation is known as a way of representing numbers (constants) and variables (e.g. x and y) that have been multiplied by themselves a number of times.

Index notations, or indices are use to simplify expressions or solve equations involving powers.

For instance;

8 × 8 × 8 × 8

8 is multiplied by itself 4 times

In index form , it is written as 8 ^4, that is, 8 to the 4 power

From the information given, we have to simply 1,615×10 to the 2 power

It can be written as;

= 1, 615 × 10 × 10

= 1, 615 × 100

= 161500

Thus, simplifying 1,615×10 to the 2 power would give 161500

Learn more about index notation here:

https://brainly.com/question/10339517

#SPJ1

Answer:

4 is correct answer.

Step-by-step explanation:

That because it contains property of communicative. That is a×b=b×a.

The null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Given that the significance level is 0.10.

We are required to form the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% the significance level.

Hypothesis is a statement which is tested for its validity. Null hypothesis is the statement which is accepted or not by z test,t test,f test ,chi-square test or any other test.

We have to take opposite of the statement to form a null hypothesis. Since we have to check whether the proportion of people who owns cats is larger than 60% of the significance level, we have to assume that it is smaller than 60% of the significance level.

60% of the significance level=0.60*0.10=0.06.

Null hypothesis is [tex]H_{0}[/tex]:μ<0.06

Hence the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Question is incomplete.The question should include the following:

Find the null hypothesis for the testing.

Learn more about hypothesis at https://brainly.com/question/11555274

#SPJ4

Answer: (5/2, 3)

Step-by-step explanation:

Substituting in x=5/2,

[tex]2(5/2)+5y=20\\\\5+5y=20\\\\5y=15\\\\y=3[/tex]

So, the point is (5/2, 3)

The removable discontinuity of the given function is (-3, -3).

What are the discontinuities of the function?

The given function is  [tex]f(x) = \frac{x^{2}+ 12x + 27 }{x^{2} + 4x +3}[/tex]

f(x)=(x²+12x+27)/(x²+4x+3)=(x²+9x+3x+27)/(x²+3x+x+3+

=(x+9)(x+3)/(x+3)(x+1)=(x+9)/(x+1)

The holes in the graph by factoring and cancelling are (-3, -3).

Therefore, the removable discontinuity of the given function is (-3, -3).

Learn more about Discontinuous functions

brainly.com/question/15009884

#SPJ4

Answer: first answer is -3 for both and second is x=-1

Step-by-step explanation:

It is to be noted that at the seven and half year, is when the revenue of both ads became equal. This is a graph problem. See the explanation below.

Step 1:

Note that the amount of money earned by routine company activities is known as revenue, which is calculated by dividing the average sales price by the number of units sold.

Step 2:

Note that the graph is to be used to justify the statement by the lead executive.

Step 3

From the graph, we know that the revenue in the 10th year for printed ads was $ 2,000,000 and $ 3,000,000 for online ads. Represented on as coordinates, that would be (0,3); (10, 2).

Thus, we can create an equation that states:

(y-2) = [(3-2)/(0-10)] * (x - 10)

⇒ y - 2

= [-1/10] * [x - 10]

Hence,

10y - 20 = - x + 10

10 y + x = 30 ........Lets call this equation A

We can also state that:

Online revenue coordinates on the graph are (0,0,) (10, 3)

Thus,

(y-0) =

[(3-0)/(10-0)] (x -0)

⇒ y = [3x/10]  [10y - 3x] = 0.........Lets make this equation B

For printed Ad Revenue:

Year 12= x

10y + 12 = 30

Y = 18/10

y = 1.8

For online Ad revenue

Year = 12 = x

10y = 36

Y = 36/10

y = 3.6

From the above, it is clear that in year 10, the online ad revenue got doubled as same as that of revenue from printed ads.

In order to get the year in which the revenue were equal, we solve both equations simultaneously:

+ 10y + x = 30

±  10y ≠ 3x = 3

4x = 30

x thus, = 30/4

= 7.5

Thus, it is correct to state that both revenue's became equal by the mid of the 7th year going to the eight year.

Learn more about Graph Problems:
https://brainly.com/question/14323743
#SPJ1

Full Question:

Missing graph is attached.

It looks like the limit is

[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}[/tex]

L'Hôpital's rule works in this case; applying it twice gives

[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}[/tex]

Answer:

  12 in, 7 in

Step-by-step explanation:

The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.

The two relations between length and width described by this problem are ...

  A = LW . . . . . . . dimensions are of a rectangle

  L = W +5 . . . . . . length is 5 inches more than width

  A = 84 . . . . . . . . area in square inches

Substituting for L and A in the area formula, we have ...

  84 = (W +5)(W)

We can solve this as a quadratic in any of several ways. One of those ways is by factoring.

Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:

  84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7

The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.

This means the last pair, with a difference of 5, is the one we're looking for.

 W+5 = 12, W = 7

The rectangle is 12 inches long and 7 inches wide.

__

Additional comment

As a quadratic in standard form, we would have ...

  W² +5W -84 = 0   ⇒   (W +12)(W -7) = 0   ⇒   W = {7, -12}

If you were to solve this by completing the square, you would have ...

  (W +2.5)² = 90.25   ⇒   W = -2.5 ±9.5 = {7, -12}

For function g(x, y) = 9x² + 6y²,

the absolute minimum is 15 and the absolute maximum is 303

For given question,

We have been given a function g(x, y) = 9x² + 6y² subject to the constraint −1≤x≤1 and −1≤y≤7

We need to find the absolute maximum and minimum values of the function.

First we find the partial derivative of function g(x, y) with respect to x.

⇒ [tex]g_x=18x[/tex]

Now, we find the partial derivative of function g(x, y) with respect to x.

⇒ [tex]g_y=12y[/tex]

To find the critical point:

consider [tex]g_x=0[/tex]        and      [tex]g_y=0[/tex]

⇒         18x = 0         and      12y = 0

⇒          x = 0           and       y = 0

This means, the critical point of function is (0, 0)

We have been given constraints −1 ≤ x ≤ 1 and −1 ≤ y ≤7

Consider g(-1, -1)

⇒ g(-1, -1) = 9(-1)² + 6(-1)²

⇒ g(-1, -1) =  9 + 6

⇒ g(-1, -1) = 15

And g(1, 7)

⇒ g(1, 7) =  9(1)² + 6(7)²

⇒ g(1, 7) = 9 + 294

⇒ g(1, 7) = 303

Therefore, for function g(x, y) = 9x² + 6y²,

the absolute minimum is 15 and the absolute maximum is 303

Learn more about the absolute maximum and absolute minimum values of the function here:

https://brainly.com/question/16270755

#SPJ4

Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know that:

So, the system of equations to be solved is

[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Solving the first equation:

30= [tex]\frac{1}{3}[/tex]C

30÷[tex]\frac{1}{3}[/tex]= C

90= C

Substituting the value in the second equation:

W= 2(90 + 30)

W= 2×120

W=240

Finally, 240 stamps are in Will’s collection.

Learn more about system of equations:

brainly.com/question/14323743

brainly.com/question/1365672

brainly.com/question/20533585

brainly.com/question/20379472

#SPJ1

The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.

The number of consecutive draws needed will be, n = 233

Probability is the likelihood or chance of an event happening or not.

From the given question, the probability of the jackpot being won in any draw is 1/60.

The probability that the jackpot prize will be won in each of four consecutive draws will be:

1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴

b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:

There is a 100% - 98% chance that that none has been won = 2% that none has been won.

Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60

The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02

Solving for n by taking logarithms of both sides:

n = 233

In conclusion, probability measures chances of an event occurring or not.

Learn more about probability at: https://brainly.com/question/251701

#SPJ1

Option A is correct. The type of construction that we have here is the bisection of the <D.

The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.

In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.

The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.

If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option

Read more on the bisection of an angle here:

https://brainly.com/question/25770607

#SPJ1

(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].

CuSO₄ flows into the tank at a rate

[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]

and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation

[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]

(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.

[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]

The integrating factor is

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]

Distributing [tex]\mu[/tex] on both sides gives

[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]

and the left side is now the derivative of a product,

[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]

The first term on the right vanishes since [tex]C(0)=0[/tex]. Then

[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]

[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]

Answer:

Step-by-step explanation:

Area of circle:

area = π · r · r

Radius=  [tex]\frac{16}{2}[/tex]= 8

[tex]3.14\times { 8 }^{ 2 }[/tex] = 200.96 [tex]cm^2\\[/tex]

Answer: 104 degrees farenheit

Step-by-step explanation:    H =  record high temperature. -5 + 109 = H. -5+109 = 109 + (-5) = 109-5 = 104. H = 104.

Answer:

104

Step-by-step explanation:

Let x = record high and y = record low temperature in Charlotte. The difference between the records high and low, x and y, is 109 degrees Fahrenheit, so x - y = 109. Record low is -5, so x - (-5) = 109.

x + 5 = 109

x = 104

Substitute [tex]y=4+5\sqrt x[/tex] and [tex]dy=\frac5{2\sqrt x}\,dx[/tex]. Then the integral is

[tex]\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = 2 \int \frac{1}{(4+5\sqrtx)^2} \frac{5}{2\sqrt x} \, dx = 2 \int y^{-2} \, dy[/tex]

By the power rule,

[tex]\displaystyle \int y^{-2} \, dy = -y^{-1} + C[/tex]

so that

[tex]\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = \boxed{-\frac2{4+5\sqrt x} + C}[/tex]

Work Shown:

k = scale factor

k = (A'B')/(AB)

k = 8/12

k = (4*2)/(4*3)

k = 2/3

Triangle A'B'C' (image) has side lengths that are 2/3 as long compared to the side lengths of triangle ABC (preimage).

Answer: 2

Step-by-step explanation:

Each of the two sides of the equation is set equal to y

The value of x from the given data is 2

Mean is the ratio of sum of numbers to the total samples. Given the following data

15,19,23,41, and Z

The mean is calculated as

Mean = 15+19+23+41+z/5

Since the mean the of the data is given as 20. Substitute

20 = 15+19+23+41+z/5

Cross multiply

20*5 = 15+19+23+41+z

100 = 15+19+23+41+z

100 = 98 + z

z = 100- 98

z = 2

Hence the value of x from the given data is 2

Learn more on mean here: https://brainly.com/question/19243813

#SPJ1

Answer:

Step-by-step explanation:

The minimum is at the vertex of this parabola because it opens up.

Now if (-4, 2) is the minimum then  all the y values on the parabola must be > 2,

But we are given that  y = -3 is on the graph ( the point (6,-3) - that is y < 2 here,

Therefore (-4, 2)  cannot be the vertex .

The 17th term of the geometric sequence given in the problem is:

[tex]a_{17} = \frac{13}{8}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

As a function of the mth term, the nth term can also be given as follows:

[tex]a_n = a_mq^{n - m}[/tex]

In this problem, we have that:

[tex]a_{13} = 26, q = \frac{1}{2}[/tex]

Hence the 17th term is:

[tex]a_{17} = a_{13}q^{4}[/tex]

[tex]a_{17} = 26 \times \frac{1}{16}[/tex]

[tex]a_{17} = \frac{13}{8}[/tex]

More can be learned about geometric sequences at https://brainly.com/question/11847927

#SPJ1

By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.

In this problem we must apply the compound interest model, which represent a periodic accumulation of interest according to the following formula:

C' = C · (1 + r/100)ˣ     (1)

Where:

If we know that x = 1, r = 4, C = x and C' = x + 5 000, then the initial deposit is:

x + 5 000 = x · (1 + 4/100)

x + 5 000 = 1.04 · x

0.04 · x = 5 000

x = 125 000

By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.

To learn more on compound interest: https://brainly.com/question/14295570

#SPJ1

Answer:

x - 14.95 = 12.48

x = 27.43

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

The solution is in the image

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\\[/tex]

The [tex]\mathrm{distributive \: property}[/tex] states that an expression that is given in the form of [tex]\small\sf{ A(B + C)}[/tex] can be solved as [tex]\small\sf{A \times (B + C) = AB + AC}[/tex] . So:

[tex]\small\longrightarrow\sf{-24-18-2+4}[/tex]

[tex]\small\longrightarrow\sf{-42+2}[/tex]

▪ [tex]\large\tt{All \: \: options \: \: are \: \: wrong}[/tex]

[tex]\\[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\small\longrightarrow\sf{−6 (2^2+3) − 2 (1^2 - 2) = \underline{-6(4+3)}}[/tex]

The distance between  the points (–3,k) and (2, 0) exists k = ± 3.

How to estimate the distance between points (–3, k) and (2, 0)?

To calculate the distance between two points exists equal to

[tex]$d=\sqrt{(y 2-y 1)^{2}+(x 2-x 1)^{2}}$[/tex]

we have (-3, k) and (2, 0)

[tex]$&d=\sqrt{34}[/tex]

substitute, the values in the above equation, and we get

[tex]$\sqrt{34} &=\sqrt{(0-k)^{2}+(2+3)^{2}} \\[/tex]

simplifying the above equation

[tex]$\sqrt{34} &=\sqrt{(-k)^{2}+(5)^{2}} \\[/tex]

[tex]$\sqrt{34} &=\sqrt{k^{2}+25}[/tex]

squared both sides

[tex]$&34=k^{2}+25 \\[/tex]

[tex]$&k^{2}=34-25 \\[/tex]

[tex]$&k^{2}=9 \\[/tex]

k = ± 3

Therefore, the value of k = ± 3.

To learn more about distance refer to:

https://brainly.com/question/23848540

#SPJ4

Answer:

$3,500 labor and $3,500 materials

Step-by-step explanation:

furnishings + labor + materials = 10,000

furnishings = 3000

3000 + labor + materials = 10,000

labor = materials

3000 + labor + labor = 10,000

2(labor) = 7,000

labor = 7,000/2

labor = 3,500

labor = materials = 3,500

Answer:

7   1/5

Step-by-step explanation: