Geometric Series
It has 6 terms, increases by a factor of 4, and has a sum of 1365. Find the value of the first term.

25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.

Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.

Then y - x will be the length between the man and the tip of the shadow.

Since two triangles are similar, we can write

[tex]\frac{y-x}{y} =\frac{6}{15}[/tex]

⇒15(y-x) = 6y

15 y - 15 x = 6y

9y = 15x

y = 15/9 x

y = 5/3 x

Differentiate both sides

dy/dt = 5/3 dx/dt

dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.

Given that dx/dt = 5 ft/s

Thus dy/dt = (5/3)×5 ft/s

dy/dt = 25/3 ft/s

Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.

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The radius of each of the smaller molds is r = 1/3 ft. Using the volume of the given hemisphere, the required radius is calculated.

The volume of the hemisphere is calculated by using the formula,

= [tex]\frac{2}{3}[/tex] × π × r³ cubic units

where r is the radius of the hemisphere.

It is given that,

A hemisphere-shaped bowl with a radius r = 1 ft is filled with chocolate.

So, the volume of the bowl is

V =  [tex]\frac{2}{3}[/tex] × π × (1)³

  =  [tex]\frac{2}{3}[/tex] × π cubic feets

The volume of each smaller hemisphere-shaped mold =  [tex]\frac{2}{3}[/tex] × π × r³ cubic units

So, for 27 molds, the volume = 27 × [tex]\frac{2}{3}[/tex] × π × r³ cubic units

All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.

Then,

[tex]\frac{2}{3}[/tex] × π = 27 × [tex]\frac{2}{3}[/tex] × π × r³

⇒ r³ = 1/27

⇒ r = 1/3 ft

Therefore, the required radius of each of the smaller molds is 1/3 foot.

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The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.

Probability is the rate of successful outcomes to the total outcomes of an event.

P(E) = n(E)/n(S)

Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.

It is given that,

An aerospace company has submitted bids on two separate federal government defense contracts.

The probability of winning the first contract is - 45%

The probability of winning the second contract if they win the first contract is  - 73%

The probability of winning the second contract if they lose the first contact is - 45%

So, the probability that they win both contracts is

= (probability of winning the first contract) × (probability of winning the second contract)

= 0.45 × 0.73

= 0.3285 ≅ 0.33

⇒ 33%

Therefore, the probability that they win both contracts is 33%.

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The area of the pool that needs to be covered is 960.42 square feet.

According to the question:

Let us find the perimeter of our given pentagon by multiplying each side length by 5.

[tex]Perimeter of community pool $=5 \times 23.62\\Perimeter of community pool $=118.1$[/tex]

Now let us find apothem of our pentagon by using Pythagoras theorem.  

[tex]a^{2}=20.10^{2}-11.81^{2}\\$a^{2}=404.01-139.4761\\$a^{2}=264.5339\\$a=\sqrt{264.5339}\\$a=16.2645$[/tex]

Upon substituting our given values in above formula we will get,

[tex]Area of community pool =\frac{1}{2} \times 16.2645 \times 118.1\\Area of community pool $=8.13224907 \times 118.1\\Area of community pool $=960.418615627971 \approx 960.42$[/tex]

Therefore, the area of the pool that needs to be covered is 960.42 square feet.

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Answer: B). 960 ft2

Step-by-step explanation:

The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³

x = k × w²

w = 4, x = 48

48 = k × 4²

48 = k × 16

48 = 16k

k = 48/16

k = 3

So,

x = k × w²

x = 3 × w²

x = 3w²

y = k/x³

x = 2, y = 14

14 = k / 2³

14 × 2³ = k

14 × 8 = k

112 = k

So,

y = k/x³

y = 112/x³

y = (1/112)x³

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The triangles are similar by SAS principle.

Similar triangles have the same shape but may have different sizes.

In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are congruent.

Therefore, using SAS ratio,

6 / 8 = 8 × 3 / 32

6 / 8  = 24 / 32 = 3 / 4

Therefore, the corresponding sides are a ratio of each other.

Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal

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Answer:

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

Let the number of boys be b and girls be g.

The ratio is:

And the number of girls is:

Substitute the number into ratio and find the value of b:

A process that behaves the same way as a procedure so that similar results are produced is called a simulation.

In this question,

Simulations are used for finding probabilities for compound events. The probability model of a random phenomenon consists of a sample space of possible outcomes, associated events, random variables, and a probability measure that specifies probabilities of events and determines distributions of random variables.

Procedure is a method of analyzing or representing statistical data; a procedure for calculating a statistic. The goal of statistical analysis is to identify trends.

Hence we can conclude that a process that behaves the same way as a procedure so that similar results are produced is called a simulation.

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The equation of the line that is parallel and passes through the point (2,3) is; x +2y =8.

If follows from the task content that the slope of the first line is; (-4-0)/(4-(-4)) = -1/2.

Hence, since the lines are parallel, they have the same slope and the equation of the second line is;

-1/2 = (y-3)/(x-2)

-x+2 = 2y -6

x +2y =8.

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Answer: b on edg

Step-by-step explanation:

Answer:

69%

Step-by-step explanation:

Overall grade = 0.35*minor grade + 0.65*major grade

major grade: 0.65*61 = 39.65

minor grade: 0.35*84 = 29.4

total: 39.65+29.4 = 69.05

Rounded = 69%

The total cost in 5 hours is $225

Given that the charges of a supply fee of an artist is $50

The charges per hour classes is $35

The total cost is expressed by c

The number of hours expressed by h

We need to calculate the total cost in 5 hour lesson

As per the given statement ,

C= 50 +35h

Where h is the number of hours

h = 5 hours

C = 50 + 35h

C = 50 + 35(5)

C = 50 +175

C = $225

The total cost in 5 hours is $225

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Answer:

y = 0.5x

Step-by-step explanation:

y = rx

4.5/9 = 0.5

7/14 = 0.5

15/30 = 0.5

y = 0.5x

Answer:

The lines are parallel, this is because they both have the same slope/gradient of 6.

Answer:

parallel lines

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 3 ← is in slope- intercept form

with slope m = 6

y = 6x - 4 ← is in slope- intercept form

with slope m = 6

• Parallel lines have equal slopes

then the 2 given lines are parallel

The scientific notation of 6.3 is written as 6.3 × 10^0; option A

Therefore, since there are only two significant number in 6.3, the decimal point can not be moved.

6.3 in scientific notation

= 6.3 × 10^0

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Answer: A

Explanation: 6.3 x 10^0

Using translation concepts, the equations are given as follows:

a) [tex]y = \sqrt{16 - 4x^2}[/tex]

b) [tex]y = 3\sqrt{16 - x^2}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is:

[tex]y = \sqrt{16 - x^2}[/tex]

In item a, when it is horizontally compressed by a factor of 2, it means that x -> 2x, hence:

[tex]y = \sqrt{16 - (2x)^2} = \sqrt{16 - 4x^2}[/tex]

In item b, the transformations are given as follows:

Then:

[tex]y = 3\sqrt{16 -(-x)^2} = 3\sqrt{16 - x^2}[/tex]

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As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever the sample size is large.

Thus, as a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when the sample size is large and each element is selected independently from the same population.

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Answer:

Fraction form: 9/2

Mixed number form: 4 1/2

Decimal form: 4.5

Step-by-step explanation:

To divide the two number, follow these steps.

3/4÷1/6

3/4×6/1=18/4

Reduce.

18/4=9/2 or 4 1/2

Hope this helps!

Answer:

[tex]\dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]

Step-by-step explanation:

[tex] \dfrac{3}{4} \div \dfrac{1}{6} = [/tex]

To divide a fraction by a fraction, rewrite the first fraction and multiply it by the reciprocal of the second fraction. To get the reciprocal of a fraction, flip it. The reciprocal of 1/6 is 6/1.

[tex] = \dfrac{3}{4} \times \dfrac{6}{1} [/tex]

[tex] = \dfrac{3 \times 6}{4 \times 1} [/tex]

[tex] = \dfrac{18}{4} [/tex]

[tex]= \dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]

Based on the speed of the plane, the number of hours it will take to fly 3,008 miles is 5.47 hours.

The speed of the plane is given as 550 miles per hour

In order to reach 3,008 miles, the plane should travel for:

= Distance / Speed

= 3,008 / 550

= 5.47 hours

Rest of the question is:

how many hours will it take a plane to go 3 008 miles if it travels at 550 mph

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Answer:

Option (1)

Step-by-step explanation:

From the unit circle, we see that y, which represents sin(x) when x is 0 or pi.

Answer: 1/2

Step-by-step explanation:

Scale factor = (image)/(preimage) = 6/12 = 1/2

Answer: C.

Step-by-step explanation:

The first number is a positive 4, which is your a1. Then the geometric sequence goes to a negative implying that it is multiplied by a negative. So the a1 = 4 and it is being multiplied by a negative 3.

Answer: C

[tex]\left \{ {{a_{1}=4 } \atop {a_{n}=a_{n-1}*(-3) }} \right.[/tex]

Step-by-step explanation:

The starting amount (a1) = 4

The rate is -3 because 4 * -3 = 12 and -12 and -12 * -3 = 36 etc.

Answer:

The answer is the first option; 6^1/12

Step-by-step explanation:

We can simplify the question by using the radical rule to rewrite it as
6^1/3 ÷ 6^1/4

Then we use exponent rule which states that when we are dividing exponents of the same base, we have to subtract them. We see that the exponents are 1/3 and 1/4. So we use basic fractional division, here's the subtraction:

= 1/3 - 1/4
= 4/3 - 3/4 (we criss-crossed)
= 1/12 (we subtracted the denominators and multiplied the denominators)

Now that we have subtracted the exponents, we can write the answer as 6^1/12

Answer:

Option #1: [tex]6\frac{1}{2}[/tex]

Step-by-step explanation:

#1: Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] and [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]:

[tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}} * \frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]

#2: Combine and simplify the denominator:

- Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] by [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] = [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6} \sqrt[4]{6}^3}[/tex]

- Raise [tex]\sqrt[4]{6}[/tex] to the power of 1

- Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6}^{1+3}}[/tex]

- Add 1 and 3

- Rewrite [tex]\sqrt[4]{6}^4[/tex] as 6: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^3}{6}[/tex]

#3: Simplify the numerator:

- Rewrite the expression using the least common index of 12: [tex]\frac{\sqrt[12]{6^4} \sqrt[12]{216^3}}{6}[/tex]

- Combine using the product rule for radicals: [tex]\frac{\sqrt[3]{6^4 *216^3}}{6}[/tex]

- Rewrite 216 as [tex]6^3[/tex]: [tex]\frac{\sqrt[3]{6^{4}*(6^{3})^{3}}}{6}[/tex]

- Multiply the exponents in [tex](6^{3})^3[/tex]: [tex]\frac{\sqrt[12]{6^{4}*6^{9}}}{6}[/tex]

- Use the power rule [tex]a^{m}a^{n}=a^{m+n}[/tex] to combine exponents and add [tex]4+9[/tex]:

[tex]\frac{\sqrt[12]{6^{13}}}{6}[/tex]

- Raise 6 to the power of 16: [tex]\frac{\sqrt[12]{13060694016}}{6}[/tex]

- Rewrite 13060694016 as [tex]6^{12}*6[/tex]: [tex]\frac{\sqrt[12]{6^{12}*6}}{6}[/tex]

- Pull terms out from under the radical: [tex]\frac{6\sqrt[12]{6}}{6}[/tex]

#4: Cancel the common factor of 6:

[tex]\frac{\sqrt[12]{6}}{6}=6\frac{1}{2}[/tex]

The correct simplified answer for [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] is Option #1: [tex]6\frac{1}{2}[/tex].

The value of x in the trapezoid is 11.

Therefore, the angle 9x and 7x + 4 are supplementary.

Hence,

9x + 7x + 4 = 180

16x + 4 = 180

16x  = 180  - 4

16x = 176

x = 176 / 16

x = 11

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Answer:11

Step-by-step explanation:Easy

The volume of the cone of  radius 5 units and height 3 units is 78 cubic units.

Given radius of cone 5 units and height of cone be 3 units.

We are required to find the volume of cone.

Volume is the amount of substance that a container can hold in its capacity.

Formula of cone is 1/3 *π[tex]r^{2} h[/tex] in which  r is radius and h is height of cone.

We have to just put the values in formula.

Volume=1/3 *π[tex]5^{2} 3[/tex]

=25*3π/3

=75π/3

=25π

Put π=3.14 as said in the question.

=25*3.14

=78.5 cubic units.

After rounding we will get 78.

Hence the volume of cone whose radius is 5 units and height is 3 units is to be 78 cubic units.

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Question is incomplete as it should include the figure.

1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.

Total number of people in the club = 12

total number of positions = (president, vice president, secretary) = 3

From 12 people 3 people are taken at a time.

That is, using the formula for permutation we get,

ⁿPₓ = [tex]\frac{n!}{(n-x)!}[/tex]

Here n = 12 and x = 3

P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320

Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.

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The correct answer is 7.

A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that collectively make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.

I am aware that this query's equation is,

6b + 6 = 48

subtract 6 from both side in the equation.

6b + 6 - 6 = 48- 6

6b = 42

now, divide by 6 from both side in the equation.

6b/6 = 42/6

b = 7.

Therefore, the correct answer is 7.

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I understand this is the question.

Oksana wrote the equation below on the whiteboard.

6 b + 6 = 48

What is the value of b?

(a)4

(b)7

(c)8

(d)9

Answer: 2/3

Step-by-step explanation:

The common denominator would be 3(x-1). Thus, you need to multiply the expression on the right by 3/3 to achieve a common denominator. Then you would have 3x/3(x-1).

The equation then is 2/3(x-1) = 3x/3(x-1)

You can cancel out the denominators now, and you have 2 = 3x, so x = 2/3

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(0) = √49 - x^2

f(0) means that wherever you see an x on the right, you put a zero.

so f(0) = √49 - 0^2

f(0) = √49

f(0) = 7

f(-7) = √49 - x^2

Again the meaning is that where you see an x on the right, you substitute - 7 for that x.

f(-7) = √49 - (-7)^2

f(-7) = 7 - 49

f(-7) = - 42

f(9) = √49 - (9)^2

f(9) = 7 - 81

f(9) = - 74

In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.

According to the statement

we have to tell about the that type of distribution in which two nonadjacent values occur more frequently than any other values in a set of data

A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution.

and from this definition we have clear that the in this distribution the values are repeated.

it shows the probability distribution with two peaks in the graphical mode.

Bimodal distribution show repeated value.

it is used in many types of data representation because of two peaks graphical representation than the simple graph.

it is the easiest method than the others distributions.

So, In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.

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