x+3 x + 2
——— X ——————
4 2
x + 4x + 3

Multiply and simplify

Answer:

75.4

Step-by-step explanation:

The circumference of the circle whose diameter is 24 inches is 75.36 inches.

We have,

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

Given:

The diameter of the circle, d = 24 inches,

Calculate the circumference of the circle as shown below,

we know that,

Circumference is:

C = 2 × π r

  = π d

so, we get,

C = π × 24

Calculate the circumference as shown below,

C = 3.14× 24

we know that,

24x3.14 = 75.36

C = 75.36

Thus, the circumference is 75.36 inches.

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Answer:

y = 5/4x - 3.5

Step-by-step explanation:

slop intercept form = y = 5/4x - 3.5

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Multiply the time spent on the bus the the total length of the bus trip:

57 x 2/3 = 114/3 = 38 minutes

Now add the amount of time they walk:

38 + 10 + 10 = 58 minutes total.

Answer: C. 58 minutes

Step-by-step explanation:

Since this is a rectangle these two equations for the length have to equal each other.

2x+4=7x-1

We now need to get all of the x's on one side and constant numbers on the other side.

add 1 to both sides and subtract 2x from both sides.

5=5x

divide 5 from both sides.

x=1

Answer:

the square root of 9b2=25 =my correct answer is 5 hope its helful

Answer:

$1,248.00, or 1,248 dollars.

Step-by-step explanation:

First, multiply 4, which is the dollars per hour, by 2, which is 8. Then, multiply four with ten, which is 40. Next, multiply 4 with 3, which is 12, and add two zeros on the back, which is 1,200. Finally, add them all together for a total of $1,248.00, or 1,248 dollars.

Using translation concepts, the graph of h(x) = -3/x is given at the end of the answer. Compared to the parent function, it was vertically stretched by a factor of 3 and reflected over the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent and translated functions are given, respectively, by:

The translations are described as follows:

The graph of h(x) is given at the end of the answer, containing points such as:

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Answer:

35.92 m

Step-by-step explanation:

To have a better comprehension of the problem, we can draw it as in the image attached.

If we use the tangent relation in both triangles, we have:

tangent(35) = h/x

tangent(20) = h/(150-x)

From the first equation, we have:

x = h/tangent(35) = h/0.7

From the second equation, we have:

0.364 = h / (150 - h/0.7)

54.6 - 0.52h = h

1.52h = 54.6

h = 35.92 m

The probability of selection of diagonal which is not shortest nor longest is 13/17.

We know very well that Icosagon has 20 sides.

If any diagonal is possible, it can be possible by connecting two points, so to choose r objects from n objects can be done by ⁿ \(C_{r}\) = \(\frac{n!}{r! (n-r)!}\)

So, number of ways to choose diagonal = \(^2^0C_{2}\)

After that we need to subtract 20 ways as single point can lead to diagonal making.

So, total number of ways to choose 20 diagonals =  170

Now, talking about the shorter diagonal

so, shorter diagonal =Diagonal connecting(A₁A₃, A₂A₄,.....) =20 diagonals.

Now, talking about longer diagonal=Diagonal connecting(A₁A₈,A₂A₉.........) = 20 diagonals

So, we have total chances of ⁿ \(C_{r}\) = \(\frac{n!}{r! (n-r)!}\) and possible number of chances of selection of shorter and longer diagonal

So, according to the formula,

Probability= Favorable outcome /Total outcome

Probability = [(Total ways to select diagonals - (Ways to select shorter diagonal) - Ways to select longer diagonal)]/(Total number of ways)

Probability = (170-20-20)/170

Probability = 130/170

Probability = 13/17

Hence, the probability of selecting a  diagonal such that it is not shortest nor longest is 13/17.

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Answer:

50 gallons of each.

Step-by-step explanation:

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.

Order of events: The order in which events are presented can create a sense of mystery or suspense.

Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.

Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.

Time manipulation: The manipulation of time can also be used to create suspense.

Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.

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The expression 2log9y is the correct equivalent expression for log92y.

The expression log92y represents the logarithm of y to the base 9. To find an equivalent expression, we can use the logarithmic identity log_b(x^a) = a * log_b(x).

Applying this identity to log92y, we can rewrite it as log9(y^2). This step is valid because raising y to the power of 2 is equivalent to multiplying y by itself, which is represented by y^2.

Therefore, an equivalent expression for log92y is log9(y^2).

Among the given options, the correct answer is 2log9y. This can be derived by applying another logarithmic identity, log_b(x^a) = a * log_b(x), in reverse. In this case, we have log9(y^2) = 2 * log9(y). Thus, we can rewrite 2log9y as log9(y^2), which is equivalent to log92y.

Therefore, the expression 2log9y is the correct equivalent expression for log92y.

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Answer:

Robert got 35 problems right if he received an 87.5% oh his test.

Step-by-step explanation:

As Robert got right 87.5% on his test.

so the expression becomes

87.5% × 40

= 87.5/100 × 40

= 0.875 × 40

= 35

Therefore, Robert got 35 problems right if he received an 87.5% oh his test.

The total revenue between the two companies is $3,200

To find the Nash Equilibrium, we need to look for a situation where neither firm has an incentive to change their strategy. This occurs when both firms are charging a price of $8 per month and each has 200 customers, resulting in total revenue of $3,200.

At this price and quantity, neither firm can increase their revenue by changing their strategy. If Netflix were to increase its price above $8, some of its customers would switch to Flixbuster, and Netflix's revenue would decrease. Similarly, if Flixbuster were to decrease its price below $8, it would gain customers from Netflix, but its revenue would still decrease.

Therefore, the Nash Equilibrium in this scenario is a price of $8 and 200 customers for each firm, resulting in total revenue of $3,200 between the two companies.

In mathematical terms, the Nash Equilibrium is a solution to the following system of equations:

Qn = 300 - P

Qf = 300 - P

TRn = P(Qn)

TRf = P(Qf)

where Qn and Qf are the quantities demanded by Netflix and Flixbuster, respectively, P is the price, and TRn and TRf are the total revenues earned by Netflix and Flixbuster, respectively. Solving this system of equations, we get P = 8 and Qn = Qf = 200, which results in total revenue of $3,200.

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Complete Question:

The following table shows a small community's demand for monthly subscriptions to a streaming movie service. Assume that only two firms (Nextflix and Flixbuster) sell in this market, that each firm offers the same quality of service and movie selection, and that each firm's marginal cost is constant and equal to 0 (zero) due to excess capacity.

Price/Month    Number of Total (P) Customers (Q)        Revenue/Month(TR)

$10                                                     0                                                         $0

9                                                      100                                                     900

8                                                      200                                                1,600

7                                                      300                                               2,100

If the two companies are behaving in each best interest, and the market is able to reach a Nash Equilibrium. What is the total revenue between the two companies?

Answer: arc CG=arc CE+ arc EG

Step-by-step explanation:

The arc CG is the sum of arc CE and arc EG option fourth arc CG = arc CE + arc EG is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle shown in the picture.

As we can see the arc CG is marked on a circle.

CG is the sum of CE and EG.

or

arc CG = arc CE + arc EG

Thus, the arc CG is the sum of arc CE and arc EG option fourth arc CG = arc CE + arc EG is correct.

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The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

Given that:

∫3−5f(x)dx=6

∫3−5g(x)dx=3

We need to find: ∫3−5[2f(x) 6g(x)]dx

To solve this problem, we will use the properties of integration:

Property 1:

If c is a constant, then

∫cf(x)dx=c∫f(x)dx

Property 2:

If f(x) and g(x) are two functions, then

∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx

Using Property 1, we can rewrite the given equation as:

∫3−5[2f(x) 6g(x)]dx = ∫3−5[12f(x)g(x)]dx

Using Property 2, we can further simplify the equation as:

∫3−5[12f(x)g(x)]dx = ∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx

Now we can substitute the given values:

∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx = 12∫3−5f(x)dx + 12∫3−5g(x)dx

Substituting the given values for the integrals of f(x) and g(x), we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3)

Simplifying, we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3) = 12(9) = 108

Therefore, the answer is

∫3−5[2f(x) 6g(x)]dx = 108

The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

the complete question is :

if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx will be equal to  ?

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Answer:

4.52

Step-by-step explanation:

volume of cone is

\(\pi {r}^{2} \frac{h}{3} \)

h is 2.2

and

r is 1.4

Mac must get 90 on the eighth exam to raise his average to 80%.

The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the total number of observations by the total number of observations.

Given:

Mac has taken seven math exams this year.

His average mark is 78%.

Let x be the required score.

To find the mark to raise his average to 80%:

According to the question,

78(7) + x  = 8(80)

546 + x = 640

x = 640 - 546

x = 90

Therefore, the required mark is 90.

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Answer:

-11x = -48 +15

x = (-48+15) / (-11)

x = -33 / -11

x= 3

hope that help

Step-by-step explanation:

4e88s45etds8sistzerse8rse85t8ss

Answer:

The answer is B.

Step-by-step explanation:

The answer would be B because dividing 250,000 would get you 25,000 which would be 10% of the total cost. Dividing by 10 again would get you 2500 which would be 1% of the total cost. Divide 2500 by 2 and you'll get 1250. 1250 + 2500 would be 1.5% of the total cost.

Answer:

375 paper clips

Step-by-step explanation:

7 + 8= 15 15*25= 375

ANSWER:

To calculate the money spend on a membership,Assuming a 2% increase each year, the cost of the zoo membership for the second year would be $81.60 (which is $80 + 2% of $80). For the third year, it would be $83.23 (which is $81.60 + 2% of $81.60). This pattern would continue for each subsequent year.

To calculate the total cost of the membership over 20 years, you can use the formula for the sum of a geometric series:

Total cost = a(1 - r^n) / (1 - r)

where:
a = initial cost = $80
r = common ratio = 1.02 (since the cost is increasing by 2% each year)
n = number of years = 20

Plugging in the values, we get:

Total cost = 80(1 - 1.02^20) / (1 - 1.02)
Total cost = $1,978.16

Therefore, you would spend a total of $1,978.16 on a zoo membership over 20 years if the cost increases by 2% each year starting from an initial cost of $80.

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You would spend $1943.79 on a membership over 20 years.

To calculate the total cost of a zoo membership over 20 years, considering a 2% annual increase, we can use the formula for the sum of a geometric series:

Sum = \(a * (1 - r^n) / (1 - r),\)

where:

a is the initial cost of the membership,

r is the common ratio (1 + annual increase rate),

n is the number of years.

In this case, the initial cost of the membership (a) is $80, the annual increase rate is 2% (or 0.02), and we want to calculate the total cost over 20 years (n = 20).

Let's substitute these values into the formula:

Sum = \(80 * (1 - (1 + 0.02)^2^0) / (1 - (1 + 0.02)).\)

Calculating this expression:

Sum = \(80 * (1 - 1.02^2^0) / (1 - 1.02)\)

≈ 80 * (1 - 1.485947) / (-0.02)

≈ 80 * (-0.485947) / (-0.02)

≈ 80 * 24.29735

≈ 1943.788

Therefore, you would spend approximately $1943.79 on a zoo membership over 20 years.

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Answer:

1093

Explanation:

Given expression:

Summation:

Formula:

Compute:

\(\rightarrow \sf 3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6\)

\(\rightarrow \sf 1 + 3 + 9 + 27 + 81 + 243 + 729\)

\(\rightarrow \sf 1093\)

Answer:

\( \boxed{\rm \: SUM = 1093 }\)

Step-by-step explanation:

Given:

\( \huge\rm {{ \sum}^6_{n=0\:} (3)^n}\)

To Find:

Sum of the given finite series

Solution:

We'll use this formula:

\( \boxed{\rm SUM = a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)}\)

where,

Let's find out the ratio R by using this formulae:

\( \rm \: r = \cfrac{a_{n + 1} }{a_n}\)

According to the question,

Substitute:

\( \rm \: r = \cfrac{3 {}^{n + 1} }{3 {}^{n} } \)

Apply law of exponents:[a^m/a^n] = a^m-n

\( \rm \: r = {3}^{n + 1 - n} \)

Rearrange it as:

\( \rm \: r = 3 {}^{n - n + 1} \)

\( \rm \: r = 3 {}^{1} = 3\)

So,the ratio R is 3.

Now let's find out the First term A.

To find, substitute the value of n in 3^n:

\( \rm \: a = 3 {}^{0} \)

\( \rm \: a = 1\)

Hence, first term A is 1.

NOW Substitute the value of the first term A and ratio R onto the formulae of sum:

\( \rm \: a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)\)

Simplify.

\( \rm SUM = \rm \: 1 \times \cfrac{1 - 3 {}^{7} }{ 1 - 1 \times 3} \)

\( \rm \: SUM = \cfrac{ - 2186}{1 - 3} \)

\( \rm \: SUM = \cfrac{ \cancel{ - 2186} \: \: {}^{1093} }{ \cancel{ - 2} \: \: ^{1} } \)

\( \rm \: SUM = 1093\)

We're done!

Hence, the sum of the given Finite series is 1093.

\( \rule{225pt}{2pt}\)

The closest answer is 80 cupcakes per minute, so the correct option is .8. The closest answer is 165 minutes, so the correct option is 165.

The throughput capacity of the icing stage can be calculated by dividing the number of cupcakes in a batch (100) by the time required to process each cupcake (1.25 minutes).

Throughput capacity = Number of cupcakes in a batch / Time to process each cupcake

Throughput capacity = 100 cupcakes / 1.25 minutes

Throughput capacity = 80 cupcakes per minute

The closest answer is 80 cupcakes per minute, so the correct option is .8.

The throughput time for a batch of cupcakes is the time required to process the entire batch, including the setup time.

Throughput time = Time for setup + (Number of cupcakes in a batch * Time to process each cupcake)

Throughput time = 40 minutes + (100 cupcakes * 1.25 minutes per cupcake)

Throughput time = 40 minutes + 125 minutes

Throughput time = 165 minutes

The closest answer is 165 minutes, so the correct option is 165.

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

axis of symmetry, x = - 2

Step-by-step explanation:

Given the quadratic function, f(x) = x² + 4x + 6:

where a = 1, b = 4, and c = 6.

Every parabola is symmetric about its axis, which means that if it were folded along its axis, the two parts would match.  The fold or line that divides the parabola into two matching halves is called the axis of symmetry. The highest or lowest point of a parabola is its vertex, which is on the axis of symmetry, x = h.

The x-coordinate of the axis of symmetry is: x = -b/2a

Substitute the given values into the formula:

x = -b/2a = -4/2(1) = -4/2 = -2

Therefore, the axis of symmetry, x = - 2