Find the missing terms in each geometric sequence. 7,1,__,__,1/343,

No, it is not possible to have a simple graph with n vertices, where n is any integer greater than or equal to 5, such that all vertices have different degrees.

In a simple graph, the degree of a vertex refers to the number of edges connected to that vertex. The maximum degree possible in a graph with n vertices is (n-1), which occurs when one vertex is connected to all other vertices.

To create a graph where all vertices have different degrees, we would need to assign a unique degree to each vertex. However, if n is greater than or equal to 5, we cannot assign n unique degrees to n vertices while satisfying the conditions of a simple graph.

To see why, consider the case of n = 5. We need to assign degrees 1, 2, 3, 4, and 5 to the vertices.

The vertex with degree 5 must be connected to all other vertices, leaving us with four remaining degrees (1, 2, 3, and 4) to assign to the remaining four vertices. However, no matter how we distribute these degrees, at least two vertices will have the same degree.

This argument can be extended to any value of n greater than 5. Therefore, it is not possible to construct a simple graph with n vertices where all vertices have different degrees for any integer n ≥ 5.

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Answer:

The equation in a point-slope form that  represents their distance from

home, y miles, after x hours, is y - 110 = 55(x - 2)

Step-by-step explanation:

The point-slope form of the linear equation is

\(y-y_{1}=m(x-x_{1})\) , where

m is the slope of the line (average)

\((x_{1},y_{1})\) is a point on the line

→ The family is driving home  from vacation at an average speed

    of 55 miles per hour

∴ m = 55

→ After 2 hours they  are 110 miles from home

∵ x is the number of hours

∵ y is the distance in miles after x hours

∴ \(x_{1}\) = 2

∴ \(y_{1}\) = 110

→ Substitute these values in the form of the equation above

∴ y - 110 = 55(x - 2)

The equation in a point-slope form that  represents their distance from

home, y miles, after x hours is y - 110 = 55(x - 2)

(D) "Your type of employment is dependent on things you can control" is a pro of being a wage earner.

This is a pro of being a wage earner because, although you may not have complete control over your job responsibilities, you do have control over your skills and qualifications that can help you secure and maintain employment.

Additionally, being a wage earner often provides stability and benefits such as health insurance and retirement plans.

However, it is important to note that there are also potential cons to being a wage earner such as limited upward mobility and the potential for layoffs or job insecurity.

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\({\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}\)

\({\dashrightarrow\sf{3 \bigg(5x + 3 \bigg)= 4\bigg(1 + x \bigg)}}\)

\({\dashrightarrow\sf{\bigg(5x \times 3 + 3 \times 3 \bigg)= \bigg(1 \times 4 + x \times 4 \bigg)}}\)

\({\dashrightarrow\sf{\bigg(15x + 9 \bigg)= \bigg(4 + 4x\bigg)}}\)

\({\dashrightarrow\sf{15x - 4x =4 - 9 }}\)

\({\dashrightarrow\sf{11x =4 - 9 }}\)

\({\dashrightarrow\sf{11x = - 5 }}\)

\({\dashrightarrow\sf{x = - \dfrac{5}{11}}}\)

\(\bigstar{\underline{\boxed{\sf{\red{x = - \dfrac{5}{11}}}}}}\)

∴ The value of x is -5/11.

\(\begin{gathered}\end{gathered}\)

\({\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}\)

\({\dashrightarrow\sf{ \bigg(\left\{5 \times - \dfrac{5}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{10}\right\}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg(\left\{- \dfrac{25}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{11}\right\}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{ - ( 25 )+ (3 \times 11)}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{(1 \times 11) - (5 \times 1)}{11}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{ - 25+ 33}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{11 - 5}{11}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{6}{11}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4}{3} \times \dfrac{6}{11}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4 \times 6}{3 \times 11}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{24}{33}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\cancel{\dfrac{24}{33}}\bigg)}}\)

\({\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg({\dfrac{8}{11}}\bigg)}}\)

\(\bigstar{\underline{\boxed{\sf{\red{LHS = RHS}}}}}\)

∴ Hence Verified !

Answer:

\(x = - \frac{5}{11} \\ \)

Step-by-step explanation:

\(5x + 3 = \frac{4}{3} (1 + x) \\ 5x + 3 = \frac{4}{3} + \frac{4x}{3} \\ 5x - \frac{4x}{3} = \frac{4}{3} - 3 \\ \frac{3(5x) - 4x}{3} = \frac{4 - 3(3)}{3} \\ \frac{15x - 4x}{3} = \frac{4 - 9}{3} \\ \frac{11x}{3} = - \frac{5}{3} \\ 11x = - \frac{5}{3} \times 3 \\ 11x = - 5 \\ x = - \frac{5}{11} \\ \)

Answer: B) No, every x-value does not have exactly one y-value

Explanation:

We have the input x = 3 map to the outputs y = 2 and y = 8 at the same time. A function is only possible if any given x value goes to exactly one y value.

Put another way, if x repeats itself, then we don't have a function. This assumes we don't repeat the same y value when we repeat the x value.

All x values such that log base 12 (2x + 6) + log base 12 (x + 2) = 2 are x = -3 and x = 8.

What is the product rule in logarithms?

The product rule for logarithms states that for any positive numbers a and b, and for any positive base b, the following holds true:

\(log_b(ab) = log_b(a) + log_b(b)\)

In other words, the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers.

To solve for all x values such that log base 12 (2x + 6) + log base 12 (x + 2) = 2, we can first use the product rule to rewrite the given equation as:

\(log_{12}((2x + 6)(x + 2)) = 2\)

Then, we can apply the logarithm to both sides of the equation to obtain:

(2x + 6)(x + 2) = 12²

This simplifies to:

(2x + 6)(x + 2) = 144

We can then solve for x by factoring or using the quadratic formula. The solutions are x = -3 and x = 8.

Hence, all x values such that log base 12 (2x + 6) + log base 12 (x + 2) = 2 are x = -3 and x = 8.

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A large mean difference and small sample variances. The correct option is B.

A statistical measure known as the effect size () assesses the magnitude of the link (numerically) between two variables. The difference between the weights of male and female candidates, for instance, is known as the effect size. If we obtain information on the weights of male and female candidates and discover that men are, on average, heavier than women, for example.

The weight difference between men and women will increase as the effect size increases. Statistic effect size aids in determining whether a difference is real or the result of changing variables. Effect size, power, sample size, and critical significance level are all related to hypothesis testing.

Therefore, a large mean difference and small sample variances. The correct option is B.

The complete options are given below:-

a. A small mean difference and small sample variances ​

b. A large mean difference and small sample variances ​

c. A small mean difference and large sample variances ​

d. A large mean difference and large sample variances

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the value of F(9) is approximately 23.308.

To find the value of F(9) given that F(x) is an antiderivative of (ln x)^3/x and F(1) = 0, we can use the fundamental theorem of calculus.

According to the fundamental theorem of calculus, if F(x) is an antiderivative of a function f(x), then:

∫[a,b] f(x) dx = F(b) - F(a)

Since F(1) = 0, we can write:

∫[1,9] (ln x)^3/x dx = F(9) - F(1)

To evaluate the integral, we can make a substitution:

Let u = ln x, then du = (1/x) dx

The integral becomes:

∫[ln 1, ln 9] u^3 du

Integrating u^3 with respect to u:

[(1/4)u^4] | [ln 1, ln 9] = (1/4)(ln 9)^4 - (1/4)(ln 1)^4

Since ln 1 = 0, we have:

(1/4)(ln 9)^4 - (1/4)(ln 1)^4 = (1/4)(ln 9)^4

Therefore, F(9) - F(1) = (1/4)(ln 9)^4

Since F(1) = 0, we can conclude that F(9) = (1/4)(ln 9)^4.

Calculating this value:

F(9) = (1/4)(ln 9)^4 ≈ 23.308

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Answer:

3 hours

Step-by-step explanation:

each hour is 2,000 gallons filled up 1 hour = 2,000

                                                           2 hours = 4,000

                                                           3 hours = 6,000or 4,850

If the swimming pool is filled with 2,000 gallons per hour, time taken to fill it with 4,850 gallons of water is 2.4 hours.

Given that;

The pool is filled with 2,000 gallons in 1 hour

To fill with 4850 gallons, we require x hours

Cross multiply, hence;

x = ( 1hr × 4850 gallons ) / 2,000 gallons

x = 4850hrs / 2000

x = 2.4 hours

Therefore, if the swimming pool is filled with 2,000 gallons per hour, time taken to fill it with 4,850 gallons of water is 2.4 hours.

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The weight of food packed in certain containers is a random variable with a mean of 16 0z. and a standard deviation of 0.6 oz. If 36 packages are randomly selected, the probability that the mean will be greater than 16.2 oz is 2.28%.

Given that the weight of food packed in containers is a random variable with a mean (µ) of 16 oz. and a standard deviation (σ) of 0.6 oz, we want to find the probability that the mean weight of a sample of 36 packages (n) will be greater than 16.2 oz.
Step 1: Calculate the standard error (SE) of the sample mean.
SE = σ / √n = 0.6 / √36 = 0.6 / 6 = 0.1
Step 2: Calculate the z-score for 16.2 oz.
z = (sample mean - population mean) / SE = (16.2 - 16) / 0.1 = 2
Step 3: Find the probability that the mean weight will be greater than 16.2 oz.
To find the probability for a z-score of 2, we can look it up in a standard normal (z) table or use a calculator that provides the area to the left of the z-score.
Using the table or calculator, we find the area to the left of the z-score 2 is approximately 0.9772. Since we are looking for the probability of the mean weight being greater than 16.2 oz, we want the area to the right of the z-score. To find this, subtract the area to the left from 1:
1 - 0.9772 = 0.0228
So, the probability that the mean weight of the 36 packages will be greater than 16.2 oz is approximately 0.0228 or 2.28%.

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Let the number of goals Connor scored = x

Sadies scored 3 times as many so you multiply x by 3 to get 3x

Together they scored 12 so now add x and 3x together to equal 13:

X + 3x = 13

Simplify:

3x + x = 4x

4x = 12

Divide both sides by 4:

X = 3

Connor = x = 3

Sadie = 3x = 3(3) = 9

Connor did not score 4 goals.

Answer:

y=3x-2

Step-by-step explanation:

Answer:

y =2x -3

Brainiest pls :)

Slope is calculated as the change in y over the change in x so you would need to do 5- (-5) which turns the negative sign to a positive making it 5+5=10 and the same thing with the 2s 2-(-2)=4 so the answer would be 10/4 or 5/2. Billy did the reciprocal.

Answer:

correct answer is 5/2

Step-by-step explanation:

the mistake was the student took the difference of the x-values and it in the numerator and the difference of the y-values should be the denominator

5-(-5) / 2-(-2) = 10/4 or 5/2

Answer:  True

Step-by-step explanation:

quantative is numbers and stats

A detection system has a probability of 0.91 to detect a missile attack. It is recommended to have multiple detection systems as it increases the overall probability of detecting an attack and allows for redundancy in case one system fails.

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Answer:

The answer is 38.

Step-by-step explanation:

You have to substitue c = -4 into the expression :

Let c = -4,

\( {( - 4)}^{2} - 5( - 4) + 2\)

\( = 16 + 20 + 2\)

\( = 38\)

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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The probability that every even number appears at least once before the first occurrence of an odd is 1/20.

Given:

A fair 6-sided die is repeatedly rolled until an odd number appears.

There are 6! ways to order the 6 numbers and 3!(3!) ways to order the evens in the first three spots and the odds in the next three spots.

so the probability = 3!*3! / 6!

= 3!*3! / 6*5*4*3!

= 3*2*1 / 6*5*4

= 6*1 / 30*4

= 6/120

= 1/20

Therefore the probability that every even number appears at least once before the first occurrence of an odd is 1/20.

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Answer:

314

Step-by-step explanation:

A=4πr^2

A= (4)(3.14)(5)^2

A=314

Question :-

Answer :-

\( \rule{180pt}{3pt}\)

Diagram :-

\(\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{5 \: inches}}\end{picture}\)

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 5 inches. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

\(\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}\)

Substitute the given values into the above formula and solve for surface area:

\(\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2\)

\(\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(5 \: in)^2\)

\(\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(25 \: in^2)\)

\(\sf:\implies Surface \: Area_{(Sphere)} = (4)(78.5 \: in^2)\)

\(\sf:\implies \bold{Surface \: Area_{(Sphere)} = 314 \: inches^2}\)

Therefore :-

\(\\\)

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The line has a -2 slope and a 0 intercept. The line's equation is y = -2x.

What is en equation?

Formula for Lines

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If you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

To calculate the monthly payment for each financing option, we'll use the information provided:

1. 0% financing for 48 months:

Since the financing is offered at 0% interest, the monthly payment can be calculated by dividing the total purchase price by the number of months.

Purchase Price: $26,050

Number of Months: 48

Monthly Payment = Purchase Price / Number of Months

Monthly Payment = $26,050 / 48 ≈ $543

Therefore, the monthly payment for the 0% financing option for 48 months is approximately $543.

2. Rebate offer and car loan at the bank:

If you choose the rebate offer, you'll need to finance the remaining balance after deducting the rebate amount. Let's calculate the remaining balance:

Purchase Price: $26,050

Rebate Offer: $2,900

Remaining Balance = Purchase Price - Rebate Offer

Remaining Balance = $26,050 - $2,900 = $23,150

Now, we'll calculate the monthly payment using the remaining balance and the loan terms from the local bank:

Remaining Balance: $23,150

Interest Rate: 5.24% (compounded monthly)

Number of Months: 48

Monthly Payment = (Remaining Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

First, let's calculate the Monthly Interest Rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 5.24% / 12 ≈ 0.437%

Now, we can calculate the Monthly Payment using the formula mentioned above:

Monthly Payment = ($23,150 * 0.437%) / (1 - (1 + 0.437%)^(-48))

Monthly Payment ≈ $557

Therefore, if you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

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Answer:

See below ~

Step-by-step explanation:

Question 1

The missing angles

⇒ The sides are equal

⇒ Angles are not 90°

⇒ It is a rhombus

Question 2

\(3\) and \(116^{\circ}\) are supplementary angles.

Therefore

\(m\angle 3+116^{\circ}=180^{\circ}\\m\angle 3=64^{\circ}\\\)

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

24

Step-by-step explanation:

Since there are 3,600 seconds in 1 hour, there are 3,600 times fewer fracmes in a second than in 1 hour.

86,400/3,600 = 24

Answer:

102

Step-by-step explanation:

These angles are congruent due to corresponding angles thm

3x + 21 = 6x - 60

3x - 6x = -60 - 21

-3x = -81

x = 27

3x + 21

3(27) + 21

81 + 21

102

Answer:

1. g. $0.10 per square inch

2. c. $0.08 per square inch

3. f. $10

4. m. $8

5. h. 79 in²

6. j. 113 in²

Step-by-step explanation:

1. A = πr²

   r = diameter ÷ 2 = 10 ÷ 2 = 5

   A = π(5)² = 25π in² ≈ 78.53981

   $8.00/25π = $0.10 per square inch

2. A = πr²

   r = diameter ÷ 2 = 12 ÷ 2 = 6

   A = π(6)² = 36π in² ≈ 113.0973355

   $10.00/36π = 0.088419 = $0.08 per square inch

3. information/answer was provided

4. information/answer was provided

5. A = πr²

   r = diameter ÷ 2 = 10 ÷ 2 = 5

   A = π(5)² = 25π in² ≈ 79 in²

6. A = πr²

   r = diameter ÷ 2 = 12 ÷ 2 = 6

   A = π(6)² = 36π in² ≈ 113 in²