What is the sum of the first ten terms in the geometric series 4 – 12 + 36 – 108 + ...?

Answer:

b = 2

Step-by-step explanation:

Using the midpoint formula

(2, 1) = [ [tex]\frac{1}{2}[/tex](- 4 + 8), [tex]\frac{1}{2}[/tex](b + 0) ]

considering the y-coordinate, then

[tex]\frac{1}{2}[/tex] b = 1 ( multiply both sides by 2 )

⇒ b = 2

Answer:

true

Step-by-step explanation:

on a football feild there are 4,320 inches and on a basketball court there are 2,865 centemeters

Answer:

The correct option is b. approximately 68% of the data falls within 1 standard deviation (+-1) of the mean

Explanation:

According to the empirical rule of normal distribution:

1. Approximately 68% of the data falls within 1 standard deviation [tex]\pm 1[/tex] of the mean

2. Approximately 95% of the data falls within 2 standard deviations [tex]\pm 2[/tex] of the mean

3. Approximately 99.7% of the data falls within 3 standard deviations [tex]\pm 3[/tex] of the mean.

Therefore, among the given options, only option b adheres to the empirical rule of the normal distribution. Therefore, the option b is correct

The true statement about a normally distributed dataset is that approximately 68% of the data falls within 1 standard deviation (±1) of the mean, which is known as the 68-95-99.7 rule or the empirical rule.

This question pertains to properties of a normally distributed dataset. In such a distribution, a majority of the data falls within a specific range of the mean (average), defined by the standard deviations. Understanding standard deviations allows us to comprehend how spread out the data is from the average.

In the case of normally distributed data, it is factually correct that approximately 68% of the data falls within 1 standard deviation (±1) of the mean. This is known as the 68-95-99.7 rule or the empirical rule, which states that 68% of data falls within 1 standard deviation, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations of the mean for a normal distribution.

Therefore, the correct statement from the list provided in your question is option (b).

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Answer:

The product of the 5^56 x 5^22 x 5^-96= 1/5^18.

Step-by-step explanation:

The problem represents the Laws of Exponents.  When you multiply using exponents, you keep the base and add the exponents.  In this case, the base is 5 and our exponents are 56 + 22 + -96.  We we add these three integers, we get a total of -18, which gives us a base of 5 and exponent of -18 or 5^-18.  We don't typically have negative exponents, so our next rule to follow is when you have negative exponents, you flip the base, or make it a fraction, and make the exponent positive.  This gives us a final answer of 1/5^18.  

The value of the product is 5^56 × 5^22 × 5^(-96) is 1/(5^18)

         While multiplying two exponents with the same base then we should add the powers to get the result.

            Example: x^a + x^b = x^(a+b)

              5^56 × 5^22 × 5^-96 = 5^(56+22+(-96))

                                                    = 5^(-18)

       A non-zero real number with negative power is written as

    1/ (non-zero number with the positive power of the same number).

     Example:  x^(-2) = 1/(x^2)

  So, we can write 5^(-18) as 1/5^(18).

   Hence,

       5^56 × 5^22 × 5^-96 = 1/5^(18).

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Answer:

He earns 9.75 per hour.

Step-by-step explanation:

195/20 = 9.75 and 9.75 x 20 = 195.

Answer:

All you will need to do is just divide 195 by 20 and your answer will be $9,75 cents. Hope this helps!!!!!

Answer:

120 people voted against building the new basketball court.

Step-by-step explanation:

if you divide 200 by 100 then you know how many people equal 1 percent of the 200. knowing that for every 2 people they are equal to 1 percent. so if you do 100 -40 you get 60. the 100 represents the 100 percent and you subtract 40 because these are the people who are voting for the basketball court. The 60 represents the percent of people who are voting against building the basketball court. then you multiply 60 by 2 and you get 120.

The given polynomial only has one exponent, so the degree of the polynomial is the number of the exponent.

The degree is 3.

Answer:

Step-by-step explanation:

1) [tex](a^3)^{-2}  = a^{-6}\\[/tex]

2) [tex](a^{-1} * a^{-2} )^{-3} = (a^{-1 + (-2)})^{-3} }=a^{-9}[/tex]

3) [tex]((a^{2})^{-2})^{2}=(a^{-4})^{2}=(a^{-8})[/tex]

4) [tex](a*a)^{2} =  (a^{2})^{2}=a^{4}[/tex]

[tex]Use\ (a^n)^m=a^{(n)(m)}\\\\((-3)^2)^3=(3^2)^3=3^{(2)(3)}=3^6\\\\((-3)^2)^3=(-3)^{(2)(3)}=(-3)^6[/tex]

Two answers: A. (-3)^6 and B. (3)^6.

Answer:

A and B

Step-by-step explanation:

using the law of exponents

• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex], hence

[tex]((-3)^2)^{3}[/tex] = [tex](-3)^{6}[/tex] → A

note that (- 3)² = 9 = 3², hence

[tex](-3)^2)^{3}[/tex] = (3²)³ = [tex](3)^{6}[/tex] → B

Answer:

The answer is 47 rows.

Step-by-step explanation:

If we have 846 students, and each row can hold 18 people.

We just divide the total students into the number of people sitting by row.

846 ÷ 18 = 47.

Answer:  The required ratio in simplest form is 7 : 5 : 8.

Step-by-step explanation:  Given that in a fruit punch drink, the 3 ingredients are apple juice orange juice and cranberry juice. [tex]\frac{1}{4}[/tex] of the drink is apple juice and [tex]\frac{2}{5}[/tex] is orange juice.

We are to find  the ratio of cranberry juice to apple juice to orange juice in its simplest form.

Let x, y and z be the fractions of the cranberry juice, apple juice and orange juice in the fruit punch drink.

Then, according to the given information, we have

[tex]y=\dfrac{1}{4},~~z=\dfrac{2}{5}.[/tex]

Now,

[tex]x+y+z=1\\\\\\\Rightarrow x+\dfrac{1}{4}+\dfrac{2}{5}=1\\\\\\\Rightarrow x=1-\dfrac{1}{4}-\dfrac{2}{5}\\\\\\\Rightarrow x=\dfrac{20-5-8}{20}\\\\\\\Rightarrow x=\dfrac{7}{20}.[/tex]

Therefore, the ratio of cranberry juice to apple juice to orange juice is given by

[tex]x:y:z\\\\\\=\dfrac{7}{20}:\dfrac{1}{4}:\dfrac{2}{5}\\\\\\=\dfrac{7}{20}:\dfrac{5}{20}:\dfrac{8}{20}\\\\=7:5:8.[/tex]

Thus, the required ratio in simplest form is 7 : 5 : 8.

It will take 15 weeks for Nancy’s account to have twice as much money as Fred's.

We are looking for the number of weeks it will take for Nancy’s account to have twice as much money as Fred’s account. Both Fred and Nancy start with $15. Each week, Nancy adds $3 to her account and Fred adds $1 to his account.

So we have to solve the equation: 15 + 3x = 2 * (15 + x), where x is the number of weeks. Simplifying the equation gives us x = 15 weeks. Thus, it will take 15 weeks for Nancy’s account to have twice as much money as Fred’s account.

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Answer:

22662

Step-by-step explanation:

14000(1+3.5/100)^14

The population after 14 years is 22662.

It is given that,

Explanation:

The exponential growth model is:

[tex]P=P_0\left(1+r\right)^t[/tex]

Where, [tex]P[/tex] is population after [tex]t[/tex] years, [tex]P_0[/tex] is the initial population and [tex]r[/tex] is the growth rate.

Substituting [tex]P_0=14000,r=0.035,t=14[/tex] in the above equation.

[tex]P=14000\left(1+0.035\right)^{14}[/tex]

[tex]P=14000\left(1.035\right)^{14}[/tex]

[tex]P=22661.7233[/tex]

[tex]P\approx 22662[/tex]

Thus, the population after 14 years is 22662.

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Answer: 25.90

Step-by-step explanation:

Edge

The total interest charged for the first 6 months is $36.00.

The total interest charged for the first 6 months can be calculated by adding up the interest charged for each month. From the table, we can see that the interest charged for each month is $6.00. Since there are 6 months, we can calculate the total interest charged as follows:

Total Interest Charged = Interest Charged per Month x Number of Months
Total Interest Charged = $6.00 x 6
Total Interest Charged = $36.00

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Answer:

TRUE

Step-by-step explanation:

Given that line segment JK and LM are parallel. From picture we see that LK is transversal line.

We know that corresponding angles formed by transversal line are congruent.

Hence ∠JKL = ∠ MLK ...(i)

Now consider triangles JKL and MLK

JK = LM  {Given}

∠JKL = ∠ MLK { Using (i) }

KL = KL  {common sides}

Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congurent.

Hence given statement is TRUE.

The statement that if JK and LM are congruent and parallel, then angles JKL and MLK are congruent is false. Congruency of angles depends on more than just the congruency and parallelism of two lines.

In the field of geometry, just because two lines are congruent and parallel, this does not necessarily mean that the angles formed by the intersection of the lines with a third line are congruent. The statement 'If JK and LM are congruent and parallel, then JKL and MLK are congruent' is false. Congruency of angles JKL and MLK depends on the relationship between the two other sides of the angles, not solely the lines JK and LM. Therefore, for the angles to be congruent, additional conditions besides the congruency and parallelism of JK and LM must be satisfied.

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Answer:

B) simple random

The sampling method described in the scenario is "simple random sampling." Option B

With basic random sampling, every unit in the population has an equal chance of being chosen, and there is no set pattern or grouping involved in the selection process.

In this instance, the hammers are put into boxes, and a random box is chosen for quality assurance inspection. It meets the criteria for simple random sampling because each box has an equal probability of being picked.

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Answer:

The slope is 2

The slope represents  how much it costs per visit the pool.

We have a positive slope when lines go  from bottom left to top right

The y intercept is where we cross the y axis which is 4.

x is the  number of visits to the pool

y is the  total cost in dollars

f(x) = 2x+4

Step-by-step explanation:

To find the slope we take two point ( 0,4) and (1,6)

and use the formula

m = (y2-y1)/(x2-x1)

  = (6-4)/(1-0)

 m= 2/1

The slope is 2

It represents  how much it costs per visit the pool.

We have a positive slope when lines go  from bottom left to top right

The y intercept is where we cross the y axis which is 4.

x is the  number of visits to the pool

y is the  total cost in dollars

f(x) = mx+b  where m is the slope and b is the y intercept

f(x) = 2x+4

Answer:

the answer is D edge 2021

Step-by-step explanation:

Answer:

[tex]x^4-5x^2-36=0[/tex]

Step-by-step explanation:

We need to find equation that has exactly two real and two non real solutions

2 real  and 2 non real solution means 4 solutions

x^3 equation has maximum of 3 solutions

So we ignore equation that has largest exponent x^3

We ignore options B  and D

Let check option A

[tex]x^4 - 36x^2=0[/tex]

factor the left hand side

Factor out x^2

[tex]x^2(x^2 - 36)=0[/tex]

WE set each factor =0  and solve for x

x^2 =0  so x=0

x^2 - 36 =0 so x= +-6

So solutions are x=0, x=6 , x=-6. Only 3 real solutions we got

LEts check with option C

[tex]x^4-5x^2-36=0[/tex]

Factor left hand side

[tex] (x^2-9)(x^2+4)=0[/tex]

set each factor =0  and solve for x

x^2 -9 =0  so x= -3, + 3

x^2 + 4 =0 , x^2 = -4, so x= +2i, -2i

So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

Answer:

C. x^4 - 5x^2 - 36 = 0

Final answer:

To model the cost of purchasing concert tickets where each ticket is $44 and there's a fixed handling fee of $12, the equation is T = 44n + 12, with T representing the total cost and n the number of tickets.

Explanation:

The question deals with constructing a mathematical model for the situation where an online ticket seller charges a fixed price for a concert ticket plus a handling fee. Here, the unknown variable is the total cost (T) for purchasing a certain number of tickets (n). The fixed price for each ticket is $44, and there is a flat handling fee of $12 regardless of the number of tickets purchased. Therefore, the equation to model the total cost would be:

T = 44n + 12

This equation clearly defines how the total cost is determined by the number of tickets purchased, with n representing the number of tickets and T the total cost.

Since there are 55 candies in the bag, and there are 20% of blue candies, it would look like this:

55 x 0.20 = 11

Now that we have 11, you multiply it by the damage coating, so

11 x 0.10 = 1.1

Approximately 1 blue chocolate had a damaged candy coating from Kathleen's bag since 20% of the 55 chocolates were blue (resulting in 11 blue chocolates), and 10% of these were damaged (resulting in approximately 1 chocolate).

Kathleen has a bag with a total of 55 candy-coated chocolates. Since 20% of these chocolates are blue, we first need to compute the number of blue chocolates. 20% of 55 translates to 0.20 × 55, which gives us 11 blue chocolates.

Of these blue chocolates, 10% had a damaged candy coating. To find out how many are damaged, we calculate 10% of 11, which is 0.10 × 11. This calculation results in 1.1, which we round to approximately 1 since we cannot have a fraction of a chocolate. Therefore, about 1 of the blue chocolates had a damaged coating.

The correct answer to the question is B. 1

Answer:

A polynomial needs to have either addition, subtraction or multiplication in the equation.

The 2nd, 3rd and 4th answers have subtraction and addition, so those are polynomials.

The first answer is a fraction, which is a division problem, therefore is not a polynomial.

Answer:

[tex]g(x)= 24(3)^{x-2}+6[/tex]

Step-by-step explanation:

f(x)=8(3)^x−2 +2

The graph of f(x) is stretched vertically by a factor of 3 to form the graph of g(x)

When f(x) is stretched vertically then we multiply f(x) by 3 to get g(x)

g(x) = 3f(x)

[tex]g(x)= 3(8(3)^{x-2}+2)[/tex]

Now we distribute 3 inside the parenthesis

[tex]g(x)= 24(3)^{x-2}+6[/tex]

This is our required g(x)

Answer:

57 years

Step-by-step explanation:

Divide 400 by 7.

Answer:

last one

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Trust me i just did it on USA TP

Hello from MrBillDoesMath!

Answer:

Choice C    (6)

Discussion:

Since it is an isosceles trapezoid the length of the two legs (i.e.  AB = 5y-10 and CD = 2y+8) are equal.  In other words,

5y - 10 = 2 y + 8

Subtract 2y from each side:

5y - 2y - 10 = 8

Now add 10 to each side

5y - 2y - 10 + 10 = 8 + 10 =>

3y + 0 = 18 =>

3y = 18 =>

y = 6

Regards,  

MrB

To find the value of y in the isosceles trapezoid ABCD, set up an equation using the given measurements for AB, BC, and CD. Solve the equation to find the value of y.

To find the value of y in the isosceles trapezoid ABCD, we can set up an equation using the given measurements for AB, BC, and CD. Since AB and CD are the legs of the trapezoid, they should be equal. Therefore, we can set AB equal to CD and solve for y:

5y - 10 = 2y + 8

Subtract 2y from both sides:

3y - 10 = 8

Add 10 to both sides:

3y = 18

Divide both sides by 3:

y = 6

Therefore, the value of y is 6. Answer choice C) 6 is correct.

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Answer:

3

Step-by-step explanation:

D. 3

the scale factor of △TOE to △CUP is 3

A scale factor is a number that's used as multiplier when scaling the size of the object. It can be used to scale objects in one, two, and three dimensions and as fractions, ratios, percentages, and decimals. When a scale factor is applied, the size of the object is increased or decreased according to the desired scale.

What does the scale factor stand for?

To scale measurement to the smaller measurement, to instance, when making the blueprint, simply divide the real measurement by a scale factor. The scale factors are commonly expressed as 1:n or 1/n, where n means the factor. For example, a scale factor is 1:8 or the real measurement is 32, divide 32 ÷ 8 = 4 to convert.

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Answer: D

Step-by-step explanation:

log₂ (x - 4) = 4

        x - 4 = 2⁴

        x - 4 = 16

        x      = 20