An ancient culture labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are square numbers. Complete parts a through c below. . . . .
1 4 16 25 36, 49, 64
Describe a procedure to determine the next five square numbers without drawing the figures.
A. Square 6, 8, 10, 12, and 14.
B. Add the last two square numbers together to get the next one.
C. Double the previous square number and then subtract half of the previous from that.
D. Square 6, 7, 8, 9 and 10. ​

Do parentheses first:

6 +4-2 = 8

Now do brackets:

128/8 = 16

Now multiply:

16 x 8 = 128

The answer is 128

Answer:

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 86

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 2

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 71

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 1

B) The distribution is approximately normal.

[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]

Therefore, the probability that the sample mean is greater than 73 = 0.0228

[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]

The probability that the sample mean is less than or equal to 69 is 0.0228

[tex]\mathbf{P( 69.8 \leq \overline x \leq 72.5) = 0.8181}[/tex]

Thus, the probability that the sample mean is between 69.8 and 72 is 0.8181.

Step-by-step explanation:

We are to determine the [tex]\mu_{\overline x}[/tex] and [tex]\sigma_x[/tex] from the given parameters of a population and sample size.

Given that :

population mean [tex]\mu[/tex] = 86

population standard deviation [tex]\sigma[/tex] = 16

sample size n = 64

From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex]  is equal to the population mean [tex]\mu[/tex]

∴

[tex]\mu_{\overline x}[/tex]  = [tex]\mu[/tex] = 86

The standard deviation of the sampling distribution can be computed by using the formula:

[tex]\sigma_{\overline x } = \dfrac{\sigma }{\sqrt{n}}[/tex]

[tex]\sigma_{\overline x } = \dfrac{16 }{\sqrt{64}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{16 }{8}[/tex]

[tex]\mathbf{\sigma_{\overline x } = 2}[/tex]

∴

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 86

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 2

Suppose a simple random sample of size n = 36  is obtained from a population with mu = 71 and sigma = 6.

i.e

sample size n = 36

population mean [tex]\mu[/tex] = 71

standard deviation [tex]\sigma[/tex] = 6

From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex]  is equal to the population mean [tex]\mu[/tex]

∴

[tex]\mu_{\overline x}[/tex]  = [tex]\mu[/tex] = 71

The standard deviation of this sampling distribution [tex]\sigma_{\overline x}[/tex] can be estimated as :

[tex]\sigma_{\overline x }= \dfrac{\sigma }{\sqrt{n}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{6 }{\sqrt{36}}[/tex]

[tex]\sigma_{\overline x } = \dfrac{6 }{6}[/tex]

[tex]\mathbf{\sigma_{\overline x } = 1}[/tex]

∴

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 71

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 1

A)

The correct option from the  given question is:

B) The distribution is approximately normal.

B) What is P (xbar > 73)?

i.e

[tex]P(\overline x >73) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 \times 6 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{12 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > 2 \end {pmatrix}[/tex]

[tex]P(\overline x >73) = 1- P \begin {pmatrix} Z < 2 \end {pmatrix}[/tex]

Using the Excel Function ( =NORMDIST(2) )

[tex]P(\overline x >73) = 1- 0.9772[/tex]

[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]

Therefore, the probability that the sample mean is greater than 73 = 0.0228

C) What is P (xbar ≤ 69)?

i.e

[tex]P(\overline x \leq 69) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{69 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix}Z \leq \dfrac{-2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-2 \times 6 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-12 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq -2 \end {pmatrix}[/tex]

Using the EXCEL FUNCTION ( = NORMSDIST (-2) )

[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]

The probability that the sample mean is less than or equal to 69 is 0.0228

NOTE: This text editor can't contain more than 5000 characters so the last part of the question is attached in the image below.

Answer:

-4 1/2

Step-by-step explanation:

1/3(-15+3/2)

1/3(-13 1/2)

1/3(-27/2)

-27/6

-4 3/6

-4 1/2

Answer:

-8/4-21x

Step-by-step explanation:

Distribute inside the parantheses

Divide -8 and 4

Add the two terms

Simplify

Answer:

Sarah answered 7 multiple choice questions and 3 free response questions correctly.

Step-by-step explanation:

Given that: she has 36 points.

                   3 points each for the multiple choice question (MCQ)

                   5 points each for the free response question (FRQ)

To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.

  3x + 5y = 36   ............ 1

Since she answered a total of 10 question, then;

  x + y = 10

 x = 10 - y  ................  2

Substitute equation 2 into 1,

3(10 - y) + 5y = 36

30 - 3y + 5y = 36

2y = 6

y = 3

Substitute the value of y in equation 2,

x = 10 - y

  = 10 - 3

  = 7

x = 7, y = 3

Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.

Answer:

60in^2

Step-by-step explanation:

Area of a triangle = Height x Base X 1/2

Base = 10

Other 2 sides = 13

Now, let's split the Base into 2 parts.

=> 1 part = 5 and 2 part = 5

We can find the height using Pythagorean theorem

=> Isosceles triangle

=> (1 part of the base)^2 + Height^2 = The Hypotenuse^2  = the longer side of a triangle = 13^2

=> 5^2 + Height ^2 = 13^2

=> 25 + Height^2 = 169

=> 25 - 25 + Height ^2 = 169 - 25

=> Height^2 = 144

=> Height = Square root of 144

=> Height = 12

Area = 12 x 10 x 1/2

=> 12 x 5

=> 60 in^2

So, the Area is 60 in ^2

Answer:

13 hours

Step-by-step explanation:

8:00 plus 4 is twelve ( 12 o'clock )

then you have 9hrs left.

( 4+9=13 )

Ans

8 option b.

Step-by-step explanation:

3+4/2+3

=3+2+3

=5+3

=8

Answer:

5

Step-by-step explanation:

Answer:

-0.66666666666

Step-by-step explanation:

1/3-5/5

Answer:

1079

Step-by-step explanation:

Hello,

18-5 = 13

31-18=13

44-31=13

161=5+13*12

So we need to compute

[tex]\displaystyle \sum_{k=0}^{k=12} \ {(5+13k)}\\\\=\sum_{k=0}^{k=12} \ {(5)} + 13\sum_{k=1}^{k=12} \ {(k)}\\\\=13*5+13*\dfrac{12*13}{2}\\\\=65+13*13*6\\\\=65+1014\\\\=1079[/tex]

Thanks

The required sum of the arithmetic series 5+18 +31 +44 + ... 161 is 1079.

Given that,
Arithmetic series: 5+18 +31 +44 + ... 161.

The Sum of the series is to be determined.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
From the given series
First term A = 5, Common difference D = 13 and last term L = 161
Last term = An + (n -1)
161 = 5 + (n - 1)13
n - 1 = (161 - 5) / 13
n = 12 + 1
n = 13

Now the sum of an arithmetic series,
S = n /2 (A + L)
S = 13 / 2 (5 + 161)
S = 13 / 2 * 166
S = 13 * 83
S = 1079

Thus, the required sum of the arithmetic series 5+18 +31 +44 + ... 161 is 1079.

Learn more about arithmetic progression here: https://brainly.com/question/20334860
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25.36+5.09+11.45= 41.9$ intotal

Answer:

41,9

Step-by-step explanation:

25.36+5.09+11.45

Answer:

2513.3

Step-by-step explanation:

cylinder volume = π[tex]r^{2}[/tex]h

cylinder volume = π [tex]20^{2}[/tex](2)

cylinder volume = 2513.27

cylinder volume = 2513.3

Answer:

x=35 hrs

1 hour =105

cross mutiply

105÷35=3

The equation that describes the situation is 35x = 105.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, and quadratic equations.

William drove 35 miles per hour for a total of 105 miles.

The total miles William drove is 105 miles.

The speed at which he drove is 35 miles/ hour.

The total time he drove is given by x hours.

The equation has to be formed for this situation.

Speed is defined as the distance traveled with respect to time.

35 = 105 / x

35x = 105

This equation describes the given situation.

To know more about Equation

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Answer:

10/25

Step-by-step explanation:

2/5 = x/25

We need to multiply the bottom by 5 to get to 25

5*5 = 25

What we to the bottom, we do the the top

2/5 * 5/5 = 10/25

Answer:

10/25

Step-by-step explanation:

2/5 = x/25

cross multiply

2 • 25 = 50

5 • x = 5x

set equal to each other

5x = 50

divide both sides by 5

x = 10

8^15 ÷ 1/8^3 = 8^15 x 8^3=8^18

1.8014399e+16

Step-by-step explanation:

So before you can divide the numbers you have to simplify the exponents. You probably learned P(parentheses) E(exponents) M(multiply) D(divide) A(add) S(subtract.

Answer:

first answer

Step-by-step explanation:

Hello, you know that

[tex]\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\cdot \dfrac{d}{c}[/tex]

So, the quotient we need to estimate is

[tex]\begin{aligned}\dfrac{x^2-36}{x+8}\cdot\dfrac{4x+32}{x^2+12x+36}&=\dfrac{x^2-6^2}{x+8}\cdot \dfrac{4(x+8)}{(x+6)^2}\\\\&=\dfrac{4(x-6)(x+6)}{(x+6)^2}\\\\&=\dfrac{4(x-6)}{x+6}\end{aligned}[/tex]

Thank you

Answer:

X = -1

Y = 1

Step-by-step explanation:

The solution of the equations x = 6y - 7 and 4x + y = -3 will be (-1, 1).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The linear equation is given below.

x = 6y - 7           ...1

4x + y = - 3       ...2

Simplify the equation, then we have

4(6y - 7) + y = -3

24y - 28 + y = - 3

25y = 25

y = 1

The value of the variable 'x' will be calculated as,

x = 6(1) - 7

x = 6 - 7

x = - 1

The solution of the equations x = 6y - 7 and 4x + y = -3 will be (-1, 1).

More about the solution of the equation link is given below.

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Answer:

600/11

Step-by-step explanation:

scoops of

strawberry= x

chocolate= y

vanilla ice cream= z

X+y+z= 100

The snack bar sold 3 times as many scoops of chocolate as it did strawberry

3x= y

X= y/3

and 2 times as many scoops of

vanilla as it did chocolate

2z= y

Z= y/2

X+y+z= 100

Y/3 + y +y/2 = 100

2y + 6y + 3y = 600

11y= 600

Y= 600/11

This question is incomplete, the complete question is;

A rocket is launched straight into the air with initial velocity 200 ft/s. Assume the launch is instantaneous. How high will it go, and how long will that take (use time increments of 0.01 seconds)? G= - 32.2 ft/s² , H₀=0 (the ground)

V(t)=V₀ + g t

H(t)= H₀ + V₀ t + ½ g t²

The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec. How long does it take to reach the ground

Answer:

a) maximum height S is 621.12 ft and time taken to reach it is 6.21 sec.

b) The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec,

Time taken to travel t = 24.79 sec

NOW total time taken = 27.55 sec

Step-by-step explanation:

Given that,

initial velocity u = 200 ft/s

acceleration a = 32.2 ft/s²

vertical displacement ( maximum height) S = ?

final velocity at highest point Ц = 0

NOW from the equation of motion

v² - u² = 2as

we substitute

0² - (200)² = 2 (-32.2) × s

s = 621.12 ft

time taken t = (v -u)/a = (0-200)/-32.2

t = (-200) / (-32.2)

t = 6.21 sec

distance traveled by rocket from t=6.21sec to t=9sec

Δt = (9-6.21) = 2.79sec

s = ut + 1/2at²

s = 0 + 1/2(32.2)(2.79)² = 125.32 ft

Remaining distance = 621.12 ft - 125.32 ft = 495.8 ft

Time taken to travel = t = s/v = (495.5ft) / (20 ft/sec)

t = 24.79 sec

NOW total time taken = 2.79sec + 24.79sec = 27.55 sec

Answer:

natural numbers - positive integers (whole numbers)

• 1

• 2

• 3

• 4

• 5

whole numbers - a number without fractions

• 10

• 11

• 12

• 13

• 14

rational numbers - a number that can be expressed as the ratio of two integers

• 1/3 or 0.3333...

• 17

• -34

• 25

• -10

integers - a whole number; a value that is not a fraction

• -5

• 49

• 68

• 439

• 35

Answer:

4×(x+8)=25.

use the 4 to multiply the numbers in the bracket.

which is 4x+32=25.

then collect like terms which is...

4x=25-32...

4x=-7.

x=-7/4= -1.75 or -1 whole number 3/4.

Answer:

Negative of 5 exists

It continues in the left part of a number line...

Hence the answer is false it does exist

Answer: false

Additive identity - the number 0; when added to any number, the value of the number does not change

( one is multiplicative identity )

Answer:

z^4-z²-20

Step-by-step explanation:

( z^2 + 4 ) ( z^2 – 5)

z^4+4z²-5z²-20

z^4-z²-20

Answer:

Here is your solution-

x³ times x⁷

means, x³×x⁷

Here you just have to add the powers as aⁿ×aᵐ=aⁿ⁺ᵐ

x³⁺⁷

x¹⁰

Answer:

The confidence interval is  [tex]13.4< \mu < 13.8[/tex]

Step-by-step explanation:

From the question we are told that

   The sample  mean is [tex]\= x = 13.6[/tex]

     The standard deviation is [tex]\sigma = 1.9[/tex]

     The sample  size is  [tex]n = 189[/tex]

given that the confidence level is  85% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 85 )\%[/tex]

            [tex]\alpha = 0.15[/tex]

Next we obtain the critical value  of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  the value  is  

      [tex]Z_{\frac{\alpha }{2} } = 1.44[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

=>     [tex]E = 1.44* \frac{1.9}{\sqrt{189} }[/tex]

=>     [tex]E = 0.1990[/tex]

The  85%  confidence interval is mathematically represented as  

        [tex]\= x - E < \mu <\= x + E[/tex]

=>      [tex]13.6- 0.1990 < \mu < 13.6+ 0.1990[/tex]

=>      [tex]13.4< \mu < 13.8[/tex]

Answer:

Step-by-step explanation:

x- intercept, vertex (v) and axis of symmetry, parabola form:x²+bx+c

vertex(h,k)

f(x)=x²-9  a=1,b=0 ,c=-9

h=-b/2a=0

k=f(0)=-9

vertex(0,-9) , x intercept is when f(x)=0

(x-3)(x+3)=0 either x-3=0⇒ x=3 or x+3=0 then x=-3

x=3, x=-3 (-3,0) and (3,0)

the x of symmetry is the h of the vertex=0

g(x)=x²-2x-3 a=1, b=-2,c=-3

h=-b/2a⇒-(-2)/2(1)⇒h=1

k=f(1)=1²-2(1)-3⇒k=-4

v(1,-4)

x of symmetry=h=1

(x+1)(x-3)=0

x+1=0⇒x=-1 (-1,0)

x-3=0 ⇒x=3  (3,0)

x intercept :-1,3

vertex(-3,9)

x intercept:(0,0) and (-6,0)

axis of symmetry =-3

vertex(3,-8)

axis of symmetry=3

x intercept : (5,0), (1,0)

vertex(-1/2,1)

x of symmetry=-1/2

x intercept : (0,0)(-1,0)

vertex(3,0)

x intercept (3,0)

axis of symmetry = 3