what is the 6th term of the geometric sequence where a1 = −4,096 and a4 = 64? a. −1 b. 4 c. 1 d. −4

The median age of the presidents at their death is 69.

The median is the value that is exactly in the middle of a dataset when it is arranged in order. It is a measure of central tendency which separates the lowest 50% from the highest 50% of values.

The median formula is {(n + 1) / 2}th, where “n” is the number of items in the set and “th” means the (n)th number. To find the median, first arrange the data points from smallest to largest.

The steps for finding the median differ depending on whether we have an odd or an even number of data points. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

In this case, the number of data points is even, that is 38. So, the median is:

= {(n + 1) / 2}th

= {(38 + 1) / 2}th

= 19,5th

Thus, it means the median is the average of the 19th and 20th in the data points. So, it will be:

Median = (68 + 70) / 2

Median = 138 / 2

Median = 69

Hence, the median age of the presidents at their death is 69.

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Although part of your question is missing, you might be referring to this full question: This list shows the age at which 38 U.S. Presidents died.

46 58 64 68 73 80 90

49 60 65 70 74 81 93

53 60 66 71 77 83

56 63 67 71 78 85

56 63 67 71 78 88

57 64 67 72 79 90

What is the median age of the presidents at their death?

A. 69

C. 68

b. 67.5

d. 70

The coordinates of the vector v are (x, y) = (7, 3). (Correct choice: C)

The picture shows a vector u, that is, (x, y) = (21, 9) and we need to find the resultant of multiplying that vector by a scalar, which is equal to 3. By mutiplying a vector by a scalar:

u = k · v

Where k is the scalar multiple.

If we know that u = (21, 9) and k = 3

(21, 9) = 3 · (x, y)

(21, 9) = (3 · x, 3 · y)

(x, y) = (7, 3)

The coordinates of the vector v are (x, y) = (7, 3). (Correct choice: C)

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Answer:

(0, -7)

Step-by-step explanation:

y = -3x - 7

y -int - > (0,-7)

hope this helps!

Answer:

AThe factory can expect to have an average of 50 cans dented each day they are produced at the factory.

Step-by-step explanation:

1/20 of 1000 is 50

so A is your answer

The factory can expect to have an average of 50 cans dented each day they are produced at the factory.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

There are 1000 cans of cat food produced daily at a factory.

In the meeting last week, the company stated that of the cans produced daily there is a probability of 1/20 of being dented.

The number of cans of cat food the company expects to be dented is given by;

\(\rm = Total \ number \ of \ can \ produced \ daily \times Denied \ can\\\\=1000\times \dfrac{1}{20}\\\\=50\)

Hence, the factory can expect to have an average of 50 cans dented each day they are produced at the factory.

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Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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Answer:

49.12?

Step-by-step explanation:

half circle= 4 squared *3.14/2=25.12

triangle=pythagorean theorem to find h=8. 8*6/2= 24

25.12+24=49.12

Answer:

40

Step-by-step explanation:

y = 4

z = 2

8y + 12 - 2z

8(4) + 12 - 2(2)

32 + 12 - 4

44 - 4

40

Answer:

40

Step-by-step explanation:

An expression that represent the combined inventory of the two stores include the following: B. 7/2(g²) - 4/5(g) + 15/4.

In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value.

Next, we would add the two (2) given polynomials as follows;

Polynomial = 1/2(g²) + 7/2 + 3g² - 4/5(g) + 1/4

By rearranging and collecting like-terms, we have the following:

Polynomial = [1/2(g²) + 3g²] - 4/5(g) + [1/4 + 7/2]

Polynomial = 7/2(g²) - 4/5(g) + 15/4

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Answer:

-4/7

Step-by-step explanation:

2/3(1+n)=-1/2n

2/3+2/3n=-1/2n

2/3=-1/2n-2/3n

2/3=-3/6n-4/6n

2/3=-7/6n

n=(2/3)/(-7/6)

n=(2/3)(-6/7)

n=-12/21

simplify

n=-4/7

Answer:

True

Step-by-step explanation:

7+25+33=(7+33)+25

Solve Parentheses

7+25+33=40+25

Combine Like Terms

65=65

Answer:

true

Step-by-step explanation:

7+25+33 =(7+33)+25

65=(40)+25

65 =65

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

\(y=\dfrac{2}{7}x-12\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Given:

The y-intercept is the y-value when x = 0.

Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:

\(\implies y=\dfrac{2}{7}x-12\)

Answer:

the 2nd one

Step-by-step explanation:

Answer:

Step-by-step explanation:

The second statement is correct.  The comma indicates that the "favorite fruits" are identified right there and then.

x² + y² + z² + 2xyz = 1, hence proved.

Given: sin⁻¹ x + sin⁻¹ y + sin⁻¹ z = π/2

Prove that: x² + y² + z² + 2xyz = 1

Proof: First, using the formula:

sin⁻¹ x + sin⁻¹ y = sin⁻¹ (x√(1-y²) + y√(1-x²))

from the addition formula for sine of two angles, we can rewrite

sin⁻¹ x + sin⁻¹ y + sin⁻¹ z = π/2 as sin⁻¹ (x√(1-y²) + y√(1-x²)) + sin⁻¹ z = π/2

Simplifying, we have

sin(sin⁻¹ (x√(1-y²) + y√(1-x²)) + sin⁻¹ z) = sin(π/2)

Using the formula for sine of the sum of two angles,

sin(a + b) = sin a cos b + cos a sin b

we can rewrite the left-hand side as follows:

sin(sin⁻¹ (x√(1-y²) + y√(1-x²))) cos sin⁻¹ z + cos(sin⁻¹ (x√(1-y²) + y√(1-x²))) sin sin⁻¹ z

We have, sin(sin⁻¹ t) = t and cos(sin⁻¹ t) = √(1-t²) for all t.

Using these formulas, we can simplify the above expression as follows:

(x√(1-y²) + y√(1-x²))√(1-z²) + √(1-(x√(1-y²) + y√(1-x²))²)z = 1

Squaring both sides and simplifying, we get:

x²(1-y²) + y²(1-x²) + 2xyz² + z²(1-(x√(1-y²) + y√(1-x²))²) = 1

Expanding (x√(1-y²) + y√(1-x²))² and simplifying, we get:

x²(1-y²) + y²(1-x²) + 2xyz² + z²(1-x²-y²) = 1

Rearranging terms and simplifying, we get:

x² + y² + z² + 2xyz = 1

Therefore, x² + y² + z² + 2xyz = 1 if sin⁻¹ x + sin⁻¹ y + sin⁻¹ z = π/2.

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Answer:

least to greatest

-49, -45, 43, 51

Answer:

Step-by-step explanation:

-45, 43, |-49|, |51|

Answer:

See below for answers and explanations

Step-by-step explanation:

10) The domain is (-∞,+∞) because no matter what x is, it is defined for all real numbers. The range is (-∞,3] because if y is greater than 3, then no x-value can be defined for that.

11) The domain would be (−∞,3)∪(3,∞) because of the vertical asymptote located at x=3 which means x can be any real number other than 3. The range is (-∞,0)∪(0,∞) because of the horizontal asymptote located at y=0, which means y can be any real number other than 0.

The area is equal to 324π square units.

To find the area of a circle with radius 18 units, we can use the formula for the area of a circle, which is given by A = πr^(2), where r is the radius.

Given that the radius is 18 units, we can plug this value into the formula:

A = π(18)^2

Now, square the radius:

A = π(324)

Next, multiply 324 by π:

A = 324π

Therefore, the area of the circle with radius 18 units is 324π square units.

Now, let's compare the options with the given options:

a) 18π units^(2)- This is incorrect, as we calculated the area to be 324π square units.

b) 36π units^(2)- This is also incorrect, as our calculated area is 324π square units.

c) 9π units^(2)- This is incorrect, as our calculated area is 324π square units.

d) 324π units^(2)- This is the correct option , as we calculated the area to be 324π square units.

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Answer:

in explanation

Step-by-step explanation:

0.27227222722227

The next 6 digits are

0.27227222722227222227

Answer:

8 Liters

Step-by-step explanation:

Percentage of Alcohol in water= 2L X 0 =0

Percentage of Alcohol to be added = xL X 0.9 =0.9x

Therefore:

0+0.9x=0.72(x+2)

0.9x=0.72x+1.44

Collect like terms

0.9x-0.72x=1.44

0.18x=1.44

Divide both sides by 1.44

x=8 Liters

Therefore, Shanice must add 8 Liters of 90% alcohol solution to create the desired mixture

Answer:

10)

11x-1+20x-3=151 (the exterior angle of an triangle is equal to the sum of two opposite interior angles)

31x-4=151

31x=151+4

31x=155

x=155/31

x=5°

11)

14x-13=4x+13+6x+2

14x-4x-6x=13+13+2

4x=28

x=28÷4

x=7°

The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.

In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.

Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.

To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.

In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.

Therefore, the correct answer is: c. 0.00

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The solution of the equation is x=±i or x=±i√2.

Given that the equation is x⁴+3x²+2=0 and use u substitution method to solve.

We can rewrite our given equation as:

(x²)²+3x²+2=0

Let's assume that the (x²)=u.

The given equation is rewritten as u²+3u+2=0.

Factorize the quadratic equation by adding or subtracting two number that gives the sum of 3u and product 2u² as

u²+2u+u+2=0

u(u+2)+1(u+2)=0

Taking out (u+2) as common and get

(u+2)(u+1)=0

Compare each equation with 0 and get

u+2=0 or u+1=0

u=-2 or u=-1

Performing back substitution by substituting the values of u in x²

when u=-1 then x is

x²=-1

x=±√(-1)

As we know that √(-1)=i.

So, we get

x=±i

And when u=-2 then x is

x²=-2

x=±√(-2)

As we know that √(-1)=i.

So, substituting this, we get

x=±i√2

Hence, the solutions of the x⁴+3x²+2=0 is x=±i and x=±i√2.

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a. Predictor (x): odometer readings. Response (y): price.

b. Predictor (x): household size. Response (y): monthly water bill.

c. Predictor (x): time spent in the gym. Response (y): weight.

a. In this case, we want to predict the price of a used car based on its odometer reading. The price is the response variable, and the odometer reading is the predictor variable. It is reasonable to assume that the more miles a car has on it, the lower its value will be, all else being equal.

b. In this case, we want to predict the monthly water bill based on household size. The monthly water bill is the response variable, and the household size is the predictor variable. It is reasonable to assume that the more people living in a household, the higher their monthly water bill will be, all else being equal.

c. In this case, we want to predict a client's weight based on the time they spend in the gym. Weight is the response variable, and time spent in the gym is the predictor variable. It is reasonable to assume that the more time a person spends in the gym, the more likely they are to lose weight or maintain a healthy weight, all else being equal.

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The work done on a 28.0 kg crate initially moving with a velocity of 4.20 m/s at 37.0∘ west of north to change its velocity to 5.62 m/s at 63.0° south of east is 309 Joules.

To solve this problem, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. The formula for kinetic energy is

KE = 1/2mv^2

where m is the mass of the object, and v is its velocity.

We can find the initial kinetic energy of the crate using its initial velocity

KE1 = 1/2(28.0 kg)(4.20 m/s)^2

KE1 = 249 J

We can also find the final kinetic energy of the crate using its final velocity

KE2 = 1/2(28.0 kg)(5.62 m/s)^2

KE2 = 558 J

The change in kinetic energy is therefore:

ΔKE = KE2 - KE1

ΔKE = 558 J - 249 J

ΔKE = 309 J

Since the work done on the crate is equal to the change in its kinetic energy, we can find the work using

W = ΔKE

W = 309 J

Therefore, the amount of work that must be done on the crate to change its velocity is 309 Joules.

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Answer:

4x2(2x – 3)(x + 6)

Step-by-step explanation:

Given expression: 8x^4 + 36x^3 - 72x^2

Step 1: Identify the greatest common factor (GCF) of the terms.

In this case, the GCF is 4x^2. We can factor it out from each term.

Step 2: Divide each term by the GCF.

Dividing each term by 4x^2, we get:

8x^4 / (4x^2) = 2x^2

36x^3 / (4x^2) = 9x

-72x^2 / (4x^2) = -18

Step 3: Rewrite the expression using the factored form.

Now that we have factored out the GCF, we can write the expression as:

8x^4 + 36x^3 - 72x^2 = 4x^2(2x^2 + 9x - 18)

The factored form is 4x^2(2x^2 + 9x - 18).

Step 4: Compare the factored form with the given options.

a. 4x(2x - 3)(x^2 + 6)

b. 4x^2(2x - 3)(x + 6)

c. 2x(2x - 3)(2x^2 + 6)

d. 2x(2x + 3)(x^2 - 6)

Among the options, the one that matches the factored form is:

b. 4x^2(2x - 3)(x + 6)

So, the correct answer is option b. 4x2(2x – 3)(x + 6)

Answer:

P = -31

Step-by-step explanation:

-1 + 14p = -435

Remove the -1 by adding it from both sides.

14p = -434

Remove the 14 by dividing it from both sides.

p = -434/14

p = -31

Answer:

-31

Step-by-step explanation:

-1+14p=-435

14p=-435-(-1)

14p=-435+1

14p=-434

p=-434/14

p=-31