Find the 8th term of the geometric sequence 6, 18, 54

Answer:

32

Step-by-step explanation:

Let the number be x

x + (-11) = 37

x - 11 = 37

x = 37 + 11

x = 48

Divide this number by -12. This will be:

= 48/-12

= -4

Then, multiply by -8. This will be:

= -4 × -8

= 32

The rule of (x, y) → (-x, y), which is reflection over y-axis.

Given that, ΔABC maps to triangle ΔA'B'C'.

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).

Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.

Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.

From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.

Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.

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Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

When we divide mixed numbers we need to first convert it from mixed fractions to improper ones and then we divide them. When we divide fractions a common guideline is to conserve the first fraction and multiply it by the inverse of the second one. With this in mind let's solve the problem.

The answer to this division is 32/51

Answer:

65 mm²

Step-by-step explanation:

Total surface area of the prism = area of all parts of the prism's net

✔️Area of rectangle 1 with the following dimensions:

L = 5.2 mm

W = 2.1 mm

Area = 5.2*2.1 = 10.92 mm²

✔️Area of rectangle 1 with the following dimensions:

L = 5.2 mm

W = 4.5 mm

Area = 5.2*4.5 = 23.4 mm²

✔️Area of rectangle 3 with the following dimensions:

L = 5.2 mm

W = 5 mm

Area = 5.2*5 = 26 mm²

✔️Area of the 2 traingles with the following dimensions:

b = 4.5 mm

h = 2.1 mm

Area = ½*bh

= ½*4.5*2.1

= 4.725 mm²

Total surface area = 10.92 + 23.4 + 26 + 4.725 = 65.045 ≈ 65 mm² (nearesth while number)

Answer:

v = 7

Step-by-step explanation:

42 = v + 35

-35        -35

7 = v

The answer is D. 7

I took the quiz and got it right

Answer:

w = - 22.4

Step-by-step explanation:

w + 6.1 = -16.3

**subtract 6.1 on both sides to isolate w:

w = -16.3 - 6.1

w = -22.4

Answer:i wont answer it because the other guy is right

Step-by-step explanation:

We can use the proportion of defective gadgets in the sample to estimate the number of defective gadgets in the entire production, and then subtract that from the total number of gadgets produced to estimate the number of non-defective gadgets.

The proportion of defective gadgets in the sample is:

7/100 = 0.07

We can assume that this proportion is representative of the entire production, so we can estimate the number of defective gadgets in the entire production as:

0.07 x 5000 = 350

Therefore, we can estimate the number of non-defective gadgets in the production as:

5000 - 350 = 4650

Therefore, we can predict that there are 4,650 gadgets in the day's production that are not defective.

Answer:

y=1/2x-4

Step-by-step explanation:

y=1/2x+b

-3=1/2(2)+b

-3=1+b

-4=b

y=1/2x-4

The probability of exactly 5 occurrences is (Rounding to three Decimal places), we get P(X ≤ 3) ≈ 0.251.

a) The probability of exactly 5 occurrences is given by the Poisson probability mass function:

P(X = 5) = (e^(-λ) * λ^5) / 5! = (e^(-5.1) * 5.1^5) / 120 ≈ 0.1755

Rounding to four decimal places, we get P(X = 5) ≈ 0.1755.

b) The probability of more than 6 occurrences can be calculated as the complement of the probability of 6 or fewer occurrences:

P(X > 6) = 1 - P(X ≤ 6) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

P(X = 4) ≈ 0.174

P(X = 5) ≈ 0.1755

P(X = 6) ≈ 0.1493

Substituting these values into the formula, we get:

P(X > 6) ≈ 1 - (0.006 + 0.031 + 0.079 + 0.135 + 0.174 + 0.1755 + 0.1493) ≈ 0.249

Rounding to three decimal places, we get P(X > 6) ≈ 0.249.

c) The probability of 3 or fewer occurrences is given by the cumulative distribution function:

P(X ≤ 3) = ∑ P(X = k), for k = 0, 1, 2, 3.

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

Adding these probabilities, we get: P(X ≤ 3) ≈ 0.251

Rounding to three decimal places, we get P(X ≤ 3) ≈ 0.251.

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I don't know the answer so help

Answer: $18.75

Step-by-step explanation:

1 - 3/8 = 5/8

12 x 5/8 = 7.5

7.5 x 2.5 = 18.75

Dave spent $18.75, in filling his car's tank of capacity 12 gallons up to the capacity, which was 3/8th filled already, at the unit rate of $2.50 per gallon of gas.

The unit rate is the quantity (cost/distance/time, etc.) for one unit of another quantity (cost/distance/time, etc.).

In the question, we are informed that the gas tank of Dave's car has a capacity of 12 gallons. The tank was 3/8 full before Dave filled it to capacity. It cost him $2.50 per gallon of gas.

We are asked the amount Dave spent.

The unit rate of gas is $2.50 per gallon.

To find the total amount spent by Dave, we need to find the volume of gas he filled and then multiply that volume with the unit rate.

The capacity of Dave's car's tank = 12 gallons.

Gas it already had = 3/8th of capacity,

or, gas it already had = 3/8 * 12 = 4.5 gallons.

Therefore, the volume of gas Dave filled = 12 - 4.5 gallons = 7.5 gallons.

The amount spent by Dave = Volume filled*Unit rate = $ 7.5 * 2.5 = $18.75.

Therefore, Dave spent $18.75, in filling his car's tank of capacity 12 gallons up to the capacity, which was 3/8th filled already, at the unit rate of $2.50 per gallon of gas.

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Derivative are used to determine the nature of a function. The derivative of the function f(x) = 4x^2 is 8x

The formula for finding the derivative of a function is expressed as:

f'(x) = nax^n-1

Given the function expressed as:

f(x) = 4x^2

We are to find its derivative as shown:

f'(x) = 2(4)x^2-1
f'(x) = 8x^1 = 8x

Hence the derivative of the function f(x) = 4x^2 is 8x

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Answer:

Step-by-step explanation:

4.5

The number of the pounds of sugar that you need for triple batch will be 72 ounces.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

You have a pickle recipe that requires 24 ounces of sugar.

You want to make a triple batch of pickles.

Then the number of the pounds of sugar that you need for triple batch will be

⇒ 3 x 24

⇒ 72 ounces

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(1) The missing sides of the right triangle is r = 8√2, and t = 8.

(2) The missing sides of the right triangle cannot be determined.

(3) The missing sides of the right triangle is 60√2.

(4) The missing sides of the right triangle is y = 20, and z = 20√3.

(5) The missing sides of the right triangle is m = 2, and n = 4.

(6) The missing sides of the right triangle is p = 5√3, and O = 5.

The values of the missing sides of the right triangle is calculated as follows;

For question 1; the lengths of the right triangle is calculated as;

sin 45 = 8/r

r = 8/sin 45

r = 8√2

tan 45 = t/8

t = 8 tan(45)

t = 8

For question 2;

The value of g cannot be determined since we don't know if the triangle is a right triangle.

For question 3;  the lengths of the right triangle is calculated as;

Assuming the triangle is 45, 45, 90 triangle, then the value of x is calculated as;

sin 45 = 60/x

x = 60/sin 45

x = 60√2

For question 4;  the lengths of the right triangle is calculated as;

sin 30 = Y/40

Y = 40 x 0.5

Y = 20

cos 30 = z/40

z = 40 x cos30

z = 20√3

for question 5;  the lengths of the right triangle is calculated as;

tan 30 = m/2√3

m = 2√3  x tan30

m = 2

sin 30 = m/n

n = m/sin30

n = 2/0.5

n = 4

For question 6;  the lengths of the right triangle is calculated as;

sin 60 = p/10

p = 10 x sin60

p = 5√3

sin 30 = O/10

O = 10 x sin(30)

O = 5

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Answer:

False

Step-by-step explanation:

Graphing tells you where the solution of the system, or graph intersection occurs no matter what. You can have a quadratic and exponential function -- graphing will always show you where they intersect (or don't!)

Answer:

false

Step-by-step explanation:

hope this helps

Answer:

.25 or 25%

Step-by-step explanation:

The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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The detailed answer of this question is:

P(X > 100 | X > 50)=0.455

Given that X follows an exponential distribution, we know that the probability density function (PDF) of X is given by:

f(x) = λe^(-λx) for x ≥ 0

where λ is the rate parameter of the distribution.

We are given that P(X < 50) = 0.25. Using the cumulative distribution function (CDF) of X, we can write:

P(X < 50) = 1 - e^(-λ*50) = 0.25

Solving this equation for λ, we get:

λ = -ln(0.75)/50 ≈ 0.0278

Now, we are asked to find P(X > 100 | X > 50). Using the definition of conditional probability, we can write:

P(X > 100 | X > 50) = P(X > 100 and X > 50) / P(X > 50)

= P(X > 100) / P(X > 50)

= e^(-λ100) / e^(-λ50)

= e^(-λ*50)

Substituting the value of λ, we get:

P(X > 100 | X > 50) = e^(-0.0278*50) ≈ 0.455

Therefore, the probability that a high-risk driver will have an accident after 100 days given that they have not had an accident for the first 50 days is approximately 0.455.

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Answer:

the answer is 28 bc 2+2+4+4+8+8=28 so you answer will be twenty eight centi meters

Distance = speed x time

Distance = 68 x 4 1/2

Distance = 306 miles

Answer: 306 miles

Step-by-step explanation:

Speed= distance/time

Distance= speed•time

Time= distance/speed

Answer:

700

Step-by-step explanation:

The equation for graph in slope intercept form is  y=-3x+10.

Given the points from the graph are:

(0,10) = (x₁ , y₁)

(3,1) = (x₂ , y₂)

slope of the given points is :

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 10)/(3 - 0)

m = -9/3

m = -3

equation of the line is : y - y₁ = m(x-x₁)

we have m = -3

and point = (0,10)

therefore, y - 10 = (-3)(x-0)

y-10=-3x+0

y=-3x+10

hence the slope intercept form is :

y=mx+c

therefore, y=-3x+10

hence we get the equation of the line as y=-3x+10

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Answer: D: Square Root Of 5

Step-by-step explanation: 30/6 is 5, now fill in the sqrt symbol. Hope this helped. (This problem was one of the simpler, friendlier numbers.)

Answer:

10:4

Step-by-step explanation:

..................

Answer:

Step-by-step explanation:

es, if the original biconditional statement is true, then its contrapositive is also true.

Example: "If it rains, the grass is wet."

The contrapositive of this statement would be "If the grass is not wet, then it didn't rain."

Both the original statement and its contrapositive have the same truth value, as they are logically equivalent.

The volume of a solid formed by revolving the region bounded above by the line is (932π/15)

To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.

The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:

\(r = y^2 - 1\)

The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:

h = 3 - 1 = 2

The volume of each disk is then:

\(dV = \pi r^2h dy\)

Substituting r and h, we have:

\(dV = \pi (y^2 - 1)^2 (2) dy\)

To find the total volume, we integrate over the range of y from 1 to 3:

\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)

This integral can be simplified by expanding the squared term:

\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)

V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)

V = 2π [(1/5)(242) - (2/3)(26) + 2]

V = 2π [(242/5) - (52/3) + 2]

V = 2π [(726/15) - (260/15) + 30/15]

V = 2π [(466/15)]

V = (932π/15)

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Note: The full question is

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.