Find the sum of the first 5 terms of the geometric sequence 3, -9, 27,....

Answer:

rectangular pyramid has 8 edges

The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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a) The height of the stone 5 seconds later is: 90 feet

b) The time at which the stone hits the ground is: 7.66 secs

c) The velocity of the stone when it hits the ground is: 227 ft/sec

We are given:

Height above ground: h = 800 feet

Initial speed: u = 18 feet per second

(A.) Height of the stone at t = 5 seconds.

g = -32feet/sec²

t = 5 sec.

Since the stone is thrown vertically upward from some height X = 800 feet, so the total height will be:

h = X + ut + 1/2at²

h = 800 + (18*5) + ¹/₂ * (-32) * (5²)

h = 90 feet

(B.) At what time did the stone hit the ground, that means height, h = 0.

0 = 800 + (18t) + ¹/₂ * (-32) * (t²)

16t² - 18t - 800 = 0

t = 18 ± √-18² - 4 * 16 * (-800)/2*16

t = 7.66 sec

So at t = 7.66 secs, the stone hits the ground.

(C.) The velocity when the stone hits the ground.

Using the energy conservation theorem,

Initial total energy =  Final total energy.

¹/₂mu² + mgh = ¹/₂mv² + 0

u² + 2gh = v²

v² = 18² + 2*32*800

v=√18² + 2*32*800

v = 227 ft/sec

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Answer:

[tex](x-6)^2+(y+7)^2=4[/tex]

Step-by-step explanation:

The formula for the equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where:

From inspection of the given graphed circle, we can see that the coordinates of its center are (6, -7), and its radius is 2 units. Therefore:

To determine the equation of the graphed circle, substitute these values into the equation of a circle formula:

[tex]\implies (x-6)^2+(y-(-7))^2=2^2[/tex]

[tex]\implies (x-6)^2+(y+7)^2=4[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x-6)^2+(y+7)^2=4}[/tex]

The box in a box plot represents the middle 50% of the data (E) and the interquartile range (F).

There are 6 such paths, so there are 6 outcomes in the sample space that show Casey winning.

We can use a tree diagram to visualize the different outcomes of Casey's rolls:

Each branch of the tree represents one roll of the number cube.

The first two rolls are independent and equally likely to be any of the six numbers.

If the first two rolls are the same number, then Casey gets to roll again. If the third roll is a 6, she wins.

We can count the number of outcomes in the sample space that show Casey winning by counting the number of paths in the tree that lead to a 6 on the third roll.

These are:

1-1-6

2-2-6

3-3-6

4-4-6

5-5-6

6-6 (rolls again)-6

Therefore, the answer is 6.

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1. The Height of the stone after 5s is 490feet

2. The time it will reach the ground 8.98s

3. The velocity of the stone when it hits the ground is 287.33 feet/s

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity.

The equation of motion under gravity is given as;

H = ut ± 1/2gt²

v² = u²±2gh

v = u ± gt

1. The height = 18 × 5 -1/2 ( -32) 5²

h = 90+ 400

h = 490 feet

2. The time to reach the ground is calculated as;

h = ut + 1/2gt²

at max height u = 0

total height = 490+800

= 1290m

1290 = 1/2 × 32t²

2580 = 32t²

t² = 80.6

t = √80.6

t = 8.98s

3. The velocity when it reach the ground is

v² = u²+ 2gh

v² = 2× 32 × 1290

v ² = 82560

v = √82560

v = 287.33feet/s

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The equation has a slope of 2/3 and the y-intercept is -1. The graph is aatched with the answer below.

An equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of all the points on a straight line. It takes the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). This equation allows us to easily calculate the y-coordinate of any point on the line, given its x-coordinate.

A linear graph, also known as a straight-line graph, is a graph that represents a linear equation. The x and y coordinates of each point on the line are plotted on a graph, with the x values on the horizontal axis and the y values on the vertical axis.

The resulting graph is a straight line that passes through the y-intercept (the point where the line intersects the y-axis) and has a slope equal to the coefficient of x in the equation.

Linear graphs are useful in many fields, including mathematics, science, engineering, economics, and business, as they allow us to visualize and analyze relationships between two variables that are directly proportional to each other.

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The sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70

Using Vieta's formulas, the sum of the roots of the polynomials is 1, so the sum of the two non-positive roots is -1. Let's call these roots r and s. Then we have:

Let r and s be the non-positive roots of the polynomial P(x) = x³ - x² - 18x + k. Then we have:

r + s = -1

rs + k = 18

The sum of the squares of these roots:

r² + s² = (r + s)² - 2rs = 1 - 2(18 - k) = -35 + 2k

For the non-positive roots to be real, the discriminant of the polynomial must be non-negative, i.e.,

D = 18² - 4(1)(-k) = 72 + 4k ≥ 0

Solving for k, we get:

4k ≥ -72

k ≥ -18

So, the smallest value of k that makes the non-positive roots real is -18, and the sum of their squares is:

r² + s² = -35 + 2(-18) = -71

Finally, the sum of the roots of P(x) = 1 (by Vieta's formulas).

Therefore, the sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70

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Answer:

22

Step-by-step explanation:

4

The measure of v is 61 degree.

We have,

Interior angle = (v - 19) or v

Exterior angle = v + 42

Using exterior Angle Property

Exterior angle= Sum of opposite interior angle

v + 42 = v - 19 + v

v + 42 = 2v - 19

v - 2v = -19 - 42

-v = -61

v= 61

Thus, the value of v is 61.

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The value of the missing lengths are;

a. b =  17. 32, c = 20

b. x = 8. 49, y = 8.49

Note that the different trigonometric identities are;

These identities have their ratios written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have;

tan 30 = 10/b

cross multiply the values

b = 17. 32

Also, we have;

sin 30 = 10/c

cross multiply the values

c = 20

b. Using the sine identity

sin 45 = x/12

cross multiply the values

x = 8. 49

Also,

cos 45 = y/12

cross multiply

y = 8. 49

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The measure of the arc length AB is [tex]\frac{16\pi }{15}[/tex] centimeters.

An arc length is simply the distance between two points along a section of a curve.

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

[tex]s = \frac{16\pi }{15} cm[/tex]

Therefore, the arc length is [tex]\frac{16\pi }{15}[/tex] cm.

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The corresponding height of similar rectangular prism m is 9 centimeter.

Given that, the volume of rectangular prism m is 17 cm³ and the volume of rectangular prism n is 136 cm³.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

The height of n is 18 cm.

Here, m³/n³ = 17/136

m³/18³ = 17/136

m³/18³ = 17/136

(m/18)³ = 1/8

(m/18)³ = (1/2)³

m/18 = 1/2

m=9 cm

Therefore, the corresponding height of similar rectangular prism m is 9 centimeter.

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The circle with a chord are those that have a line joining two points on the circumferences

Recall that a chord a chord of a circle is a line segment that joins any two points on the circumference of the circle

From question number 1,  the chords are circles 1, 2 and 5.  This is because each of the circles has a line joining two points

2)  From question 2 all the chords intercepted each other.  This is because an intercept is a point where two straight lines meet. or you can say that An intercept in mathematics is a point on the y-axis through which the slope of a line passes

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The coordinates of endpoint T are (5,18).

The midpoint formula is expressed as:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.

Let's call the coordinates of point T (x,y).

Since S is the midpoint of RT, we can use the midpoint formula to find the coordinates of S:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

((13+x)/2, (-8+y)/2) = (9,5)

Solving for x:

(13+x)/2 = 9

13 + x = 2 × 9

13 + x = 18

x = 18 - 13

x = 5

Solving for y, we get:

(-8+y)/2) = 5

-8 + y = 5 × 2

-8 + y = 10

y = 10 + 8

y = 18

Therefore, the coordinates  are (5,18).

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By evaluating the function related to the second derivative f''(x) = - 25 · sin 5x is equal to f(π / 5) = (14π - 50) / 25.

In this question we find the definition of the second derivative of a function, this function must be found by integrals and initial values. First, write the entire function:

f''(x) = - 25 · sin 5x

Second, determine the first derivative:

f'(x) = (1 / 5) · cos 5x + C₁

f(0) = (1 / 5) · cos 0 + C₁

3 = 1 / 5 + C₁

C₁ = 14 / 5

f'(x) = (1 / 5) · cos 5x + 14 / 5

Third, determine the function:

f(x) = (1 / 25) · sin 5x + (14 / 5) · x + C₂

f(0) = (1 / 25) · sin 0 + (14 / 5) · 0 + C₂

- 2 = (1 / 25) · sin 0 + (14 / 5) · 0 + C₂

- 2 = C₂

f(x) = (1 / 25) · sin 5x + (14 / 5) · x - 2

Fourth, evaluate the function:

f(π / 5) = (1 / 25) · sin π + (14 / 5) · (π / 5) - 2

f(π / 5) = 14π / 25 - 2

f(π / 5) = (14π - 50) / 25

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Answer:

The 80.6 square foot roll is less expensive per square foot since it costs $0.03/square foot compared to the other which costs $0.02/square foot

Step-by-step explanation:

Because the question asks which of the two paper towel rolls is less expensive per square foot, we must find the unit rate of both rolls (specifically, cost per 1 square foot)

We can find the unit rate using a proportion:

53.7 square foot roll

[tex]\frac{1.49}{53.7}=\frac{x}{1} \\1.49=53.7x\\0.0277=x\\0.03=x[/tex]

80.6 square foot roll

[tex]\frac{1.89}{80.6}=\frac{x}{1} \\1.89=80.6x\\0.0234=x\\0.02=x[/tex]

Thus, per square foot, the 80.6 square foot roll is less expensive than the 53.7 square foot roll

Result:

The probability of getting a sum greater than 25 = 1/9.

The answer is not among the given options.

To find the probability, we would need to consider the possible combinations of the spinner and number cube that result in a sum greater than 25.

First, note that the highest possible sum we can get is 12 (that is 6 from the spinner and 6 from the number cube). Therefore, we can remove all combinations that result in a sum of 24 or less.

Next, we can consider the combinations that result in a sum of 25 like this:

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 4

Finally, we can consider the combinations that result in a sum greater than 25:

Spinner lands on 5, number cube lands on 5

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 6

Here, 4 possible combinations can result in a sum greater than 25 from a total of 6 x 6 = 36 possible outcomes.

So, the probability of getting a sum greater than 25 is 4/36 = 1/9.

Therefore, none of the given answer choices matches this result.

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The volume of 8 rectangular prism stacked base to base is 2560 in³.

Volume is a measure of three-dimensional space.

To calculate the volume of 8 rectangular prism stacked base to base, we use the formula below

Formula:

Where:

From the question,

Given:

We find the value of h using the formula for the surface area of a prism

Given:

Substitute these values into equation 2

Finally, we subtitute into equation 1

Hence the volume is 2560 in³.

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The length of Tim's deck is 1/15th of the length of Al's deck.

Finding the expressions for the length of each deck.

For Al's deck:

Area of a rectangle = length × width

60x + 40 = length × 4

length = (60x + 40) / 4

length = 15x + 10 ft

For Tim's deck:

Area of a rectangle = length × width

21x + 14 = length × 7

length = (21x + 14) / 7

length = 3x + 2 ft

Now we can find no. of times the length of Tim's deck is Al's deck by dividing the length of Al's deck by the length of Tim's deck:

(15x + 10) / (3x + 2)

Simplifying this expression:

(3(5x + 3) + 1) / (3x + 2)

(3(5x + 3) / (3x + 2)) + (1 / (3x + 2))

15 + (1 / (3x + 2))

Therefore, the length of Tim's deck is 1/15th of the length of Al's deck.

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The correct fraction that goes in the blank seven over eight > _____> three over five are,

⇒ 2 / 3

We have to given that;

The expression is,

⇒  seven over eight > _____> three over five

Now, We can write as;

⇒ seven over eight > _____> three over five

⇒ 7 / 8 > ___ > 3 / 5

Now, We can fill with fraction as;

⇒ 7 / 8 > 2 / 3 > 3 / 5

Thus, The correct fraction that goes in the blank seven over eight > _____> three over five are,

⇒ 2 / 3

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The probability of drawing 2 blue marbles in a row is 9/64

From the question, we have the following parameters that can be used in our computation:

Marbles = 1 + 3 + 4 = 8

Blue = 3

Selecting the first marble we have

P(Blue) = 3/8

The marble is returned

So, we have the probablility of the second to be

P(Blue) = 3/8

The probability of drawing two blue marbles is

P = 3/8 * 3/8

Evaluate

P = 9/64

Hence, the probability is 9/64

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Answer:

Since the first blue marble is replaced before the second draw, the probability of drawing a blue marble on the second draw is still 3/8, the same as the probability of drawing a blue marble on the first draw.

To find the probability of both events occurring, we can multiply the probabilities of each event:

P(drawing two blue marbles in a row) = P(drawing a blue marble on first draw) x P(drawing a blue marble on second draw)

P(drawing two blue marbles in a row) = (3/8) x (3/8)

P(drawing two blue marbles in a row) = 9/64

Therefore, the probability of drawing two blue marbles in a row is 9/64.

Step-by-step explanation:

Answer:

Kenneth's average stacking time is less than 8.2 seconds.

Brainly wouldn't allow me to give an explanation because apparently, it contains inappropriate words..? How odd.

Answer:

The data does not provide sufficient evidence to conclude that Kenneth's mean stacking time is is less than 8.2 seconds

Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level.

Step-by-step explanation:

Null hypothesis (H0): mu = 8.2 seconds

Alternate hypothesis (Ha): mu < 8.2 seconds

Significance level = 0.04

p-value = 0.0401

Using the p-value approach for testing hypothesis, do not reject H0 because the p-value 0.0401 is greater than the significance level 0.04.

There is not sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds.

La madre canguro saltó una distancia total de 6 millas para llegar al lago.  .

Answer:

7120.95^3

Step-by-step explanation:

Using the formula (2/3)πr^3 we get (2/3)π10^3 which equals 2094.4 for the volume of the hemisphere.

The volume for the cylinder would be 5026.55 using the formula of V=πr2h for the volume of a cylinder.

The total volume would amount to 7120.95^3

Proposition 3.9 means that if there is a third subgroup that contains the first two subgroups in group G, then when the subgroups are unified, they would still be a subgroup of G.

Put simply, a subgroup collection of Group G is directed if it contains any two subgroups that have a third subgroup containing them both. The subgroup union of this sorted collection is also a subgroup of G.

This definite conclusion occurs because the subgroup criterion states that if any small two subgroups of G are part of a union, then that union is also a subgroup of G. Additionally, a directed subgroup family can be perceived as a series of successive subgroups, with each subgroup being enclosed within the following one.

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