Continue the pattern by filling in the next 3 terms
-5, -2, 1,

Answer:

b) y = -x2 + 6x + 2

Step-by-step explanation:

to get the slope of any straight line, we simply need two points off of it, let's use the ones in the picture below.

\((\stackrel{x_1}{5}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{24}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{24}-\stackrel{y1}{12}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{ 12 }{ 2 } \implies \text{\LARGE 6}\)

When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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Answer:

Hmm I think D but don't take my word for it just a guess

Step-by-step explanation:

The surface area obtained by rotating the curve y = x² from x = 0 to x = 8 about the y-axis is 2048π square units.

We are given that the curve y = x² is rotated from x = 0 to x = 8. So our range of integration is from x = 0 to x = 8.

To use the disk method, we need to express the curve in terms of y instead of x. For the equation y = x², we can rewrite it as x = √y.

The radius of each disk is the distance between the y-axis and the curve. Since we are rotating the curve around the y-axis, the radius will be the value of x for a given y. Therefore, the radius is x = √y.

The area of each disk can be found using the formula for the area of a circle, which is A = πr². In this case, the area is A = π(x²) = π(√y)² = πy.

To find the total surface area, we need to sum up the areas of all the disks. We integrate the area function πy with respect to y from y = 0 to y = 64 (since x = 8 corresponds to y = 64).

Surface Area = ∫(πy)dy from 0 to 64

= π∫y dy from 0 to 64

= π[y²/2] from 0 to 64

= π[(64²/2) - (0²/2)]

= π[2048]

= 2048π square units.

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The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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Different letter arrangements that can be obtained from the letters of the word statistically, using all the letters= 6,48,64,800

Given,

Total number of arrangements obtained = 6,48,64,800

Given words = STATISTICALLY

Total word count = 13

Here we have repeated alphabets as -

"S"s = 2

"T"s = 3

"A"s = 2

"I"s = 2

"L" = 2

Total permutations we have here = 13! / 2!2!2!2!3!

= 6,22,70,20,800 / 96

= 6,48,64,800

A permutation of a set in mathematics is, broadly speaking, the rearranging of its components if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

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ANSWER

EXPLANATION

We want to find the solution to the system of equations given, using the graph.

On a graph, the solution of a system of equations is the point where the lines of the two equations intersect one another. This means that the ordered pair made up of the x and y coordinates of the point where the two lines meet is the solution to the system of equations.

Therefore, going by that, the solution to the given system of equations is:

Answer:

4

Step-by-step explanation:

Answer:

............462........

Answer:

470

Step-by-step explanation:

Given

z(\(y^{4}\) - x² ) ← substitute given values

= 2(\(4^{4}\) - 5² ) ← evaluate contents of parenthesis

= 2(256 - 25)

= 2(235)

= 2 × 235

= 470

Answer:

Step-by-step explanation:

The slope is the cost of a renewal: $10.

The y-intercept is the initial cost: $65.

We will use the formula of simple interest

Where I is the interest, P is the principal, r is the rate and t is the time.

In our case

P=1200

r=10.5%

t=18 meses = 1.5 years

We substitute the data

ANSWER

She will pay back in interest $189

The y-values to the nearest integer from the given x-values in the table is y = 12.015 , 7.984.

Given:

Hyperbola equation:

( x - 2 )^2 / 4^2 - ( y - 10 )^2 / 2^2 = 1

when x = 11

substitute

( 11 - 2 )^2/16 - ( y - 10 )^2/4 = 1

9^2/16 - ( y - 10 )^2/4 = 1

81/16 - 1 = y^2 + 10^2 - 2 * y * 10

81 - 16 / 16 = y^2 + 100 - 20y

65/16 = y^2 + 100 - 20y

16y^2 + 1600 - 320y = 65

16y^2 -320y + 1535 = 0

y = 12.015 , 7.984

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Full question:

IS in the image uploaded.

Answer:

Ray DB

Step-by-step explanation:

The graph shows Ray BD.  You name a ray starting at it end point.

The area of the sidewalk is 84.78 square meters if a circular flower bed is 23 m in diameter and has a 3 m wide circular sidewalk.

A circular flower bed is 23 m in diameter and has a circular sidewalk around it that is 3 m wide. The area of the sidewalk is square meters. The formula used: The area of the circle is given by:

πr²

Here, r = (d + 2w)/2, where d is the diameter and w is the width.

Substitute the values of d, w, and π in the above formula to get the area of the circular sidewalk.

Diameter of circular flower bed = 23 m

Width of circular sidewalk = 3 m

Radius of circular flower bed, r = (23+3)/2 = 13 m

Radius of circular sidewalk = (23+3+3)/2 = 14 m

Area of the circular sidewalk = π(14² - 13²) m²= π(14+13)(14-13) m²= 3.14(27) m²= 84.78 m²

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The probability that exactly 10 out of 22 cars receiving routine maintenance will not have engine failure is approximately 0.221

We can model this situation using a binomial distribution, where,

The probability of success (an engine not failing) is p = 1 - 0.234 = 0.766 (assuming routine maintenance reduces engine failure).

The number of trials is n = 22 (the number of cars receiving routine maintenance).

We want to find the probability of getting exactly k = 10 successes (cars without engine failure).

The formula for the probability mass function of a binomial distribution is:

P(k successes) = (n choose k) × p^k × (1 - p)^(n - k)

where (n choose k) = n! / (k! × (n - k)!) is the number of ways to choose k items from a set of n items.

Plugging in the values, we get

P(10 successes) = (22 choose 10) × 0.766^10 × 0.234^12

≈ 0.221

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

its 16

Step-by-step explanation:

on the graph just count how many shipments they had like 1-10 it was at 4 at 11-20 it was at 5 at 21-30 was at 4 at 31-40 was at 1 and 41-50 was at 2 so just add all of though's together 4+5+4+1+2= which gives 16

Answer:

16

Step-by-step explanation:

A number is dividable by 9 if the number is a multiple of 9

for example, 81 is a multiple of 9 and also it is dividable by 9

You can check any number if you divide this number between 9

For example

1234/9 =137.11

because you have decimal number is an indication that this number is not divisible by 9

5832/9=648

because we have an integer we can say 5832 is dividable by 9

To find the absolute maximum value of h(x) = -2x^2 + x over the interval [-3, 3], we need to identify critical points and evaluate the function at those points as well as the interval's endpoints.

First, find the critical points by taking the derivative of h(x) and setting it to 0:

h'(x) = -4x + 1

-4x + 1 = 0
4x = 1
x = 1/4

Now, evaluate h(x) at the critical point and the endpoints of the interval:

h(-3) = -2(-3)^2 + (-3) = -18
h(1/4) = -2(1/4)^2 + (1/4) = -1/8 + 1/4 = 1/8
h(3) = -2(3)^2 + 3 = -15

Comparing the values, we can see that the absolute maximum value is h(1/4) = 1/8.

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Answer:

it is parallel

Step-by-step explanation:

No, the statement the surface area of Cube B is also twice that of Cube A, is False.

Cube A is of 2 by 2 by 2

So the length of each side of Cube A is 2 units

So the surface area of Cube A = 6*2*2 = 24 square units

Cube B is of 4 by 4 by 4

So each side length of Cube B is 4 units

So the surface area of Cube B = 6*4*4 = 96 square units

So Surface area of Cube B is = 96/24 = 4 times of surface area of Cube A.

So the given statement is not true.

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The NBA Hall of Famer you are referring to is Michael Jordan. Michael Jordan is a retired professional basketball player widely considered to be one of the greatest basketball players of all time.

During his career, Jordan won six NBA championships, five NBA Most Valuable Player awards, 10 scoring titles, and was named an NBA All-Star 14 times. He is also known for his numerous signature sneakers and his successful career off the court, including his ownership of the Charlotte Hornets NBA team.

The NBA stands for the National Basketball Association, which is a professional basketball league in North America. It is composed of 30 teams, 29 in the United States and one in Canada, and is considered to be the premier men's basketball league in the world.

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Step-by-step explanation:

Principal = 250,000

Rate = 4%

Simple interest = 850,000

Time = ?

\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)

Step-by-step explanation:

the second one with x = -5.

because that relationship associates 3 different y values to one x value.

but for a function there can be only ONE associated y value for every valid x value.

Answer: Let the legs of the right triangle be a and b. We know that the radius of the inscribed circle is 4 cm, which means that the inradius is also 4 cm. The inradius is given by:

r = (a + b - c)/2

where c is the hypotenuse, so we can substitute the given values to get:

4 = (a + b - 35)/2

Multiplying both sides by 2, we get:

8 = a + b - 35

Adding 35 to both sides, we get:

a + b = 43

We also know that the area of the triangle is given by:

A = (ab)/2

where a and b are the legs of the triangle. We can use the Pythagorean theorem to relate the legs to the hypotenuse:

a^2 + b^2 = c^2

Substituting the given value for the hypotenuse, we get:

a^2 + b^2 = 35^2

Simplifying, we get:

a^2 + b^2 = 1225

Now we can use the equation for the sum of the legs to solve for one of the legs in terms of the other:

a + b = 43

b = 43 - a

Substituting this expression for b into the equation for the area, we get:

A = (a(43 - a))/2

Simplifying, we get:

A = (43a - a^2)/2

To find the maximum value of the area, we can take the derivative of A with respect to a and set it equal to 0:

dA/da = 43/2 - a = 0

Solving for a, we get:

a = 43/2

Substituting this value into the equation for the area, we get:

A = (43/2)(43/2 - 43/2)/2 = 0

This means that the area of the triangle is 0 when one of the legs has a length of 0, which is not possible. Therefore, the maximum area occurs when the legs have equal lengths, which means that the right triangle is an isosceles right triangle. In this case, we have:

a = b = (35/sqrt(2)) cm

Substituting these values into the equation for the area, we get:

A = (ab)/2 = ((35/sqrt(2))^2)/2 = 612.5 cm^2

Therefore, the area of the right triangle is 612.5 square centimeters.

Step-by-step explanation:

Answer:

Mary's class.

Step-by-step explanation:

One way to do this is to figure out how many students are in Alex's class and how many students are in Mary's class.

60% of Alex's class is 12 students

\(\frac{12*100}{60}\)  = \(\frac{1200}{60}\)= 20 students

\(\frac{2}{3}\) or 66.66% (repeating) of Mary's class is 14 students

\(\frac{14*100}{66.66}\) = \(\frac{1400}{66.66}\) = 21 students

(^^66.66 repeating)

Mary's class has more students than Alex's class.