what are the next three terms of the sequence 1,11,22,34​

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

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Answer:

Your just going to keep adding 3 and the 2 is there because you had negative -1 and then you added 3 so hope this helps probably not what you looking for but hope this helps. Have a good day.

Step-by-step explanation:

The constant ratio of successive y-values. is 1.5

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

The table of values of an exponential function

From the table, we have

x    y

0   11.25

1     16.875

Divide the y values

so, we have the following representation

Ratio = 16.875/11.25

Evaluate

Ratio = 1.5

Hence, the constant ratio of successive y-values. is 1.5

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Answer:

Step-by-step explanation:

To find the constant ratio of successive y-values of an exponential function, you need to divide one term by the previous term. That ratio should match for all y values1.

In this case, we can find the constant ratio by dividing each y-value by the previous one. For example, 7.5/5 = 1.5 and 11.25/7.5 = 1.5 and so on. Therefore, the constant ratio of successive y-values is 1.5

In hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between two groups, or that a certain parameter is equal to a specified value. In this case, the null hypothesis is that the mean difference is 0, meaning there is no significant difference between the two groups being compared.

The alternative hypothesis (Ha), on the other hand, is a statement that contradicts the null hypothesis. It can be one-tailed (directional), indicating that the mean difference is greater than or less than 0, or two-tailed (non-directional), indicating that the mean difference is not equal to 0. So, to determine the null and alternative hypotheses in this case, we know that the null hypothesis is that the mean difference is 0. The alternative hypothesis can be either one of the following:
- Ha: The mean difference is not equal to 0 (two-tailed)
- Ha: The mean difference is greater than 0 (one-tailed)
- Ha: The mean difference is less than 0 (one-tailed)

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The present value of the ordinary annuity is approximately $150.

To find the present value of the ordinary annuity, we need to calculate the amount of money that needs to be invested today to receive a series of future cash flows.

In this case, we have an annuity of $170 per month for 10 years, with a yearly interest rate of 5% compounded monthly.

1: Convert the annual interest rate to a monthly interest rate.

Since the interest is compounded monthly, we divide the annual interest rate by 12.

Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.004167

2: Calculate the total number of periods.

Since the annuity is for 10 years and there are 12 months in a year, the total number of periods is:

Total number of periods = 10 years * 12 months/year = 120 months

3: Use the present value of an ordinary annuity formula to calculate the present value:

Present value = \(Payment * (1 - (1 + r)^(-n)) / r\)

Where:
Payment = $170 (monthly payment)
r = Monthly interest rate = 0.004167
n = Total number of periods = 120

Plugging in the values into the formula:

Present value = \($170 * (1 - (1 + 0.004167)^(-120)) / 0.004167\)

Now we can calculate the present value using a calculator or a spreadsheet software.

The present value of the ordinary annuity is approximately $150.

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Answer:B.Sample space

Step-by-step explanation:

Answer:

The answer is 16

Step-by-step explanation:

Multiply  -3 by 2

(10-6)^2      ^2=power

subtract 6 from 10

4^2

Raise 4 to the power of 2

 16

.

Answer:

16

Step-by-step explanation:

= (10 - 3 x 2) ^ 2

= (10 - 6) ^ 2

= 4 ^ 2

= 16

HOPE THIS HELPS

PLZ MARK BRAINLIEST

Answer:

16.25

Step-by-step explanation:

Answer:x>-15

Step-by-step explanation:

5-2x<35

You would need to subtract both sides by 5

5-5 cancel each other out

35-5=30

Then divide 30 by -2 and you get -15

The shape of the distributive is such that; it is skewed to the right. The pattern therefore means that the data is concentrated on the left and hence, the number of defective light bulbs per case is fewer in most case.

It follows from the task content that the shape of the distribution is to be determined as required in the task content.

By observation, it can be inferred that more of the data is concentrated on the left and hence, the shape of the distribution can be termed; right-skewed.

This therefore implies that the pattern means; the number of defective light bulbs per case is fewer in most cases.

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Answer:

m= \(-\frac{1}{3}\)

Explanation:

Formula is Y=mx+b

m equals the slope (rise/run each point).

x stays for an ongoing function.

b is the y intersect(You'll see that the line crossed +4 on the vertical line).

Looking at the line from left to right, it starts from the top to the bottom instead of button to top. If this slope goes down, it is negative.

\(y=-\frac{1}{3}x+4\)

That is why \(m=-\frac{1}{3}\) instead of \(m=\frac{1}{3}\)

Answer:

B

Step-by-step explanation:

If you divide 7/8 you will get 0.875 which is equivalent to 21/24 which is 0.875.

Answer:

square roots are absolute values

Step-by-step explanation:

they cannot be any integer or negative number. they had to be an absolute value

The distance between the two towns is 165 kilometers

The initial speed = 100 kilometer per hour

Time taken = t hours

We know,

Speed = Distance / Time

Distance = Speed × t

Distance = 100 × t

New speed = 110 kilometer per hours

He saves 9 minutes

9 minutes = 9/60 hours

The time taken = t - 9/60

The distance = 110 × (t - 9/60)

= 110t - 33/2

Then the equation will be

100t = 110t - 33/2

110t - 100t = 33/2

10t = 33/2

t = 33/2 ÷ 10

t = 33/2 × 1/10

t = 1.65 hours

Then the distance = 100 × t

= 100 × 1.65

= 165 kilometers

Hence, the distance between the two towns is 165 kilometers

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Since c must be between 1 and 3, we can eliminate the negative solution and calculate that c = 2.089. Therefore, the answer is 0. The correct option is (A).The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the slope of the tangent line.

Applying this theorem to the function f(x) = 2x³ - 4x² + 1 on the interval [1,3], we know that there exists a value c in (1,3) such that the slope of the tangent line at c is equal to the slope of the secant line between f(1) and f(3).
To find the value of c, we can start by calculating the slope of the secant line:
slope = (f(3) - f(1)) / (3 - 1)
= (2(3)³ - 4(3)² + 1 - 2(1)³ + 4(1)²⁻¹) / 2
= 26
Next, we need to find the derivative of f(x):

f'(x) = 6x² - 8x
Now we can set the slope of the tangent line equal to the slope of the secant line and solve for c:
6c² - 8c = 26
3c² - 4c - 13 = 0
Using the quadratic formula, we get:
c = (4 ± sqrt(4² - 4(3)(-13))) / (2(3))
c = (4 ± sqrt(160)) / 6
c = 2.089 or c = -1.422
Therefore, the answer is 0.

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The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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Answer:

:) good day mate

Step-by-step explanation:

:) indeed

The correct option is C: Cluster around a horizontal line when graphed are distributed equally along both axes.

A level within a phase is defined as a set of observations that cluster around a horizontal line when graphed. This means that the data points tend to remain relatively constant or steady during that particular phase.

When plotted on a graph, these observations form a horizontal line, indicating little variation or change. This stability implies that the system or process being observed is in a balanced state, with minimal fluctuations or disturbances.

The horizontal line represents a steady state, indicating that the system or process being observed is maintaining a consistent level without significant fluctuations or trends.

A stable level is characterized by a consistent and predictable pattern, which can be useful in analyzing and understanding the behavior of the system or process over time.

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Answer:

  a.  0

Step-by-step explanation:

You want the limit of (k(x) -h(x))/k(x) as x approaches 0 when k(x) = sin(x)/x {x≠0} and h(x)=x+1 {x<1}.

Since we're concerned about the limit as x → 0, we don't have to be concerned with the fact that the expression is undefined at x = 0.

The function h(x) is defined as h(0) = 1, so we can just be concerned with the value of ...

  lim[x→0] (k(x) -1)/k(x)

The limit of k(x) as x → 0 is 1, so this becomes ...

  lim[x→0] (k(x) -1)/k(x) = (1 -1)/1 = 0

At x=0, sin(x)/x is the indeterminate form 0/0, so its limit there can be found using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim[x→0] sin(x)/x = lim[x→0] cos(x)/1 = cos(0) = 1

The fact that k(0) = 0 is irrelevant with respect to this limit.

__

Additional comment

We like to use a graphing calculator to validate limit values. The attachment shows the various functions involved. It also shows that as x gets arbitrarily close to 0 from either direction, the value of g(x) does likewise. This is all that is required for (0, 0) to be declared the limit. The lack of definition of g(x) at x=0 simply means the relation has a (removable) discontinuity there.

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Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

Answer:

Marcus is picking songs to play during a slideshow. The songs are each 3\dfrac123  

2

1

​  

3, start fraction, 1, divided by, 2, end fraction minutes long. The slideshow is 31\dfrac1231  

2

1

​  

31, start fraction, 1, divided by, 2, end fraction minutes long.

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

Answer:

.81818181818

Step-by-step explanation:

9/(2+9)

9/11

.81818181818

Answer:

To find the distance, we can set up an equation based on the given information. Let's assume the distance to town is represented by "d."

Since Mr. Johnson drove at 18 mph, we can express the time it took for him to reach town as "d/18."

Mr. Smith, on the other hand, biked at 12 mph, and it took him 3 hours longer than Mr. Johnson to reach town. Therefore, we can express the time it took for Mr. Smith as "d/12 + 3."

Setting up an equation, we have:

d/18 = d/12 + 3

To solve for "d," we can multiply both sides of the equation by the least common multiple (LCM) of 18 and 12, which is 36. This gives us:

2d = 3d + 108

Simplifying further, we find:

d = 108

Hence, the distance of the route to town is 108 units.

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The smallest value of n that works is 11.

We can expand the given equation using the binomial theorem:

(x^2 + 1.2)^n = ∑(k=0 to n) [n choose k] x^(2(n-k)) (1.2)^k

The coefficient of x^6 in the expansion will be given by the term where k = n - 3, i.e.,

[n choose n-3] x^(2(3)) (1.2)^(n-3) = (n(n-1)(n-2)/(3!)) x^6 (1.2)^(n-3)

We want this coefficient to be larger than 200000, so we have:

(n(n-1)(n-2)/(3!)) (1.2)^(n-3) > 200000/16

Simplifying and taking the logarithm of both sides:

(n-1)log(1.2) + log(n(n-1)(n-2)) - log(3!) > log(12500)

Using the fact that log(n) < n for all n > 0, we can approximate log(n(n-1)(n-2)) by n log(n) and simplify further:

(n-1)log(1.2) + 3log(n) - log(3) > log(12500)

Now, we can use trial and error to find the smallest value of n that satisfies this inequality. We can start with n = 10 and increase it until we get a value that works:

For n = 10: (9)log(1.2) + 3log(10) - log(3) ≈ 2.413, which is not greater than log(12500) ≈ 4.819.

For n = 11: (10)log(1.2) + 3log(11) - log(3) ≈ 4.299, which is greater than log(12500).

Therefore, the smallest value of n that works is 11.

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Answer:

a=1

b=-5

c=6

Step-by-step explanation:

ax^2+bx+c=0

Is the formula used for this question.

The given function is the same as y = 1x^2 + (-5x) + 6

Compare it to the form y = ax^2+bx+c, and we have the following:

a = 1

b = -5

c = 6

Answer:

The answer is A.8x+13

Step-by-step explanation:

Answer:

2.1 * 10 ^3

Step-by-step explanation:

5.67  * 10 ^7 ÷2.7 x 10^4

Divide the numbers

5.67 / 2.7 =2.1

Divide the exponents

10^7 / 10 ^4

Remember when dividing power, we subtract the exponents

10 ^(7-4) = 10^3

Put this back together

2.1 * 10 ^3

Verify that this is in scientific notation

Since this is in scientific notation, we are done

Answer:

2.1x10 to the power of three

Step-by-step explanation:

\frac{5.67\times 10^7}{2.7\times 10^4}

2.7×10

4

5.67×10

7

​

Divide them.

\frac{5.67}{2.7}\times \frac{10^7}{10^4}

2.7

5.67

​

×

10

4

10

7

​

Divide numbers and 10's separeately.

2.1\times 10^3

2.1×10

3

Subtract exponents.

Answer:

A. is the correct answer.

Step-by-step explanation:

The length of the rectangle is 6 meters longer than the width of the rectangle. Let's suppose the width is x meters. So, the length of the rectangle is (x + 6) meters.Area of rectangle is 28 square meters.Area of rectangle = length × width28 = (x + 6) × x.Solve for xx² + 6x - 28 = 0(x + 7)(x - 4) = 0x = -7 or 4

The negative value of x because it is not possible.So, the width of the rectangle is 4 meters.The length of the rectangle is (x + 6) meters= 4 + 6= 10 meters.The length of a rectangle is 6 meters longer than the width. If the area is 28 square meters, we need to find the dimensions of the rectangle. Let's suppose the width of the rectangle is x meters. We know that the length of the rectangle is 6 meters more than the width, so the length of the rectangle is (x + 6) meters.Area of a rectangle is the product of its length and width. So, the area of the rectangle is (x + 6) × x. We know that the area of the rectangle is 28 square meters. Therefore, we can write the following equation:28 = (x + 6) × x.To find the value of x, we need to solve this quadratic equation.28 = x² + 6x.Rearranging the terms, we get:

x² + 6x - 28 = 0

We can solve this equation by using the quadratic formula, but we will use the factoring method. We need to find two numbers whose product is -28 and whose sum is 6. These numbers are +7 and -4. Therefore, we can write:

x² + 7x - 4x - 28 = 0x(x + 7) - 4(x + 7) = 0(x + 7)(x - 4) = 0

Therefore, x + 7 = 0 or x - 4 = 0.If x + 7 = 0, then x = -7, which is not a valid solution because the width of the rectangle cannot be negative.If x - 4 = 0, then x = 4. Therefore, the width of the rectangle is 4 meters. The length of the rectangle is x + 6 = 4 + 6 = 10 meters. So, the dimensions of the rectangle are 4 meters by 10 meters.

Therefore, the width of the rectangle is 4 meters, and the length of the rectangle is 10 meters. The dimensions of the rectangle are 4 meters by 10 meters.

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