Find the first four terms of the sequence given a1=31 and an+1=an−3

Answer:

Step-by-step explanation:

Let the first number be x

Let the second number be y

For the first equation

2x + 3y = 22

For the second equation

3x + 4y = 31

Multiply the first one by 3 and the second one by 2

That's

First equation

6x + 9y = 66

Second equation

6x + 8y = 62

Subtract the second equation from the first one

That's

6x - 6x + 9y - 8y = 66 - 62

Substitute y = 4 into 2x + 3y = 22

That's

2x + 3(4) = 22

2x = 22 - 12

2x = 10

Divide both sides by 2

Hope this helps you

Answer:

156.7 miles

Step-by-step explanation:

Since [tex]x[/tex] is tangent to the circle, then it is also a right angle with the radius, from here, just do Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to solve for [tex]x[/tex].

Since 1 leg and the hypotenuse is given to you, you want to solve for the other leg, which is [tex]x[/tex] (either [tex]a[/tex] or [tex]b[/tex]). Lets use [tex]b[/tex] for [tex]x[/tex] and set up the equation.

[tex]b^{2}=c^2-a^2[/tex]

[tex]b^2=(3959+3.1)^2-3959^2[/tex]

[tex]b^2 = 3962.1^2 - 3959^2[/tex]

[tex]b^2 = 15,698,236.41 - 15,673,681[/tex]

[tex]b^2 = 24,555.41[/tex]

[tex]\sqrt{b^2}=\sqrt{24,555.41}[/tex]

[tex]b=156.7016592[/tex]

[tex]b=156.7[/tex] (round to nearest tenth)

The distance to the earth’s horizon from point P is 281.6 miles

The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

here, we have,

to determine the distance to the earth’s horizon from point P:

The tangent line from P meets the radius of the earth at a right angle.

This means that the triangle is a right triangle.

The length of x is then calculated as:

(3959 + 10)^2= 3959^2 + x^2

Rewrite as:

x^2 = (3959 + 10)^2- 3959^2

Evaluate

x^2 = 79280

Take the square root of both sides

x = 281.6

Hence, the distance to the earth’s horizon from point P is 281.6 miles

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Answer:

5sqrt(2)

Step-by-step explanation:

you can split 50 into sqrt(25×2)

and the sqrt(25) is 5, so than your left with just the 2 in the sqrt.

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a

Answer:

The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.

Answer:

87.92 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is πr² · h

1. Set up the equation

π2² · 7

2. Solve

(3.14)(4)(7) = 87.92

The volume of a cylindrical water tank with a diameter of 4 feet  and a height of 7 feet is 87.92 cubic feet.

Given that, a cylindrical water tank with a diameter of 4 feet and a height of 7 feet.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

We know that, the volume of a cylinder πr²h

Here, radius =4/2 = 2 feet

The volume of a cylinder = 3.14×2²×7

= 3.14×4×7

= 87.92 cubic feet

Therefore, the volume of a cylindrical water tank with a diameter of 4 feet  and a height of 7 feet is 87.92 cubic feet.

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Answer:  i) θ = 30°, 60°, 210°, & 240°

              ii) θ = 20° &  200°

Step-by-step explanation:

i) sin (2θ) = cos 30°

[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]

To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above.   θ = 30°, 60°, 210°, 240°

If you need ALL of the solutions (more than one rotation), add 180n to the solutions.   θ = 30° + 180n   &   60° + 180n

*********************************************************************************************

ii) cos α = sin (50 + α)

Use the Identity: cos α = sin (90 - α)

Use Transitive Property to get:   sin (50° + α) = sin (90° - α)

50° + α = 90° - α

50° + 2α = 90°

        2α = 40°

          α = 20°

To find all solutions for one rotation, add 360/2 = 180 to the solution above.

α = 20°, 200°

If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n

Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

Complete question:

The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.

Answer:

17,209

Step-by-step explanation:

The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.

Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.

The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :

From the graph:

Year - - - - - - - - - - Number of fatalities

2001 - - - - - - - - - - 17401

2002 - - - - - - - - -  17525

2003 - - - - - - - - -  17013

2004 - - - - - - - - - 16694

2005 - - - - - - - - - 16885

2006 - - - - - - - - - 17738

To get the average :

Sum of fatalities / number of years

(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6

= 103256 / 6

= 17209.333

Average number of alcohol related fatalities is 17,209 (to the nearest whole number)

Answer:

b = 4/3

Step-by-step explanation:

In an exponential equation:

f(x) = a (b)ˣ

Evaluated at x+1:

f(x+1) = a (b)ˣ⁺¹

The ratio between them is:

f(x+1) / f(x)

= (a (b)ˣ⁺¹) / (a (b)ˣ)

= b

So the decay factor b can be found by dividing the consecutive y values.

b = 16 / 12

b = 4/3

Answer:8

Step-by-step explanation:

The smallest prime is 2

cube of 2 is equal to 8

2*2*2=8

Answer:

729

Step-by-step explanation:

The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.

Hope this helped! :)

Answer:

3.924×10∧-9

Step-by-step explanation:

Royal flush contains five cards and it's probability is 0.3924%≈0.003924

Straight contain five cards and it's probability is 0.0001%≈0.000001

The probability including straight and royal flushes will be 0.003924×0.000001≈3.924×10∧-9

We have

[tex]\dfrac{1-i}{1+i}=\dfrac{e^{-i\frac\pi4}}{e^{i\frac\pi4}}=e^{-i\frac\pi2}[/tex]

which reduces to -i.

Answer:

y = 60 *x

Step-by-step explanation:

The rate is 180 miles / 3 hours = 60 miles per hour

Check by dividing 300 miles / 5 hours = 60 miles per hour

y = 60 *x  where y is miles and x = time

Answer:

Step-by-step explanation:

Answer:

theater

pls mark me as BRAINLIEST

Answer:

23 dimes, 32 nickels

Step-by-step explanation:

Let n equal the number of nickels and d be the number of dimes. We can use the information given to create a system of equations, as follows:

The total number of coins (the number of nickels plus the number of dimes) is 55, giving us the equation n + d = 55.

The total amount is $3.90. Since each nickel is worth $0.05 and each dime is worth $0.10, we get the equation 0.05n + 0.10d = 3.90.

Multiplying the second equation by 20, we get n + 2d = 78. We can subtract the first equation to get d = 23. Substituting this into the first equation, we get that n = 32.

Therefore, there are 23 dimes and 32 nickels.

Answer: 100 penny 2 qtrs 50 noclke

Step-by-step explanation:

Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:

Step-by-step explanation:

29 is 6 more than K

Let's create an equation

[tex]29 = 6 + k[/tex]

Move variable to L.H.S and change its sign

Similarly, move constant to R.H.S and change its sign

[tex] - k = 6 - 29[/tex]

Calculate

[tex] - k = - 23[/tex]

Change the sign on both sides of the equation

[tex]k = 23[/tex]

Hope this helps..

Best regards!!

The equation for the statement 29 is 6 more than K is solved and K = 23

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists  mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by the statement below

29 is 6 more than K

On simplifying , we get

29 = 6 + K

Subtracting 6 on both sides , we get

K = 29 - 6

K = 23

Therefore , the value of K is 23

Hence , the equation is K = 23

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Answer: 32

Step-by-step explanation:

Answer:

The maximum one-day percentage loss = -1.15%

Step-by-step explanation:

Let assume that with the  normal distribution, 95% of observations are smaller than 1.65 standard deviations above the mean.

Given that:

Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days.

if the expected percentage change of the euro tomorrow is 0.5 percent

and that Z value at 95% C.I level = 1.65

∵ The maximum one-day percentage loss = (expected percentage change -   Z-Value) × standard deviation

The maximum one-day percentage loss =  (0.5 - 1.65) ×  1

The maximum one-day percentage loss = -1.15  ×  1

The maximum one-day percentage loss = -1.15%

Answer:

P(9) = 1/9

Step-by-step explanation:

From the contingency table, we see that 9 appears 4 times out of the 36 possible outcomes, therefore the probability of having a sum of 9 is

P(9) = 4/36 = 1/9

The probability that the sum is 9 is 1/18.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The sample space of rolling two dice has 36 possible outcomes.  

Remember that the sample space is a set that contains all possible outcomes.  

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Let E = the event of getting a sum of that number is 9

favorable outcomes = (5,4) (4,5)

So, n(E) = 2

Sample space n(S) = 36

p(E) = n(E)/n(S)

p(E) = 2/36

p(E) = 1/18

Hence, the probability that the sum is 9 is 1/18.

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Answer:

Step-by-step explanation:

In double angle, sin2x = sin(x+x) = sinxcosx+cosxsinx

sin2x = 2sinxcosx ... 1

Applying this formula to prove that sin(4x) = 4 sinx cosx(1 − 2sin2x is shown below;

sin(4x) = sin(2x+2x)

= sin2xcos2x+cox2xsin2x

sin4x = 2sin2xcos2x ..2

also cos2x = cos(x+x) = cosxcox-sinxsinx

cos 2x = cos²x - sin²x ...3

Substituting equation 1 and 3 into 2, we will have;

sin4x = 2(2sinxcosx(cos²x - sin²x ))

sin4x = 4sinxcosx(cos²x - sin²x )

From sin²x+cos²x =1; cos²x = 1-sin²x

Substituting the expression into the resulting equation will give;

sin4x = 4sinxcosx(1-sin²x - sin²x )

sin4x = 4sinxcosx(1-2sin²x) Verified!  

Answer:  12 Tbsp

Step-by-step explanation:

Note: 1 Tbsp = 3 tsp

2 tsp x 21 = 42 tsp

42 tsp ÷ 3 = 12 Tbsp

Answer:

x = - 3h

Step-by-step explanation:

Given

[tex]\frac{x}{h}[/tex] + 1 = - 2 ( subtract 1 from both sides )

[tex]\frac{x}{h}[/tex] = - 3 ( multiply both sides by h )

x = - 3h

Step-by-step explanation:

[tex] \frac{x}{h + 1} = - 2[/tex]

Cross multiply

We have

-2(h + 1) = x

Expand the terms in the bracket

We have the final answer as

x = -2h - 2

Hope this helps you

Answer:

y={-5,-4,-5/2,-13/3}

Step-by-step explanation:

a.f(-2)=y=1/2(x)-4

substitute -2for x

y=1/2(-2)-4

y=-1-4

y=-5

b.f(0)

y=1/2(0)-4

y=0-4

y=-4

c.f(3/2)

y=1/2(3/2)-4

3/2-4

find the L.C.M=2

3/2-4/1

3-8/2

-5/2

d.f(-2/3)

y=1/2(-2/3)-4

-2/6-4

2 into itself 1 ,2 into 6 ,3

-1/3-4

find the least common multiple equal to 3

-1/3-4/1

-1-12/3

y=-13/3

Answer:

30 cm

Step-by-step explanation:

1 inch is 2.54 centimeters, and 2.54 times 12 is 30.48, which would be the closest.

The following metric units of measure is 30 cm

The correct option is (A)

Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect.

Step 1: Write the conversion as a fraction.

Step 2: Multiply or divide, as required.

Step 3: Cancel the units (same units from top and bottom)

Step 4: Write the simplified answer with its correct unit.

Now, as we know that

1 inch = 2.54 cm

So, we can write

12 inch = 2.54 * 12

12 inch= 30.48 cm

Hence, the closest unit is  30 cm in the given metric system.

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Answer:

This is skewed torwards the right. Or in other words positively skewed distribution.

Step-by-step explanation:

All of the values are fairly close together torwards the lower range. While 50.20 is more of an outlier, so this graph would gradualy skew to the right.

Answer:

1

Step-by-step explanation:

We can find the slope using

m= ( y2-y1)/(x2-x1)

   = ( -8 - -4)/( 4 - 8)

   =  ( -8 +4)/( 4 - 8)

   = -4 / -4

   = 1

Answer:

slope equals 1

Step-by-step explanation:

To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1

Answer: (a) No, the data suggests it is possible to reject the hypothesis which states that the 2 methods provide same mean value.

(b) (-10.957,-0.063)

Step-by-step explanation:

(a) Hypotheses for this data are:

[tex]H_{0}[/tex]: [tex]\mu_{1} = \mu_{2}[/tex]

[tex]H_{a}: \mu_{1} \neq \mu_{2}[/tex]

First find the differences in values:

1 => -0.31

2 => -0.63

3 => -2.85

4 => -3.46

5 => -6.43

6 => -7.52

7 => -17.39

Now, find the mean and standard deviation of the differences:

mean = [tex]\frac{-0.31+(-0.63)+...+(-17.39)}{7}[/tex] = - 5.51

sd = [tex]\sqrt{\frac{(-0.31-(-5.51))^{2}+...+(-17.39-(-5.51))^{2}}{7-1} }[/tex] = 5.89

The value of test statistics is:

t = [tex]\frac{mean}{\frac{s}{\sqrt{n} } }[/tex] = [tex]\frac{-5.51}{\frac{5.89}{\sqrt{7} } }[/tex] = - 2.4750

Analysing Student's T distribution, at a df = 7-1 = 6:

p-value = 0.025*2 = 0.05

To reject the null hypothesis, p-value must be less or equal than α. Since they are equal, reject the null hypothesis, i.e., reject the claim suggesting the 2 methods provide the same mean value for natural vibration frequency.

(b) For a CI = 95%:

t-score for α = 0.025 and df = 6 is 2.447.

mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]

-5.51 ± 2.447.[tex]\frac{5.89}{\sqrt{7} }[/tex]

-5.51 ± 5.4471

lower limit: -5.51 - 5.4471 = - 10.957

upper limit: -5.51 + 5.4471 = - 0.063

The interval on the mean difference is (-10.957,-0.063)

Answer:

C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Step-by-step explanation:

A confidence interval let us make an inference about a population parameter from a sample statistic. In this case, a sample proportion let us infere aout the population proportion with a certain degree of confidence.

With this confidence interval, we are 99% confident that the polpulation proportion falls within this interval. This means that there is 99% chances of having the population proportion within this interval.

To estimate the population proportion of adults who do not believe in UFO's we should have to construct another confidence interval with the proportion (1-p), but this parameter can not be estimated from the confidence interval for p.