Here are the first 5 terms of a sequence 3,8,17,30,47 find an expression, in terms of n for the nth term of this sequence

Answer:

Step-by-step explanation:

To calculate the amount of ice needed for this sculpture, we would apply the formula for determining the volume of a rectangular base pyramid which is expressed as

Volume = 1/3 × base area × height

Since the base is rectangular, base area = length × width = 3 × 5 = 15 m

Given that height = 3.6m, therefore, the amount of ice needed for this sculpture is

1/3 × 15 × 3.6 = 18 m³

Answer: To calculate the amount of ice needed for this sculpture, we would apply the formula for determining the volume of a rectangular base pyramid which is expressed as Volume = 1/3 × base area × heightSince the base is rectangular, base area = length × width = 3 × 5 = 15 mGiven that height = 3.6m, therefore, the amount of ice needed for this sculpture is 1/3 × 15 × 3.6 = 18 m³

Step-by-step explanation:

Answer:

15.56%

Step-by-step explanation:

The force applied, F,  to the surface is 90N.

The area, A, of the surface is [tex]20 cm^2[/tex] = [tex]0.002m^2[/tex]

The pressure on the surface is:

P = F / A = 90 / 0.002 = 45000 Nm^2

The force is increased by 5N, the new force is 95N.

The surface area is increased by 5 cm^2 = 0.0005 m^2. The new surface area is 0.0025 m^2.

The pressure is now:

P = 95 / 0.0025 = 38000 Nm^2

The percentage decreased is gotten by dividing the difference in the two values by the old value and then multiplying by 100.

=> Difference = 45000 - 38000 = 7000

% decrease is therefore:

= 7000 / 45000 * 100 = 15.56%

There was a 15.56% decrease.

The ratio of the applied force to the area to which the force is applied,

gives the amount of pressure applied.

The outcome decreases by [tex]\underline{15.\overline 5 \%}[/tex]

Reasons:

[tex]\mathrm{Pressure, P} = \dfrac{Force, \, F}{Area, \, A}[/tex]

The initial force, F₁ = 5 N

The initial area, A₁ = 20 cm²

[tex]\mathrm{ } P_1=\dfrac{F_1}{A_1 }[/tex]

[tex]\mathrm{The \ initial \ pressure \ on \ the \ surface \ is \ } P_1=\dfrac{90 \ N}{0.002 \ m^2} = 45,000 \ Pa[/tex]

The new force, F₂ = F₁ + 5 N = 90 N + 5 N = 95 N

The new area, A₂ = A₁ + 5 cm² = 20 cm² + 5 cm² = 25 cm²

The new pressure after the increase is given by the equation;

[tex]\mathrm{ } P_2=\dfrac{F_2}{A_2 }[/tex]

[tex]\mathrm{The \ surface \ pressure \ after \ the \ increase\ is \ } P_2=\dfrac{95 \ N}{0.0025 \ m^2} = \mathbf{38,000 \ Pa}[/tex]

[tex]Percentage \ change = \dfrac{New \ value - Initial \ value}{Initial \ value} \times 100[/tex]

[tex]Percentage \ change = \dfrac{38,000 - 45,000}{45,000} \times 100 = 15.\overline 5 \%[/tex]

The outcome decreases by 15.[tex]\overline 5 \%[/tex]

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Answer:

C. g(x)=1/3x^2

Step-by-step explanation:

let g(x)= ax^2

It bases through the point (3,3) × -x 3= a×3^2

-x 3= a×9 -x

a= 3/9=1/3

g(x)=1/3x^2

Answer:

x = 6.73 (corrected to 3 significant figures.)

Step-by-step explanation:

(x-5)^2=3

Square root both sides of the equation.

[tex]\sqrt{(x-5)^2} =\sqrt{3}[/tex]

[tex](x-5) = \sqrt{3}[/tex]

Add 5 to both sides.

[tex]x = \sqrt{3} + 5[/tex]

x = 6.73 (corrected to 3 significant figures.)

Answer:

x=-22 or -13

Step-by-step explanation:

(x-5)^2=3

Or,x^2-10x+25=3

Or,x^2-10x=3-25

Or,x (x-10)=-22

Either

x=-22

Or,

x-10=-22

x=-22+10

x=-12

x=-22,-12

Answer:

Step-by-step explanation:

5x+y-7=0 isolate y

y=-5x+7 (m=-5,b=7)

9x+7y-14=0

7y=14-9x ( divide both sides by 7)

y=-9x/7 +14/7

y=-9/7 + 2  (m=-9/7, b=2)

x+y=1000

4x+3y=3600 ( multiply the first equation by 3 to eliminate y)

3x+3y=3000

4x+3y=3600 ( subtract the two equations)

3x+3y-(4x+3y)=3000-3600

3x+3y-4x-3y=-600

-x=-600

x=600 ( substitute x in the equation)

x+y=1000

600+y=1000

y=1000-600=400

check : x+y=1000 , (600+400)=1000

check : 4x+3y=3600 = (4(600)+3(400))=2400+1200=3600

how many tickets are sold :

adults x=600/4=150

kids (y)=400/3=133 tickets+1 dollars left

unless( x represent kids then x=200, y represent adult = 100)

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Question 1:

[tex]5x+y-7=0[/tex]

Write in slope intercept form.

[tex]y=-5x+7 \\m=-5,b=7\\9x+7y-14=0[/tex]

Write in slope intercept form.

[tex]7y=14-9x\\y=-9x/7 +14/7\\y=-9/7 + 2\\m=-9/7, b=2[/tex]

Question 2:

[tex]x+y=1000\\4x+3y=3600[/tex]

[tex]3x+3y=3000\\4x+3y=3600\\3x+3y-(4x+3y) = 3000-3600\\3x+3y-4x-3y=-600\\-x=-600\\x=600[/tex]

[tex]x+y=1000\\600+y=1000\\y=1000-600=400[/tex]

Tickets sold:

Adults:

[tex]x=600[/tex]

Kids:

[tex]y=400[/tex]

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Answer: The correct option is 5.7/20 = x/200

Step-by-step explanation: Please refer to the diagram attached for more details.

From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;

Mean = Summation of observed data / Number of observations

Mean  = (3 + 5 + 7 + 5 + 6 + 8)/6

Mean = 34/6

Mean = 5.6667

Mean ≈ 5.7

Also the mean number of all fish is derived as follows;

Mean = Summation of observed data / Number of observations

Mean = (20 + 20 + 20 + 20 + 20 + 20)/6

Mean = 120/6

Mean = 20

Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.

Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;

StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.

OR better expressed as;

5.7/20 = x/200

Answer:

5.7/20 = x/200

Step-by-step explanation:

Answer:

The correct answer is C

Step-by-step explanation:

As you can see Town A is on top of Town B this means that Town B has symetric points to town A. This also shows how Town A is Positively skewed.

Answer:

The correct choices are;

g(0) = 0

g(1) = 1

and ;

g(-1) = 1

Step-by-step explanation:

In this question, we are to select the correct options.

So let’s take a look at the options

The term g(0) is correct

We can see that the base of the graph is sitting on the origin. At the point where x = 0, then g(x) is also = 0

g(1) is not equal to -1.

g(1) is equal to 1, mark the point 1 on the positive x-axis and trace towards the graph.

g(4) = -2 is another wrong option

The graph has no values on the negative y-axis i.e its smallest value is 0

g(1) = 1 is correct

We can trace this out from the graph

g(-1) = 1 is also correct. This is also traceable from the graph also

Answer:

B. [tex]y = 3x^2 -6x -3[/tex]

Step-by-step explanation:

Well, we can use the following formula to find the x coordianate of the vertex  -b / 2a.

So let’s start with a)

-6 / 6

-1

A. is wrong because its vertex starts with -1.

b)

6 / 6

1

now that we have our x coordinate we can plug it into the equation to get our y.

3 - 6 - 3

So the y coordinate is -6.

Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]

look at the image below.

Answer:

h(x) = 12x – 6

Step-by-step explanation:

To know which is the function that represents the area of a triangle, you take into account the degree of the given polynomials.

If the degree is 2, the graph of the function is a parabola.

If the degree is 1, the graph of the function is a line.

By comparing all functions you can conclude that only the last option (h(x)=12-x-6) is convenient to construct a triangle. The y-intersect of the function is at y=-6, the slope is positive and the x-intersect is x=1/2. This forms a triangle in the fourth quadrant of the coordinate system.

Answer:

B. g(x) = 12x2 – 6x

Step-by-step explanation:

correct on edge 2020

Answer:

x=8.

Step-by-step explanation:

x+(-13)=-5 makes x =8.

reason:

(-13)+??=-5.

-5+8=-13

therefore x=8

Answer:

B

Step-by-step explanation:

The measure of the tangent- chord angle XYZ is half the measure of its intercepted arc, thus

arc YZ = 2 × 84° = 168° → B

hello,

the first term is 250 so this is the initial invested amount

[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]

is to compute 8% annual interest compounded monthly (there are 12 months in a year)

and then multiply by 4 means that it is computed for 4 years so

finally the answer is

$250 is invested at 8% annual interest compounded monthly for 4 years

hope this helps

Answer:

525%

Step-by-step explanation:

set 5 1/4 as a decimal.

5.25 then move decimal point two places to the right to get the percent

525%

Answer:

d

Step-by-step explanation:

Answer:

The mean egg production 2499 million

Step-by-step explanation:

P(Z > a) = 3% = 0.03

P(Z > a) = 1 - ∅(a)

1 - ∅(a) = 0.03

∅(a) = 1 - 0.03

∅(a) = 0.97

Checking the normal distribution curve, for ∅(a) = 0.97, z = 1.88

This means that area under the normal curve is 3% (0.03) to the right of z = 1.8808

X = μ + (zб)

X = 2,655 millions

б = 83 million

2655 =  μ + (1.88 * 83)

2655 =  μ + 156.04

μ  = 2655 - 156.04

μ = 2498.96

The mean egg production, is therefore, 2499 million

Answer:

n=65th term

Step-by-step explanation:

AP:3,15,27,39......

From the AP

a=3

a+d=15

a+2d=27

3+d=15 (1)

3+2d=27 (2)

Subtract (1) from (2)

We have,

2d-d=27-15

d=12

54th term=a+(n-1)d

=3+(54-1)12

=3+(53)12

=3+636

=639

The term is 132 more than the 54th term

132+54th term

=132+639

=771

Find the term

771=a+(n-1)d

771=3+(n-1)12

771-3=12n-12

768=12n-12

768+12=12n

780=12n

n=780/12

=65

n=12

The term which is 132 more than the 54th term is the 65th term

Answer:

Option B is the right option.

solution,

Old price=$ 1.25

New price=$ 1.35

Now,

percentage increase:

[tex] \frac{new \: price - old \: price}{old \: price} \times 100 \: percent \\ = \frac{1.35 - 1.25}{1.25} \times 100 \: percent \\ = \frac{0.1}{1.25} \times 100 \: percent \\ = 8 \: percent[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

B.8%

Step-by-step explanation:

First, you figure out that the price increased by ten cents by subtracting the old price from the new one.

Then you figure out what one percent of 1.25 is by dividing it by 100 to get 0.0125.

Finally you can plug in each answer and multiply it with 0.0125 so you end up with 10 cents or 0.1.

8 is the correct answer.

Answer:

1. Coordinates of the other endpoint are (13, -10)

2. Coordinates of the other endpoint are: (8, 8)

Step-by-step explanation:

1. The endpoint (-9, 8) is located in the second quadrant. The midpoint (2, -1) is located in the fourth quadrant. That is to the right and down from the endpoint. Notice that the difference in the horizontal axis between the x-coordinates of the endpoint (-9, 8) and the midpoint (2, -1) is: | 2 - (-9) | = 11

And the difference in the vertical axis is: | -1 - 8 | = 9

So the midpoint is located 11 units to the right,and 9 units down from the endpoint. Then the other endpoint should be located also 11 units to the right, and 9 units down but from the midpoint. That is at: (2 + 11, -1 - 9) = (13, -10)

2. In this case, both, endpoint and midpoint are in the first quadrant, but notice that the midpoint is further away from the origin of coordinates.

The differences now are:

horizontal: 4 - 0 = 4

vertical: 5 - 2 = 3

and in both cases units are added to the endpoint coordinates to get to the midpoint coordinate values.

So to find the other endpoint we add 4 units to the x-value of the midpoint, and add 3 units to its y-value:

Other endpoint at : ( 4 + 4, 5 + 3) = (8, 8)

Answer:

b is the intercept of the graph. When x is 0, b is the y-value.

b affects the y-values, rather than the x-values. That means that it translates the graph up or down the y-axis by b units.

Hope this helps!

Answer: w = 13 m, L = 19.5 m

Step-by-step explanation:

P = 3w + 2L

     3w + 2L = 78

              2L = 78 - 3w

                [tex]L=\dfrac{78-3w}{2}[/tex]

A = w · L

[tex]A=w\bigg(\dfrac{78-3w}{2}\bigg)\\\\\\A=\bigg(\dfrac{78w-3w^2}{2}\bigg)\\\\\\A=39w-\dfrac{3}{2}w^2\\\\\\0=-\dfrac{3}{2}w^2+39w-A[/tex]

    a=-3/2   b=39

[tex]\text{Axis of Symmetry}:w=\dfrac{-b}{2a}=\dfrac{-39}{2(-\frac{3}{2})}=\dfrac{-39}{-3}=\large\boxed{13}[/tex]

[tex]\text{Maximum}:L=\dfrac{78-3w}{2}=\dfrac{78-3(13)}{2}=\dfrac{78-39}{2}=\dfrac{39}{2}=\large\boxed{19.5}[/tex]

Answer:

-3

Step-by-step explanation:

x-6=3x

2x=-6

x=-3

The required number is -3 decreased by 6 equals 3 times.

A number to be determine when decreased by 6 equals 3 times the number.

it explores the numbers of operations according to the statements.

Let the number be x,
Now,
x-6=3x
x= -3

Thus, the required number is -3 decreased by 6 equals 3 times.

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Answer:  No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:  

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y ==100

19x - 17y =101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!

Answer:

G

Step-by-step explanation:

Looking at the confidential explaniation, 0.7 + 3.89 would be 4.59z

Answer:

B.

choosing any marble

Step-by-step explanation:

Answer: 6 cajas de cada tipo de fruta.

Step-by-step explanation:

En cada caja de manzanas, tenemos 13 manzanas.

En cada caja de limones, tenemos 17 limones.

Si el numero total de cajas es C, entonces el numero total de manzanas es:

C*13

y el numero total de limones es: C*17.

Si en total tenemos 180 frutas, entonces tenemos que:

C*13 + C*17 = 180

C*(13 + 17) = 180

C*30 = 180

C = 180/30 = 6

Tenemos 6 cajas de cada tipo de fruta.

Answer:

[tex]\large \boxed{\text{6 boxes of apples and 6 boxes of lemons}}[/tex]

Step-by-step explanation:

     Let m = the number of boxes of apples. Then

        13m = the number of apples

       Let l = the number of boxes of lemons. Then  

          17l = the number of lemons and

13m + 17l = the total number of fruits

You have two conditions:

[tex]\begin{array}{rrclr}(1) & m & = &l\\(2) & 13m + 17l & = & 180\\\end{array}[/tex]

Solve the equations for m and l

[tex]\begin{array}{rrcll}(1) & m & = & l&\\(2) & 13m + 17l & = & 180\\(3)&13m +17m & = & 180 & \text{Substituted (1) into (2)}\\&30m& = &180 &\text{Simplified}\\(4)&m& = &\mathbf{6} &\text{Divided each side by 30}\\& 6& = &l& \text{Substituted (4) into (1)}\\& l& = &\mathbf{6}& \\\end{array}\\\text{You have $\large \boxed{\textbf{6 boxes of apples and 6 boxes of lemons}}$}[/tex]

Check:

[tex]\begin{array}{ccc}6 = 6 & \qquad & 13(6) + 17(6) = 180\\& \qquad & 78 + 102 =180\\& \qquad & 180 = 180\\\end{array}[/tex]

It checks.

Answer:

81 students.

Step-by-step explanation:

If 10% of the 90 students were absent, then that means that 9 students were absent. To find the number of students present, simply subtract.

90 - 9 = 81.

- Hope this helped.

Answer:

x=6.09cm

Step-by-step explanation:

Working out AB:

7.5²+4.9²

= √80.26

AB= 8.96cm

To work out x:

AB is the opposite, where BC is the adjacent. This means that we have to use TOA.

x=8.96/Tan(55.8)

x= 6.09cm

Answer:

6.1 cm

Step-by-step explanation:

Use the Pythagorean theorem for triangle ABD to find the hypotenuse.

7.5^2+4.9^2=c^2. After solving you get that the missing length is about 9 cm. The hypotenuse of ABD is also a leg for ABC so you can use a trigonometric function, tangent, to find x. Set up the equation for opposite and adjacent sides to angle measure 55.8. The equation is tan(55.8)=9/x. In order to isolate the variable you multiply both sides by x to get (x)tan(55.8)=9, then divide both sides by tan(55.8), this leaves you with x=9/tan(55.8). You can then plug this into the calculator to get x is approximately 6.1 cm.

There’s 6 numbers that can be used.

The first digit can be any of the 6

The 2nd digit can be any of the 5 left

The 3rd digit can be any of the 4 left

The 4th did fit can be any of the 3 left

The 5th digit can be any of the 3 left

The 6th digit would be the last number left.

Total combinations = 6 x 5 x 4 x 3 x 2 x 1 = 720