g(1)=51 g(n)=g(n-1)+2 fina an explicit formula for g(n)

Answer:

[tex]Sin(\alpha)=\frac{2}{3}[/tex]

Step-by-step explanation:

We need a simple identity to solve for sine of an obtuse angle (angle greater than 90 degrees).

We know,

[tex]Sin(180-\alpha)=\alpha[/tex]

So the value of [tex]Sin\alpha[/tex] would depend on the triangle we can make on the left side of the coordinate system shown.

The triangle would be as shown in the attached figure.

This triangle has base length of [tex]\sqrt{5}[/tex] and height of 2. The hypotenuse, r, can be solve using pythagorean theorem:

[tex](\sqrt{5} )^2+(2)^2=r^2\\5+4=r^2\\9=r^2\\r=3[/tex]

We know sin of an angle is "opposite" side over "hypotenuse". The triangle's opposite is "2" and hypotenuse is "3". So we can finally write:

[tex]Sin(\alpha)=\frac{Opposite}{Hypotenuse}=\frac{2}{3}[/tex]

Answer:

x = 1

Step-by-step explanation:

Assuming you require to calculate the value of x

Since the triangle is right use Pythagoras' theorem

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(x + 1)² + (x + 3)² = (2[tex]\sqrt{5}[/tex])² ← expand and simplify left side

x² + 2x + 1 + x² + 6x + 9 = 20

2x² + 8x + 10 = 20 ( subtract 20 from both sides )

2x² + 8x - 10 = 0 ← in standard form

Divide through by 2

x² + 4x - 5 = 0 ← factor the quadratic

(x + 5)(x - 1) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 1 = 0 ⇒ x = 1

However, x > 0 ⇒ x = 1

Answer:

i think x = 1

Step-by-step explanation:

Hi, I hope this helps you out. Have a great day! :)

Answer:

Your answer is false.

A quadrilateral needs to have both opposite sides congruent to be a parallelogram.

Answer:

So, Correct option is B i.e [tex]5.6^{-2} \times 3.4^{-11}\\[/tex]

Step-by-step explanation:

The expression here contains exponents so, we will use exponent rule.

The exponent rule says that the power of the same bases can be added if two same bases are multiplied i.e.

[tex]x^2 X y^2 X x^2 X y^1 \\can \,\, be \,\, written\,\, as\,\,\\x^{2+2} X y^{2+1}\\x^4 X y^3\\[/tex]

using this rule we can solve our question

[tex]5.6^{-5} \times 3.4^{-7} \times 5.6^3 \times 3.4^{-4}\\5.6^{-5+3} \times 3.4^{-7-4}\\ 5.6^{-2} \times 3.4^{-11}\\[/tex]

So, Correct option is B i.e [tex]5.6^{-2} \times 3.4^{-11}[/tex]

Answer

[tex] B)\: {5.6}^{ - 2} \times {3.4}^{ - 11} [/tex]

step-by-step explanation

For the expression

[tex] {5.6}^{ - 5} \times {3.4}^{ - 7} \times {5.6}^{3} \times {3.4}^{ - 4} [/tex]

we rewrite the expression to get

[tex] {5.6}^{ - 5} \times {5.6}^{3} \times {3.4}^{ - 7} \times {3.4}^{ - 4}[/tex]

One of the laws of indices states that

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

which means that if multiplying expressions of the same bases, repeat one of the bases and add the exponents

This implies that

[tex] {5.6}^{ - 5} \times {5.6}^{3} \times {3.4}^{ - 7} \times {3.4}^{ - 4} [/tex]

[tex]={5.6}^{( - 5 + 3)} \times {3.4}^{ (-7 - 4)}[/tex]

[tex]={5.6}^{-2} \times {3.4}^{-11} [/tex]

Answer:

V = 576 pi cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = pi * (6)^2 * 16

V = pi *36*16

V = 576 pi cm^3

Answer:675(d)

Step-by-step explanation:so you take ratio

90-600

810-x

x=5400

After you divide 5400 by 8 hours and you get 675- to get how much figures he get for one hour

Final answer:

To find out how many action figures are made per hour, divide the amount of plastic used per hour by the amount of plastic used to make one action figure. In this case, 113 action figures are made per hour.

Explanation:

To find out how many action figures are made per hour, we need to determine the amount of plastic used per hour and then divide it by the amount of plastic used to make one action figure.

First, we need to find the amount of plastic used per hour. Since 810 pints of plastic are used in an 8-hour shift, we divide 810 by 8, which gives us 101.25 pints of plastic per hour.

Next, we need to determine how many action figures can be made with 101.25 pints of plastic. We divide 101.25 by 90 (the amount of plastic used to make 600 action figures), which gives us 1.125 action figures per pint of plastic.

Finally, we multiply 1.125 by 101.25 to find the number of action figures made per hour. This gives us 113.4375 action figures per hour. Since we can't have a fraction of an action figure, we round this to the nearest whole number, which is 113 action figures per hour.

Answer: tasha needs at least 252 inches of ribbon

your exact answer should be 252 inches

Step-by-step explanation: multiply the width times height to find the area of a rectangle

Tasha requires 64 inches of ribbon to decorate the outer edge of her bulletin board. To determine this, we use the formula for the perimeter of a rectangle, 2*(length+breadth), substituting the dimensions of the board.

To calculate the amount of ribbon Tasha requires, you need to find the perimeter of the bulletin board. The perimeter of a rectangle (which is the shape of the bulletin board) is calculated by the formula 2*(length+breadth).

In this instance, the length is 18 in, and the width (or breadth) is 14 in. Substituting these values into the formula we get: 2*(18 in + 14 in) = 2*32 in = 64 inches. Thus, Tasha needs 64 inches of ribbon to decorate the entire outer edge of the bulletin board.

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The mean is the average.

Add the number of contacts and divide by the number of people:

112 + 104 + 96 + 54 +98 +120 = 584

584 / 6 = 97.3

The mean = 97.3

Now add the standard deviation to the mean for the higher value and subtract the standard deviation from the mean for the lower value:

97.3 - 21 = 76.3

97.3 +21 = 118.3

The answer would be D.

Answer:

The distance between the two trees is [tex]98.92\ ft[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]c^{2}=a^{2} +b^{2} -2(a)(b)cos (C)[/tex]

where

c -----> is the distance between the two trees

a ----> is the distance between the transit and the first tree

b ----> is the distance between the transit and the second tree

we have

[tex]a=62\ ft[/tex]

[tex]b=58\ ft[/tex]

[tex]C=111\°[/tex]

substitute and solve for c

[tex]c^{2}=62^{2} +58^{2} -2(62)(58)cos (111\°)[/tex]

[tex]c^{2}=9,785.38[/tex]

[tex]c=98.92\ ft[/tex]

Answer: [tex]y=log_2(x-3)[/tex]

Step-by-step explanation:

To obtain the inverse of the function [tex]y= 2^x + 3[/tex], you need to solve the equation for the variable "x":

[tex]y= 2^x + 3\\\\y-3=2^x\\\\log_2(y-3)=log_2(2^x)\\\\x=log_2(y-3)[/tex]

Now you need to exchange the variable "x" with the variable "y". Then:

[tex]y=log_2(x-3)[/tex]

Finally, you get that the inverse of the function [tex]y= 2^x + 3[/tex] is:

[tex]y=log_2(x-3)[/tex]

Answer:

[tex]\large\boxed{c.\ \triangle CDE\sim\triangle FGH}[/tex]

Step-by-step explanation:

[tex]\text{Calculate the maeasure of the angle}\ E:\\\\180^o-(60^o+53^o)=180^o-113^o=67^o\\\\\angle C\cong\angle F\\\\\angle E\cong\angle H\\\\\angle D\cong\angle G\\\\\text{Therefore:}\\\\\triangle CDE\sim\triangle FGH[/tex]

Answer:  The correct option is

(c) [tex]\triangle CDE\sim \triangle FGH.[/tex]

Step-by-step explanation:  We are given to write a similarity statement for the triangles shown in the figure.

In the given triangles, we have

m∠C = 60°,  m∠D = 53°,  m∠F = 60°  and  m∠H = 67°.

Fist, we have to fin d the measures of angles E and G.

From angle sum property of a triangles, we can write

[tex]m\angle C+m\angle D+m\angle E=180^\circ\\\\\Rightarrow 60^\circ+53^\circ+m\angle E=180^\circ\\\\\Rightarrow 113^\circ+m\angle E=180^\circ\\\\\Rightarrow m\angle E=180^\circ-113^\circ\\\\\Rightarrow m\angle E=67^\circ.[/tex]

Similarly, we have

[tex]m\angle F+m\angle G+m\angle H=180^\circ\\\\\Rightarrow 60^\circ+m\angle G+67^\circ=180^\circ\\\\\Rightarrow 127^\circ+m\angle G=180^\circ\\\\\Rightarrow m\angle G=180^\circ-127^\circ\\\\\Rightarrow m\angle G=53^\circ.[/tex]

So, we get

m∠C  =  m∠F,

m∠D  =  m∠G

and

m∠E  = m∠H.

Therefore, by angle-angle-angle similarity postulate. we get

[tex]\triangle CDE\sim \triangle FGH.[/tex]

Thus, option (c) is CORRECT.

Answer:

B

Step-by-step explanation:

Given

y = f(x), then

y = f(x ± a) is a horizontal translation of a units

• If f(x + a) then shift of a units left ←

• If f(x - a) then shift of a units right →

When you transform a function by writing

[tex]f(x)\mapsto f(x+h)[/tex]

You're translating the function horizontally, h units to to the left if h is positive, and h units to the right if h is negative.

So, for example, given the "standard" parabola [tex]f(x)=x^2[/tex]

We have that the child function [tex]f(x+3) = (x+3)^2[/tex] has the same shape, but it's translated 3 units to the left.

=======================================================

Explanation:

If you had one coin, then there are 2 outcomes because of the two sides heads or tails, which I'll shorten to H and T respectively.

With two coins, there are 2*2 = 4 outcomes (HH, HT, TH, or TT)

Having 3 coins there are 2*2*2 = 2^3 = 8 outcomes

4 coins and we have 2^4 = 2*2*2*2 = 16 outcomes

and so on

With 9 coins there are 2^9 = 512 different outcomes

Answer:

There are 2 outcomes per flip.

Therefore the answer is 2^9 which equals 512 outcomes.

Step-by-step explanation:

They need to make sure you will be able to pay the loan back

Hope this helps :)

Lenders verify income before approving loans to assess borrowers' creditworthiness and ensure they have the means to repay. They use income information, credit checks, cosigners, and collateral to mitigate the risks associated with uncertain future income and potential default.

A lender will verify and carefully consider your income before approving you for a loan because income indicates your ability to repay the loan. In a financial capital market, banks assess the creditworthiness of a borrower to manage uncertainty and the risk of default. They require information about income sources, perform credit checks, and might ask for additional security measures such as a cosigner or collateral. Collateral could include property or equipment that the bank has the right to seize if the loan is not repaid. This scrutiny is crucial because lenders face imperfect information and cannot predict with certainty whether the borrower will fulfill their repayment obligations.

Answer:

Absolute: 39 pounds

Relative: 6.5%

Step-by-step explanation:

To find the absolute difference, we simply have to see by how much pounds the estimation was off.

The real measure was 639 pounds, the estimated weight was 600.

D = 639 - 600 = 39 pounds.

For the percent of error, we divide the absolute difference (39) by the real value (639) and we'll get the % of error.  So,

%D = 39 / 600 = 0.0610, so 6.1%

We don't need to round it to the nearest tenth, since it's already to that precision level.

Answer:

Absolute error = 39 pounds

Percent error = 6.10%

Step-by-step explanation:

We are given that the actual weight of the beam was 639 pounds while its estimated weight was 600 pounds.

We can find the absolute error by subtracting the original weight from the estimated weight.

Absolute error = 639 - 600 = 39 pounds

Next, we will use the following formula to find the percent error.

Percent error = (Estimated value - actual value / actual value) * 100

Percent error = 639 - 600 / 600 * 100 = 6.10%

Answer:

Inverse variation

Step-by-step explanation:

Given equation is [tex]y=\frac{3}{x}[/tex].

Now we need to identify the type of variation represented by  [tex]y=\frac{3}{x}[/tex].

We know that there are two type of variations direct and inverse.

If y and x are in direct variation then we write equation as  [tex]y=kx[/tex].

where k is the constant of variation.

If y and x are in inverse variation then we write equation as   [tex]y=\frac{k}{x}[/tex].

Given equation  [tex]y=\frac{3}{x}[/tex] looks similar to  [tex]y=\frac{k}{x}[/tex].

So that means finala answer is "Inverse variation".

Answer:

c

Step-by-step explanation:

i think is right because i got most of the answers correct

5×5×5×5×5=3125

Hope this helped :)

Answer:

well these are all the possible solutions that make the inequality statement correct.

Step-by-step explanation:

you can recheck by placing the pairs into the equation

hope that helps

It’s 6, wow that question was really worded weird.

Answer:

3/4 pound or less , thinks this is the answord

Step-by-step explanation:

To find the total number of cans collected, when Bob brought 40% to the pantry equaling 160 cans, we set up the equation 0.40 * x = 160 and solve for x to get 400 cans.

The student has asked to calculate the total number of canned goods collected if Bob brought 40% of them to the pantry and that amounted to 160 cans. To find the total, we can set up a proportion where 40% of the total number of cans equals to 160 cans, and then solve for the total.

First, express 40% as a decimal, which is 0.40. Then, let the total number of cans be represented by x. According to the problem, 0.40 times x equals 160 cans.

So the equation is:

0.40 * x = 160

To solve for x, divide both sides of the equation by 0.40:

x = 160 / 0.40

x = 400

Therefore, a total of 400 cans were collected.

Answer:

The answer is...

Step-by-step explanation:

Each interior angle measures 108 degrees. All of the angles are congruent. The sum of the measures of the interior angles is 108(5-2) degrees.

The true statements about regular polygons are given below.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

We have a regular polygon.

So, the true statements about polygons:

It has equal length sides.

All its interior angles are equal.

The sum of its exterior angles is 360°.

Therefore, true statements are given above.

To learn more about the interior angles;

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Answer:

B)

Step-by-step explanation:

3 multiplied by 2 is 6

6+2 is 8

Answer: $4.69

Step-by-step explanation:

Make equivalent fractions for each fruit.

Apples: 1.62/1 = x/2.5

X = $4.05 for 2.5 pounds of apples

Bananas: 0.48/1 = x/1.3333333333

X = .64 for 1.3333333333 pounds of bananas

Now add the results together to find the total cost.

4.05 + .64 = $4.69

Answer:

A

Step-by-step explanation:

On solving the given inequality, we get x > 11.81

Given is the following inequality -

81 - 11/5x ≤ 55

We have -

81 - 11/5x ≤ 55

(11/5)x ≥ 81 - 55

(11/5)x ≥ 26

(11/5)x ≥ 26

x ≥ = (26 x 5)/11

x > 11.81

Therefore, on solving the given inequality, we get x > 11.81

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Answer:

[tex]\large\boxed{D.\ -\dfrac{4}{3}<x<\dfrac{10}{3}}[/tex]

Step-by-step explanation:

[tex]2|3x-3|-6<8\qquad\text{add 8 to both sides}\\\\2|3x-3|<14\qquad\text{divide both sides by 2}\\\\|3x-3|<7\iff3x-3<7\ \wedge\ 3x-3>-7\qquad\text{add 3 to both sides}\\\\3x<10\ \wedge\ 3x>-4\qquad\text{divide both sides by 3}\\\\x<\dfrac{10}{3}\ \wedge\ x>-\dfrac{4}{3}[/tex]

Answer:

answer: D

Step-by-step explanation:

look this solution :

Answer:

Step-by-step explanation:

3/20x100

=15

15% of the boxes are damaged.

To find the percentage of damaged boxes, we need to divide the number of damaged boxes by the total number of boxes and then multiply the result by 100 to get the percentage.

Let's perform the calculation step-by-step:

So, 15% of the boxes are damaged.

Answer:

slope = [tex]\frac{3}{14}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (5, - 3) and (x₂, y₂ ) = (- 9, - 6)

m = [tex]\frac{-6+3}{-9-5}[/tex] = [tex]\frac{-3}{-14}[/tex] = [tex]\frac{3}{14}[/tex]

more information is needed

To determine the total number of possible raffle ticket numbers with two letters followed by three digits, we multiply the number of possibilities for each position (26 for each letter and 10 for each digit): 26 x 26 x 10 x 10 x 10 = 676,000 possible combinations.

To calculate how many raffle ticket numbers are possible with the given format—two letters followed by three digits—we need to consider the total number of options for each position in the sequence. Each letter in the raffle ticket can be one of 26 possible letters (assuming we're using the English alphabet), and each digit can be one of 10 digits (0-9).

For the two letters, the number of possibilities for each letter is 26. Since there are two letters, the total number of possibilities for the letters is 26 times 26. For the three digits, assuming each digit can be any number from 0-9, the number of possibilities for each digit is 10. The total number of possibilities for the digits is 10 times 10 times 10.

Thus, to find the total number of possible raffle ticket numbers, we multiply the possibilities for the letters and the digits together:

Total possibilities = 26 times 26 times 10 times 10 times 10 = 676,000.

Answer:

Step-by-step explanation:

[tex]6x^2-2x^4+4+3x\\\\\text{Look at the power of variables.}\\\text{Arrange the terms in order from the largest exponent to the smallest.}\\\\-2x^4+6x^2+3x+4[/tex]