glenn is building aa ramp out of plywood. he is going to use plywood sheets that are each 23 square feet. How many plywood sheets will glenn need to build all five sides of the ramp, assuming the bottom is also covered with plywood

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

Answer:

the period of this graph is 2\(\pi\)

Step-by-step explanation:

The period is the length of the section that repeats.  So for this graph, we need to calculate the distance between 2 peaks or 2 troughs of the curve.

Let's look at the peaks (maximums).

One is at x = 0 and the next is at x = 2\(\pi\)

2\(\pi\) - 0 = 2\(\pi\)

Therefore, the period of this graph is 2\(\pi\)

Answer:

A

Step-by-step explanation:

Geometric sequences involve multiplication and the ratio of 2 means each number is multiplied by 2 to get the next number.

Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

Answer:

The answer is 0.26.

I wish you luck on your assignments.

Answer: 0.26

Step-by-step explanation:

1. The hundredths place is two digits from the decimal point

2. Look at the thousandths place and if it is larger or equal to 5 then we round up, otherwise we round down and the hundredths digit remains the same

3. 7 is larger than 5 therefore the hundredths place digit of 5 rounds to a 6

4. Our final answer is 0.26

Answer:

B

Step-by-step explanation:

because yea

Answer:

Step-by-step explanation: I just did it on imagine math.

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Answer:

The number 2

Step-by-step explanation:

Answer: easy question.The ratios are 1. 32:1122) 2. 8:28 hope that helps u

Step-by-step explanation:

The range of the exponential function is: B. \(g(x)>-6\)

Recall:

Range of any function includes all possible values of y (output)

Domain of any function includes all possible values of x (input).

Thus:

The values of y in the exponential function greater than -6 on the y-axis as shown in the graph given.

Therefore:

Range of the exponential function given in the graph is: B. \(g(x)>-6\).

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The cone that has the greatest volume is cone C

The given parameters in the question are

Cone A

Height = 10 cm

Diameter = 4 cm

Cone B

Height = 20 cm

Diameter = 4 cm

Cone C

Height = 10 cm

Diameter = 8 cm

The volume of a cone can be calculated using the following volume equation

Volume of a cone = 1/3π(d/2)²h

Where

h = height of the cone

r = radius of the cone

d = diameter of the cone

Using the above equations, we have the following computations

Volume of a cone A = 1/3π * (4/2)² * 10

Volume of a cone A = 40/3π

Volume of a cone B = 1/3π * (4/2)² * 20

Volume of a cone B = 80/3π

Volume of a cone C = 1/3π * (8/2)² * 10

Volume of a cone C = 160/3π

We can see that 160/3π is greater than 40/3π and 80/3π

Hence, cone C has the highest volume

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Answer:

(-3+5i)(1)=-3+5i

Step-by-step explanation:

The multiplicative identity is given by :

\(a\times 1=a\)

Where

a can be any number

Out of 4 options, in option (2), (-3+5i) is multiplied by 1 and after multiplying we get (-3+5i).

Hence, the correct option is (b).  

Answer:

c= 70?

a= 66? I think im not too sure

Answer:

x

+

6

y

=

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.

Answer:

2 pounds

Step-by-step explanation:

I hope this helps!

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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Answer:

2 units

Step-by-step explanation:

vertical distance will be the magnitude of the difference in the 'y' coordinates

| -.8 - 1.2| = 2 units

The given statement is:

41 fewer than the quantity t times 307 is equal to n.

The equation is given by:

Answer:

√ 42  lies between  6  and  7

Step-by-step explanation:

We know that  √ 42  will lie between  √ 36  and  √ 49

And  √ 36 = 6  ;  √ 49 = 7

Hence we can be sure that  √ 42  lies between 6  and  7

Answer:

$37

Step-by-step explanation:

Let $x be the amount Kelly saved.

Kelly saved $x.

Indhu saved $(x-16). (Kelly saved $16 more than Indhu)

Marvin saved $2(x-16). (Marvin saved twice the amount Indhu saved)

They saved $100 together.

Therefore we could set up an equation.

x+(x-16)+2(x-16)=100

x+x-16+2x-32=100

4x=148

x=37

Therefore Kelly saved $37.

Answer:

Step-by-step explanation:

An expression that represents the distance that Reggie travels on the highway in h hours is Distance, D = 55h

An expression that represents Reggie's total distance from the

airport h hours after reaching the highway is Distance, D = 10 + 55h.

A distance is defined as an object's total movement without regard for direction. Distance is also defined as the amount of ground travelled by an object from its starting point to its final destination.

A distance can also be thought of as a scalar quantity, which means that the distance travelled by an object is independent of its motion direction. It is the entire path taken by an object. To calculate distance, we can use the formula below:

Distance[d] = Time[t] x Speed[s]

Displacement simply refers to a change in the position of a specific object. When an object moves from point A to point B, displacement occurs. Displacement is a vector quantity with both magnitude and direction.

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Answer:

Step-by-step explanation:

∠ EGF=180-∠FGH

          = 180-(180-112)

          = 112°

∠LKM= 90= 8X -6

           2(4X-3)=90

             4X-3=45°

3)

22=4X-10

 X=8

NR= 3(8) +6

     = 30

Answer:

it would be 3/10

Step-by-step explanation:

add the amount of marbles, which give you 10 and put the amount of the color marble you want the probability of

Answer: 7 + 2x

Step-by-step explanation:

Hope this helps

By analyzing the question, we find that there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.

A permutation is an arrangement of a set of items in a specific order. Permutations are typically denoted using the notation "P" followed by the number of items being permuted and the number of items being chosen at a time.

The formula for calculating permutations is as follows:

P(n,r) = n! / (n-r)!

where:

P(n,r) is the number of permutations of r items from a set of n items.

n! is the factorial of n, which is the product of all positive integers less than or equal to n.

There are five fashion models and three remaining outfits, which means there are 5 ways to choose the model who wears the first outfit, 4 ways to choose the model who wears the second outfit, and 3 ways to choose the model who wears the third outfit. Therefore, there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.

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Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

\( \large{ \tt{❀ \: m \: \angle \: NML= m \: \angle \:QML + m \: \angle \: NMQ}}\)

\( \large{ \tt{⤇m \: \angle \:NML= 115 \degree + 28 \degree }}\)

\( \boxed{ \large{ \tt{⤇ \: m \: \angle \:NML = 143 \degree }}}\)

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