Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)

How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?

The solution is, 10√3cm  is the length of a diagonal of a cube with a side length of 10 cm.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

given that,

the side length is 10cm ,

then the length of diagonal of the base of the cube(x) is

X² =(10)²+(10)²

    =200cm  

so x = 10√2cm

so the length of diagonal of the cube(y) is

y² = (10)² + (10√2)²

   =300  

so y =10√3cm

Hence, The solution is, 10√3cm  is the length of a diagonal of a cube with a side length of 10 cm.

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The sum of first five terms for the geometric series is 775. The correct answer is (B).

In a geometric sequence, the ratio of two consecutive terms are always equal.

The general expression for the nth term is given as aₙ = a₁ × rⁿ⁻¹ .

The sum of n terms for this sequence is given as Sₙ = (rⁿ - 1)/(r - 1)

The given series is  400 + 200 + 100 + …

It is a geometric series.

Its first term is a₁ = 400.

And, common ratio is r = 200/400 = 0.5.

Now, the expression for the sum of n terms is given as below,

Sₙ = a(1 - rⁿ)/(1 - r)

Then, substitute the value of a₁, a₅ and n = 5 to obtain,

S₅ = 400(1 - 0.5⁵)/(1 - 0.5)

⇒ S₅ = 775.

Hence, the sum of first five terms of the given series is 775.

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Answer:

we need a diagram or somthing

Step-by-step explanation:

The value of the fourth term in the geometric sequence is 3.75.

The value of the fourth term in a geometric sequence can be found using the formula:

an = a1 * r(n-1)

Given that a1 = 30 and r = 1/2, we can substitute these values into the formula and solve for a4:

a4 = 30 * (1/2)(4-1) = 30 * (1/2)3 = 30 * (1/8) = 3.75

Therefore, the value of the fourth term in the geometric sequence is 3.75.

Final answer:

The value of the fourth term in the geometric sequence is 3.75.

Explanation:

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. In this case, the first term (a1) is 30 and the common ratio (r) is 1/2. To find the fourth term, we can use the formula:

an = a1 * r(n-1)

Substituting the values given, we have:

a4 = 30 * (1/2)(4-1)

Simplifying this expression, we get:

a4 = 30 * (1/8) = 3.75

Therefore, the value of the fourth term in this geometric sequence is 3.75.

Multiplication gives us distribution over the products, so

(a′+b+d′) (a′+b+c′+f′) = a′ (a′+b+c′+f′) + b (a′+b+c′+f′) + d′ (a′+b+c′+f′)

And then you can then distribute again each of the factors on the right.

Then you should simplify in any given number of ways. To take as an example, you have a′b and ba′, and since a′b + a′b = a′b + a′b = a′b, you can just drop one of them. Since bb = b, you can rewrite bb as b and etc.

So in the end part we should arrive at a sum of products. Then you can just invert. For example, if at the end you had:

p′ = a′b + bc′ + d′f ′+ a′f′

Then we would have

p = p′′ = (a′b + bc′ + d′f′ + a′f′)′ = (a′b)′⋅(bc′)′⋅(d′f′)′⋅(a′f′)′

Then applying De Morgan's laws to each of the factors, e.g., (a′b)′ = a+b′, so we would have

p = (a+b′)⋅(b′+c)⋅(d+f)⋅(a+f)

which is a product of sums.

The probability that Jonas will get an orange and Beth will get an apple is 20/121.

To find the probability that Jonas will get an orange and Beth will get an apple, we need to find the probability of Jonas getting an orange and then multiply it by the probability of Beth getting an apple.

The probability of Jonas getting an orange is the number of oranges in the basket (5) divided by the total number of fruits (11):

P(orange for Jonas) = 5/11

The probability of Beth getting an apple is the number of apples in the basket (4) divided by the total number of fruits (11):

P(apple for Beth) = 4/11

To find the combined probability, we multiply these two probabilities together:

P(orange and apple) = P(orange for Jonas) * P(apple for Beth) = (5/11) * (4/11) = 20/121

The transformation from f to g represents a Vertical stretch.

We are given a parent function f(x) as:

                      [tex]f(x)=\sqrt{x}[/tex]

and the transformed function g(x) as:

        [tex]g(x)=6\sqrt{x}[/tex]

We know that any function transformation of the type:

      f(x) → a f(x)

represents either a vertical stretch stretch or compression depending on the value of a.

If   0<a<1 then the transformation is a vertical compression and if a>1 then the transformation is a vertical stretch.

Here we have a=6>1

Hence, the transformation is a VERTICAL STRETCH.

To solve the equation, we cross multiply to eliminate the fractions and solve for r. The solution is r = 13. We can check the solution by substituting it back into the original equation.

To solve the equation (r - 3) / 10 = r / 13, we can cross multiply to eliminate the fractions. This gives us 13(r - 3) = 10r. Distributing, we get 13r - 39 = 10r. We can then solve for r by subtracting 10r from both sides and adding 39 to both sides. This gives us 3r = 39. Dividing both sides by 3, we find that r = 13.

To check the solution, we substitute r = 13 back into the original equation. The left side becomes (13 - 3) / 10 = 10 / 10 = 1, and the right side becomes 13 / 13 = 1. Since both sides are equal to 1, we can confirm that the solution r = 13 is correct.

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area = L x w

42 = 6 x w

w=42/6 = 7

rectangle is 6 x 7

square would be 6 x 6 = 36 square feet

36/42 = 0.857 = 85.7% ( Round answer if needed)

Answer:

-6 = -11

Distributive Property

Step-by-step explanation:

A.

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 4x + 2x - 11

6x - 6 = 6x - 11

-6 = -11

since -6 is not equal to -11, so there's no solution

B. Distributive property

Answer:

OQ > PQ > OP

Step-by-step explanation:

In this question measure of all angles in a triangle has been given.

m∠ p = (10x - 2)

m∠ q = (3x - 3)

m∠ o = (3x + 9)

Since total of all angles is 180°, so we will equate the total of all angles to 180°

∠p + ∠q + ∠o = 180°

(10x - 2) + (3x - 3) + (3x + 9) = 180°

(10x + 3x + 3x) -2 - 3 + 9 = 180

16x - (2 + 3 - 9) = 180°

16x + 4 = 180

16x = 180 - 4

16x = 176

x = [tex]\frac{176}{16}=11[/tex]

Now we will find the measure of each angle.

∠p = (10x - 2) = 10×11 - 2 = (110 - 2) = 108°

∠q = (3x - 3) = 3×11 - 3 = (33 - 3) = 30°

∠o = (3x + 9) = 3×11 + 9 = (33 + 9) = 42°

As we know in a triangle, angle opposite to the largest side is largest and angle opposite side is the smallest.

Since ∠p > ∠o > ∠q

Therefore, in Δ OPQ opposite sides to these angles will be in the same ratio.

OQ > PQ > OP

Answer with explanation:

Event Joining by two or more Simple events is called Compound Event.

When you throw a coin once, getting either Head or Tail is a Simple event.

And , when you throw a coin and dice together, getting , Head and 1 , is a Compound event.Because here we joined two simple events, one is Throwing of a coin and another one is throwing a dice.

When you toss a coin thrice, it is combination of three simple events, that is tossing of coin three times .So total possible outcome

      [tex]=2^3\\\\=8[/tex]

Which can be written as: {(HHH),(HHT),(HTH),(THH),(HTT),(THT),(TTH),(TTT)}

Probability of getting all heads on 3 coin tosses

  = Sum of three simple events

            [tex]=\frac{HHH}{\text{Total 8 Outcome}}\\\\=\frac{1}{8}[/tex]  

or

Probability of Getting head in all three throws

[tex]=\frac{1}{2}\times \frac{1}{2} \times \frac{1}{2}\\\\=\frac{1}{8}[/tex]

Yes, this is a Compound event.

Answer:

100000 in scientific notation:[tex]100,000=1.0\times 10^{5}m/s[/tex]

Step-by-step explanation:

Scientific notation is defined as the notation in which a number is expressed in the decimal form. This means that the number is always written in the power of 10 form. The numerical digit lies between 0.1.... to 9.9.....

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

We are given:  100,000

Converting this into scientific notation, we get:

[tex]\Rightarrow 100,000=1.0\times 10^{5}m/s[/tex]

As, the decimal point is shifting to left side, thus the power of 5 is positive.

Answer:

the answer is 2 and 3

Step-by-step explanation:

I took the test

Answer with explanation:

The  “heights of the women in the U.S. Congress” is Quantitative,because height of person does not represent Quality, it shows "Quantity".It means it has Magnitude.

We can find mean , median and mode of women in Congress.

So, Height of women in US congress is Quantitative.

As, different Women have different Heights, that is any rational number , so The Height of different women will be a discrete data set.For, example, height of different women can be={167 cm, 187.6, 176.6,165.5,.....}