What is the constant in the expression 4x + 2

Full Question: Below is the diagram of the base of gazebo. Hunter is building for his backyard. He plans on gazebo having a height of 4 meters with a pyramid shaped roof that is an additional 2 meters high. He needs to order shingles for the roof and needs to know how much area is covered by shingles.

Answer:

$2784$ $m^{2}$

5 0

3 years ago

Estimate the perimeter of the figure to the nearest whole number.

Paha777 [63]

Answer:

The perimeter (to the nearest integer) is 9.

Step-by-step explanation:

The upper half of this figure is a triangle with height 3 and base 6. If we divide this vertically we get two congruent triangles of height 3 and base 3. Using the Pythagorean Theorem we find the length of the diagonal of one of these small triangles: (diagonal)^2 = 3^2 + 3^2, or (diagonal)^2 = 2*3^2.

Therefore the diagonal length is (diagonal) = 3√2, and thus the total length of the uppermost two sides of this figure is 6√2.

The lower half of the figure has the shape of a trapezoid. Its base is 4. Both to the left and to the right of the vertical centerline of this trapezoid is a triangle of base 1 and height 3; we need to find the length of the diagonal of one such triangle. Using the Pythagorean Theorem, we get

(diagonal)^2 = 1^2 + 3^2, or 1 + 9, or 10. Thus, the length of each diagonal is √10, and so two diagonals comes to 2√10.

Then the perimeter consists of the sum 2√10 + 4 + 6√2.

which, when done on a calculator, comes to 9.48. We must round this off to the nearest whole number, obtaining the final result 9.

4 0

3 years ago

The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 18, meaning that among

jeyben [28]

Answer:

(a) The value of P (None) is 0.062.

(b) The value of P(at least one) is 0.938.

(c) The value of P(at most one) is 0.253.

(d) The event is not unusual.

Step-by-step explanation:

Let X = number of households watching the show.

The probability of the random variable x is, P (X) = p = 0.18.

The sample selected for the survey is of size, n = 14

The random variable X follows a Binomial distribution with parameter n = 14 and p = 0.18.

The probability of a Binomial distribution is computed using the formula:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...$

(a)

Compute the probability that none of the households are tuned to CSI: Shoboygan as follows:

$P(X=0)={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}=1\times1\times0.06214=0.062$

Thus, the value of P (None) is 0.062.

(b)

Compute the probability that at least one household is tuned to CSI: Shoboygan as follows:

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

$=1-0.062\\=0.938$

Thus, the value of P(at least one) is 0.938.

(c)

Compute the probability that at most one household is tuned to CSI: Shoboygan as follows:

P (X ≤ 1) = P (X = 0) + P (X = 1)

$={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}+{14\choose 1}(0.18)^{1}(1-0.18)^{14-1}\\=0.062+0.191\\=0.253$

Thus, the value of P(at most one) is 0.253.

(d)

An event that has a very low probability of occurrence is known as an unusual event.

The probability of the event "at most one household is tuned to CSI: Shoboygan" is 0.253.

This probability value is not low.

Hence, the event is not unusual.

5 0

4 years ago